c File: geom_base c c Author: Arthur L. Edwards (email: <edwards5@llnl.gov>, <xenops@comcast.net>) c c Version: Updated 2007 May 30 15:00. c Originated 1993 September 8 16:00. c c Source: Web site http://nuclear.llnl.gov/CNP/apt/. c c Purpose: File geom_base is a database for the GEOM code, which does a c variety of geometric, Monte Carlo, mathematical and data c manipulation operations, including 3-D ray tracing (geometric c optics) and particle tracking, and may be used to test and to c demonstrate the use of many subroutines in the APT Subroutine c Library. c c The GEOM code is an interactive code with its own command c language, including the use of subscripted variables and the c equivalents of do loops, if-endif blocks, and subroutine calls. c c File geom_base is in the form of a thoroughly cross-referenced c alphabetically organized encylopedia, with the following format: c c Between entries: c Columns 1-80: Blank. c The first line of entries: c Columns 1- 5: A flag, indicating the type of entry. c Columns 6- 6: Blank. c Columns 7-24: The entry name, if < 20 characters. c Columns 7-80: The entry name, if > 19 characters. c Columns 25-25: Blank, if the entry name has < 20 characters. c Columns 26-80: Beginning of the entry body, containing a c description or definition of the entry name, c and sometimes commands related to the entry, c if the entry name has < 20 characters. c Additional lines of entries: c Columns 28-80: The rest of the entry body. c c To find an entry, e.g. ENTRY, in this file using a general c search tool, specify the entry as "cc ENTRY" for commands, c or "cg ENTRY" for other definitions or descriptions. c See "search geom_base". c c To extract entries that contain any desired key words, see c "extract entries". c c File geom_defs contains an alphabetical list of all entries c in geom_base. c c To execute GEOM, see "GEOM execution". c c To display entries in this file during execution of GEOM, see c command "define". c c Note: In command lines, arguments shown in lower case are to be typed c literally as shown. Arguments shown in UPPER CASE are place c holders, indicating data to be provided by the user, unless c otherwise stated. Arguments in square brackets are options with c choices and/or defaults. See entry "[". c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc FLAG ENTRY DESCRIPTION OR DEFINITION
!-@-----------------------------------------------------------------------------
cc ! The exclamation point (or "bang"). The first character
cc of a comment line, or following a field delimiter in
cc a command line, the beginning of an appended comment.
cc
cc Ignored in command "hex".
cc
cc The character ";", if not bracketed by single or
cc double quotes, will terminate a comment, allowing a
cc command to follow on the same line.
cc
cc Do not use the character "!" at the beginning of the
cc name of any alias, marker, symbol or other object.
cc
cc See "c", "#", "*", "/".
cg ! In a mathematical expression, following a non-negative
cg integer, indicates the factorial function:
cg 0! = 0, 1! = 1, N! = 1 * 2 * ... * (N - 1) * N.
cc " In command "alias", delimits the replacement string.
cc Double any " in the replacement string.
cc Synonyms: [", ' (in pairs)].
cc " In command "define", delimits the entry.
cc Double any " in the entry.
cc Synonyms: [", ' (in pairs)].
cc " In command "marker", delimits the text string.
cc Double any " in the text string.
cc Synonyms: [", ' (in pairs)].
cc # If the first character of an input line, the entire
cc input line is treated as a comment, and echoed in the
cc output file. See "c".
cc Synonyms: [#, *, /].
cc # The first character of a comment line.
cc Synonyms: [#, *, /].
cc See "c", "!".
cc # An option in command "input", to switch input to the
cc previous input medium, starting with the line after
cc the last line read from that input medium, and with
cc the same specification for the final line to be read.
cc See "%", command "return".
cc $ An option in command "input", in place of LINE1 or
cc LINE2, to indicate the last line saved in memory,
cc or the end-of-file of an input file.
cc $ An option in commands "indo" and "redo", in place of
cc LINE, to indicate the last line saved in memory.
cc $ May be used as the first character of a variable name,
cc as may "@", "%" or any lower case letter, or any
cc upper case letter followed by one or more characters.
cg % In a display of data resulting from command "mcvol",
cg percent, as in "% estimated error".
cc % An option in command "input", to indicate the current
cc input file, when used in place of IN_FILE. Used to
cc move to a different line in the current input file.
cc % May be used as the first character of a variable name,
cc as may "@", "$" or any lower case letter, or any
cc upper case letter followed by one or more characters.
cc & An option in command "cluster", to indicate that
cc additional points are being added to an existing
cc cluster.
cc To add additional clusters to an existing cluster,
cc use command "cluster CLNAME cluster CLNAME ...".
cc & An option in command "pdf", to indicate that
cc additional probability bins are being specified for
cc a pdf already partially specified.
cc & An option in command "quadric", to respecify one or
cc more individual coefficients in the general implicit
cc equation of a specified quadric surface. Options
cc CFNAME1, CFNAME2, ... may be QC, QX, QY, QZ, QXY,
cc QYZ, QZX, QXX, QYY or QZZ.
cc & An option in command "zone", to indicate that
cc additional bounding surfaces are being specified for
cc a zone already partially specified.
cc ' A synonym for ", in commands "alias", "define",
cc "marker" and "variable".
cc ' In command "alias", delimits the replacement string.
cc Double any ' in the replacement string.
cc Synonyms: [", ' (in pairs)].
cc ' In command "define", delimits the entry.
cc Double any ' in the entry.
cc Synonyms: [", ' (in pairs)].
cc ' In command "marker", delimits the text string.
cc Double any ' in the text string.
cc Synonyms: [", ' (in pairs)].
cg (, ) The parenthesis characters. See "subscripts".
cg (xyz) In a display of data, indicates three coordinates of a
cg point or three components of a vector, in Cartesian
cg (x, y, z) coordinates. To convert to another
cg coordinate system, use the following commands:
cg
cg coordinate xyz
cg [point,vector] TEMP = {copy xyz coordinates here}
cg coordinate [cyl,sph]
cg angle [deg,rad]
cg [point,vector] TEMP
cg
cg See "cut and paste", "coordinate conversion",
cg "vector conversion".
cc * A synonym for # in a comment line.
cc * An option in commands "big", "icalc" and "variable",
cc argument FUNCTION, to indicate multiplication.
cc In the expression A * B, indicates that A is
cc multiplied by B.
cc * An option in command "quadric", to indicate that the
cc coefficients of the implicit equation of the quadric
cc surface are to be multiplied by argument FACT.
cc * An option in command "variable VARNEW = K * L mod M",
cc to multiply K by L.
cc * An option in command "variable", to give the variable
cc the value of the product of the specified arguments.
cc * A synonym for rel in command "vector".
cc * An option in command "variable VARNEW = K * L mod M",
cc to multiply K by L.
cc ** A synonym for ^.
cc + When used as a prefix (without a delimiter) to a
cc variable name used in place of an integer or floating
cc point argument, has no effect. See "-".
cc + In a command that creates, copies or renames an object,
cc a "+" in place of the object name indicates that the
cc object name should be formed by incrementing the base
cc name for the object type. The base name is the name
cc of the last object of that type created, or the base
cc name specified with command "last", whichever occurs
cc later.
cc The new name becomes the current base name.
cc The "+" option may not be used in command "delete",
cc or in command "rename" with option "array".
cc See command "last", "increment names", "-".
cc
cc You must be sure that incrementing a base name
cc does not create a disallowed name, that could be
cc interpreted as a key word in a command, such as
cc "all", "comp.", "h", "help", "list", "random",
cc "thru" or "?".
cc + An option in commands "big", "icalc" and "variable",
cc argument FUNCTION, to indicate addition. In the
cc expression x + y, indicates that y is added to x.
cc + An option in commands "invert", "reflect", "rotate" or
cc "scale". The delimited character "+" preceding the
cc name of a tensor operator indicates that the
cc specified tensor operator will be used (the default
cc option), rather than its inverse.
cc The word "+" is the default option, and need not be
cc included in the command.
cc + An option in command "sort", to sort in increasing
cc alphanumeric order. The default option.
cc + An option in command "variable", to give the variable
cc the value of the sum of the specified arguments.
cc + An option in command "variable VARNEW = K + L mod M",
cc to add L to K.
cc + An option in command "zone". The delimited character
cc "+" preceding the name of a bounding surface
cc indicates that the direction out of the zone is in
cc the same direction as the normal vector of the
cc bounding surface.
cc If not specified, the default argument is "+".
cc
cc For example, if the zone is inside of a sphere,
cc cylinder, cone or ellipsoid that has been created
cc by any command other that "quadric QNAME = ...",
cc the corresponding argument is blank or "+".
cc , In subscripted object names, used to separate
cc subscripts from each other.
cg - See "- |...|".
cg - When the first character of a point name, indicates the
cg point was previously a mesh point, and was released
cg from the mesh. A point with a name beginning with
cg a minus sign may not be assigned to the mesh.
cc - When used as a prefix (without a delimiter) to a
cc variable name used in place of an integer or floating
cc point argument, results in use of the negative of the
cc variable value. See "+".
cc - In a command that creates, copies or renames an object,
cc a "-" in place of the object name indicates that the
cc object name should be formed by decrementing the base
cc name for the object type. The base name is the name
cc of the last object of that type created, or the base
cc name specified with command "last", whichever occurs
cc later. The new name becomes the current base name.
cc The "-" option may not be used in command "delete",
cc or in command "rename" with option "array".
cc See command "last", "increment names", "-".
cc
cc You must be sure that decrementing a base name
cc does not create a disallowed name, that could be
cc interpreted as a key word in a command, such as
cc "all", "comp.", "h", "help", "list", "random",
cc "thru" or "?".
cc - An option in command "cluster", to remove points from
cc an existing cluster, either by point names or by
cc the names of clusters containing the points.
cc - An option in commands "big", "icalc" and "variable",
cc argument FUNCTION, to indicate subtraction. In the
cc expression x - y, indicates that y is subtracted
cc from x.
cc - An option in commands "mesh" and "point", to release
cc the assignment of mesh indices to mesh points
cc (make the mesh indices zero).
cc - An option in command "pdf", to remove probability bins
cc from an existing pdf.
cc - An option in command "plot center", to default the
cc plot center to the center of the plot axes.
cc An option in command "plot limits", to specify that
cc the plot axis limits will include all plot points.
cc - An option in command "rotate". The delimited character
cc "-" preceding the name of a rotation operator,
cc indicates that the inverse of the specified rotation
cc operator will be used.
cc Do not use this option in commands "invert" or
cc "reflect".
cc - An option in command "sort", to sort in decreasing
cc alphanumeric order.
cc - An option in command "zone". The delimited character
cc "-" preceding the name of a bounding surface
cc indicates that the direction out of the zone is in
cc the opposite direction of the normal vector of the
cc bounding surface.
cc If not specified, the default argument is "+".
cc
cc For example, if the zone is outside of a sphere,
cc cylinder, cone or ellipsoid that has been created
cc by any command other that "quadric QNAME = ...",
cc the corresponding argument is "-".
cc - An option in command "brick", option "increment".
cc The delimited character "-" preceding the name of a
cc coordinate direction indicates that bricks are to be
cc created in the negative coordinate direction from a
cc base brick.
cc - An option in command "variable VARNEW = K - L mod M",
cc to subtract L from K.
cg - |...| Indicates that the quantity bracketed by "|" characters
cg must be negative.
cg -999999999 Sometimes used for a value when no correct value can
cg be found.
cg . See ". (period)".
cc . (period) A synonym for 0, in command indo.
cc . (period) An option in command "redo". When used for R1, R2, R3,
cc ..., means to use the original argument, with no
cc replacement.
cc . (period) Command to repeat the preceding command.
cc Do not use the statement separator ";" on the same
cc line following this command.
cc
cc Forms include:
cc
ccin . help
cc
cc Display the command options.
cc
ccin .
cc
cc Repeat the preceding command.
cc This is the same as the command "input command -1".
cc To repeat the preceding N commands, use command
cc "input command -N $".
cc
cc Synonyms: [help, h].
cc .and. An option in command 'icalc", to find the Boolean
cc "and" or "intersection" of two machine words.
cc M .and. N means the Boolean "and" or "intersection"
cc of M and N.
cc Use 1 where M and N have a 1, otherwise 0.
cc See "Boolean".
cc Synonyms: [.and., .int.].
cc .and. An option in command "cluster", to create a cluster
cc consisting of all points that are in both of two
cc specified clusters. This is the Boolean "and" or
cc "intersection" of the two specified clusters.
cc .eq. A synonym for = in command "if".
cc .eqv. A synonym for .xnor. in commands "cluster" and "icalc".
cn .exrc A VI command file, for use when reading or editing this
cn file with UNIX text editor VI. Allows a search for
cn a pattern starting in column 7 by beginning the VI
cn command with "q", followed by the pattern.
cc .ge. A synonym for >= in command "if".
cc .gt. A synonym for > in command "if".
cc .int. A synonym for .and. in commands "cluster" and "icalc".
cc .le. A synonym for <= in command "if".
cc .lt. A synonym for < in command "if".
cc .nand. A Boolean operation. In the case of two binary digits,
cc returns a 0 if both are 1, otherwise returns a 1.
cc .nand. An option in command "icalc", to find the Boolean
cc "nand" of two machine words.
cc M .nand. N means the Boolean "nand" of M and N
cc (0 where both M and N have a 1-bit, otherwise 1).
cc See "Boolean".
cc .nand. An option in command "cluster", to create a cluster
cc consisting of all points that are not in both of
cc two specified clusters. This is the Boolean "nand"
cc of the two specified clusters.
cc .ne. A synonym for /= in command "if".
cc .nor. A Boolean operation. In the case of two binary digits,
cc returns a 1 if both are zero, otherwise returns zero.
cc .nor. An option in command "icalc", to find the Boolean
cc "nor" of two machine words.
cc M .nor. N means the Boolean "nor" of M and N
cc (1 where both M and N have a 0-bit). See "Boolean".
cc .nor. An option in command "cluster", to create a cluster
cc consisting of all points that are in neither of
cc two specified clusters. This is the Boolean "nor"
cc of the two specified clusters.
cc .not. A Boolean operation. In the case of two binary digits,
cc returns a 1 if the first is 1 and the second is 0,
cc otherwise returns zero.
cc .not. An option in command "icalc", to find the Boolean
cc "not" of two machine words.
cc M .not. N means the Boolean "not" of M and N
cc (1 where M has a 1-bit and N has a 0-bit).
cc See "Boolean".
cc .not. An option in command "cluster", to create a cluster
cc consisting of all points in one specified cluster
cc but not in another specified cluster.
cc .or. An option in command 'icalc", to find the Boolean
cc union of two machine words.
cc M .or. N means the Boolean "or" or "union" of M and N
cc (1 where either M or N has a 1-bit). See "Boolean".
cc Synonyms: [.or., .un.].
cc .or. An option in command "cluster", to create a cluster
cc consisting of all points that are in either of
cc two specified clusters. This is the Boolean
cc "or" or "union" of the two specified clusters.
cc .un. A synonym for .or. in commands "cluster" and "icalc".
cc .xnor. A Boolean operation. In the case of two binary digits,
cc returns a 1 if both are 0 or both are 1.
cc .xnor. An option in command 'icalc", to find the Boolean
cc "xnor" of two machine words.
cc M .xnor. N means the Boolean "xnor" of M and N
cc (1 where both M and N have a 1-bit, or both M and N
cc have a 0-bit). See "Boolean".
cc .xnor. An option in command "cluster", to create a cluster
cc consisting of all points which are in either both
cc or neither of two specified clusters. This is the
cc Boolean "equivalence" of the two specified clusters.
cc Synonymns: [.xnor., .eqv.].
cc .xor. An option in command 'icalc", to find the Boolean
cc exclusive or of two machine words.
cc M int N means the Boolean exclusive or of M and N.
cc See "Boolean".
cc .xor. An option in command "cluster", to create a cluster
cc consisting of all points that are in one, but not
cc the other, of two specified clusters. This is the
cc Boolean "exclusive or" of the two specified clusters.
cc / An option in commands "big", "icalc" and "variable",
cc argument FUNCTION, to indicate division. In the
cc expression x / y, indicates that x is divided by y.
cc / An option in command "quadric", to indicate that the
cc coefficients of the implicit equation of the quadric
cc surface are to be divided by argument FACT.
cc / A synonym for # in a comment line.
cc / An option in commands "icalc" and "variable". When
cc used for FUNCTION, indicates division of the
cc preceding argument by the following argument.
cc / An option in command "variable", to give the variable
cc the value of the sum of the reciprocals of the
cc specified arguments.
cc / An option in command "variable VARNEW = K / L mod M",
cc to multiply K by the multiplicative inverse of L, if
cc it exists.
cc /= An option in command "if", meaning not equal to.
cc Synonyms: [/=, =/, .ne.].
cc // An option in command "big", to divide one big integer
cc by another big integer as many times as possible, if
cc an exact factor.
cg /^......STRING A VI command to search for a character string STRING
cg which starts in column 7 of this file.
cc 0 An option in command "indo". When used for I1, I2, I3,
cc ..., means to use the original argument, with no
cc increment.
cc Synonyms: [0, .].
cg 10^(-99) Sometimes used for a value when no correct value can be
cg found.
cg 10^99 Sometimes used for a value when no correct value can be
cg found. As an input argument, specified as "1E99".
cc 17777777777 In command "icalc", the largest allowed octal
cc integer on a 32-bit computer.
cc Same as 2147483647 decimal, 7fffffff hex.
cg 21 A game (blackjack) which may be played with GEOM,
cg using input file 21.mac.
cc 2147483647 In command "icalc", the largest allowed decimal
cc integer on a 32-bit computer.
cc Same as 17777777777 decimal, 7fffffff hex.
cc 777777777777777777777
cc In command "icalc", the largest allowed octal
cc integer on a 64-bit computer.
cc Same as 9223372036854775807 decimal,
cc 7FFFFFFFFFFFFFFF hex.
cc 7fffffff In command "icalc", the largest allowed hexadecimal
cc integer on a 32-bit computer.
cc Same as 2147483647 decimal, 17777777777 octal.
cc 7fffffffffffffff In command "icalc", the largest allowed hexadecimal
cc integer on a 64-bit computer.
cc Same as 9223372036854775807 decimal,
cc 777777777777777777777 oct.
cc 80 Maximum number of characters read in an input line,
cc including input lines expanded by substitution of
cc an alias.
cc 9223372036854775807
cc In command "icalc", the largest allowed decimal
cc integer on a 64-bit computer.
cc Same as 777777777777777777777 octal,
cc 7FFFFFFFFFFFFFFF hex.
cc ; Separates multiple commands and/or comments on one
cc input line. Ignored if between single or double
cc quotes (as in commands "alias", "define" and
cc "marker"). Does not need to be delimited.
cc If not between single or double quotes, will
cc terminate a comment, allowing a command to follow on
cc the same line. Ignored in command "hex".
cc For example:
cc
ccin COMMAND1;COMMAND2 !COMMENT;COMMAND3 ...
cc
cc Execute commands COMMAND1, COMMAND2, COMMAND3, ...
cc
cc Can not be used after commands "do", "enddo",
cc "indo", "input", "read", "redo", "return" or"undo",
cc or their synonyms, because chaos might ensue.
cc
cc WARNING: if used in an input file, the line number
cc displayed in the output file will not be the same
cc as in the input file, but will be a statement
cc counter, instead. To reexecute lines, use command
cc "input geom_cmd ?" to find the correct line numbers
cc to use, say N1 through N2, and then use command
cc "input geom_cmd N1 N2" to execute them.
cc < An option in command "if", meaning less than.
cc Synonyms: [<, .lt.].
cc < Used in a UNIX execution line to redirect the standard
cc input. Do NOT use any of the GEOM execution lines:
cc "geom < IN_FILE" ,
cc "geom < IN_FILE > OUT_FILE",
cc "geom IN_FILE > OUT_FILE" or
cc "geom > OUT_FILE".
cc
cc The following forms are allowed, to prevent large
cc amoumts of data from being displayed on the user's
cc terminal:
cc
cc "geom IN_FILE OUT_FILE > STDOUT"
cc "geom IN_FILE OUT_FILE >! STDOUT"
cc
cc The latter form allows writing over an existing
cc file STDOUT.
cc
cc See "GEOM execution".
cg < In column 1 of the output file, indicates an input
cg line that begins with "input", "read", "return",
cg "call", "goto", "undo", "redo", "indo" or a synonym
cg for any of these, or an alias. See ">".
cc <= An option in command "if", meaning less than or
cc equal to. Also in displayed values from command
cc "root".
cc Synonyms: [<=, =<, .le.].
cc <return> The <return> key must be typed at the end of every
cc input line typed at the user's terminal.
cc = An option in some commands that create objects, between
cc the object name and the specification of the object.
cc = An option in command "if", meaning equal to.
cc Synonyms: [=, .eq.].
cc = An option in command "root", to find the real
cc coefficients of an Nth-order polynomial equation
cc with N specified real roots.
cc = An option in command "roots", to find the real
cc coefficients of a polynomial equation with from
cc one to four specified real and/or complex roots.
cc =/ A synonym for /= in command "if".
cc =< A synonym for <= in command "if".
cc => A synonym for >= in command "if".
cc > An option in command "if", meaning greater than.
cc Synonyms: [>, .gt.].
cg > In column 1 of the output file, indicates an input
cg line that does not begin with "input", "read",
cg "return", "undo", "redo", "indo" or a synonym for
cg any of these, or an alias. A new input file, which
cg will duplicate the run that made the output file, may
cg be made by selecting only those lines beginning with
cg ">" from the input file, then deleting the ">".
cg See "<".
cc > Used in a UNIX execution line to redirect the standard
cc output. Do NOT use any of the GEOM execution lines:
cc "geom < IN_FILE" ,
cc "geom < IN_FILE > OUT_FILE",
cc "geom IN_FILE > OUT_FILE" or
cc "geom > OUT_FILE".
cc
cc See "GEOM execution".
cc >= An option in command "if", meaning greater than or
cc equal to.
cc Synonyms: [>=, =>, .ge.].
cc ? The default short input prompt, if the long prompt is
cc turned off. Input may follow this prompt on the
cc same line.
cc ? A synonym for random, except in command "input".
cc ? An option in command "input", to indicate that the
cc contents of the specified file will be displayed
cc by the standard output (normally the user's
cc terminal) and in the output file, preceded by line
cc numbers, but not executed. Is not a synonym for
c random in command "input".
cc ? An option in command "sort", to sort in random
cc alphanumeric order.
cc @ May be used as the first character of a variable name,
cc as may "$", "%" or any lower case letter, or any
cc upper case letter followed by one or more characters.
cg A The frequency of the musical note Concert A, or A4,
cg is 440 Hz. Middle C (C4) is 523.2511306012 Hz.
A-------------------------------------------------------------------------------
cc a A synonym for add, when responding to question about
cc appending to an existing output file.
cc a A synonym for alias.
cc A(N) In command "variable", option "polynomial", the
cc coefficient of XARG^N in a polynomial function of
cc XARG. N = 0 to whatever will fit on the command
cc line. See command "roots", option "?".
cc A(n) In command "root", the coefficient of x^n in the
cc polynomial P(x) = sum(n=1,N) {A(n) * x^n} = 0.
cc A0 In command "roots", the constant term in the polynomial
cc equation to be solved.
cc If A0 is zero, at least one root is zero.
cc A1 In command "roots", the coefficient of z in the
cc quadratic, cubic or quartic polynomial equation to be
cc solved. If A0 and A1 are zero, at least two roots
cc are zero.
cc A2 In command "roots", the coefficient of z^2 in the
cc quadratic, cubic or quartic polynomial equation to be
cc solved. If A0 = A1 = A2 = 0, at least three roots
cc are zero.
cc A3 In command "roots", the coefficient of z^3 in the
cc cubic or quartic polynomial equation to be solved.
cc If A0 = A1 = A2 = A3 = 0, at least four roots
cc are zero.
cc A4 In command "roots", the coefficient of z^4 in the
cc quartic polynomial equation to be solved.
cc abs An option in command "variable", argument FUNCTION,
cc to indicate the absolute value function.
cc A abs B means A * abs (B).
cc abs An option in command "vector", to give the vector an
cc absolute length equal to ABSLEN (defaults to 1).
cc See "ABSLEN", "rel", "relative".
cf abs The absolute value function. Example: y = abs (x)
cf means y is positive, with the magnitude of x.
cc ABSLEN Length of a vector of type "absolute". Defaults to 1.
cc May be integer, floating point or a variable.
cc Specified with command "vector".
cg absolute A vector specified by two points is absolute if key
cg word "rel" or "*" is not used. If key word "abs" or
cg "unit" is used, the vector will have a length equal
cg to ABSLEN (defaults to 1).
cg Once a vector has been created, it no longer depends
cg on any points used to create it.
cg See "ABSLEN", "rel", "relative", "vector".
cc accel A synonym for accelerate.
cc accelerate Command to find the position, path length and velocity
cc on the parabolic trajectory of a particle with a
cc specified initial position, initial velocity and
cc constant acceleration, for a specified range of
cc times or at specified time intervals,
cc or to find the intersection of the particle path with
cc one or more points, a line, a plane or a quadric
cc surface, or to find the initial position and velocity
cc and constant acceleration for a particle, given two
cc or three positions at two or three times.
cc
cc Command "accelerate" relates to objects: axisym,
cc cluster, cone, cylinder, ellipsoid, hyperb, line,
cc plane, point, quadric, sphere, symbol, variable,
cc vector.
cc
cc Forms include:
cc
ccin help accelerate
ccin accelerate [help]
cc
cc Display the command options.
cc
ccin accelerate path PINIT VINIT VACC
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type
cc (simple linear, degenerate linear parabolic or
cc parabolic), and if parabolic, find the position,
cc path length and velocity at the vertex of its path.
cc
ccin accelerate path PINIT VINIT VACC time TMIN [DT TMAX]
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type and
cc vertex data as above, and the position, path length
cc and velocity, for time[s] TMIN [(DT) TMAX].
cc Any unspecified words at the end of the command,
cc after TMIN, default to 0.
cc
ccin accelerate path PINIT VINIT VACC point PNAME
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type and
cc vertex data as above, and the points on its path
cc that intersect or are proximal to the point PNAME,
cc and for each such point, the coordinates, the
cc velocity, the path length, the time, and the
cc distance to point PNAME.
cc If point PNAME is not on the path, find any initial
cc velocities VINIT' with the same magnitude as VINIT,
cc that will make the path intersect point PNAME.
cc
ccin accelerate path PINIT VINIT VACC cluster CLNAME
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type and
cc vertex data as above, and the other data as in the
cc preceding command, for each point in cluster
cc CLNAME.
cc
ccin accelerate path PINIT VINIT VACC line ALNAME
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type and
cc vertex data as above, and the points on its path
cc that intersect or are proximal to the line ALNAME,
cc and for each such point, the coordinates, the
cc velocity, the path length, the time, and the
cc distance to line ALNAME.
cc
ccin accelerate path PINIT VINIT VACC plane PLNAME
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type and
cc vertex data as above, and the points on its path
cc that intersect or are proximal to the plane PLNAME,
cc and for each such point, the coordinates, the
cc velocity, the path length and the time. For a
cc proximal point, find the proximal point on the
cc plane, and the distance from the plane to the
cc particle.
cc
ccin accelerate path PINIT VINIT VACC quadric QNAME
cc
cc For a particle initially at point PINIT, with
cc initial velocity vector VINIT and constant
cc acceleration vector VACC, find the path type and
cc vertex data as above, and any points on its path
cc that intersect the quadric surface QNAME, and for
cc each such point, the coordinates, the velocity, the
cc path length and the time. To check the results,
cc store each such intersection point in PNAME, and
cc use command "side PNAME QNAME".
cc If no intersection points are found, find any
cc extrema of the quadric surface equation on the
cc particle path. In general, these are NOT proximal
cc or distal points, but may be used as initial
cc guesses in finding such points.
cc
ccin accelerate fit P1 [T1 P2 T2 [P3 T3]]
cc
cc For a particle at from one to three points and
cc times P1 and T1, P2 and T2, and P3 and T3, find the
cc position and velocity at time zero, and the
cc constant acceleration vector for a parabolic
cc trajectory. Each time specified must be different.
cc If all points are the same, the velocity and
cc acceleration will be zero. If only two points are
cc specified, the acceleration will be zero. If any
cc two of three specified points are the same, the
cc acceleration will be parallel to the velocity.
cc If three specified points are collinear, the
cc acceleration will be parallel to the velocity.
cc
cc Synonyms: [accelerate, accel], [help, h],
cc [plane, pl], [quadric, q, quad], [time, t].
cg acceleration A particle initially at position P(0), with velocity
cg vector V(0) and constant acceleration vector A,
cg obeys the following equations of motion:
cg
cg V(t) = V(0) + A * t
cg VAVG(t) = 0.5 * (V(0) + V(t)) = V(0) + 0.5 * A * t
cg P(t) = P(0) + VAVG(t) * t
cg = P(0) + V(0) * t + 0.5 * A * t^2
cg
cg The path lies on a planar parabolic curve, in the
cg plane containing point P(0) and vectors V(0) and A.
cg
cg The vertex of the parabolic path is at the point
cg where the velocity and acceleration are perpendicular
cg to each other:
cg
cg V(tver) dot A = V(0) dot A + A^2 tver = 0
cg tver = -V(0) dot A / A^2
cg V(tver) = V(0) - (V(0) dot A) / A^2
cg
cg The path length may be obtained by integrating the
cg magnitude of the velocity vector over time.
cg
cg d(t) = Integral {|V(0) + A * t'| * dt'}, t' = 0, t,
cg
cg where the integrand |V(0) + A * t| is
cg
cg sqrt (V(0)^2 + 2 * V(0) dot A * t + A^2 * t^2)
cg
cg The integral may be found in a math handbook.
cg
cg If V(0) or A is zero or if V(0) and A are parallel,
cg the path is linear, and the path length is
cg
cg d(t) = VAVG(t) * t
cg
cg If two [or three] points on the particle path are
cg known at two or three times, the initial position
cg and velocity, and the zero [or constant] acceleration
cg may be found by solving the two [or three]
cg simultaneous linear equations of the particle path.
cg
cg The distance B between the particle and a plane
cg through the point Q with normal vector N is given by:
cg
cg B = (P(t) - Q) dot N / |N|
cg = (P(0) - Q) dot N + (V(0) dot N) * t +
cg 0.5 * (A dot N) * t^2
cg
cg Any intersections between the particle path and the
cg plane may be found by setting B = 0 and solving for
cg t. If no intersections exist, the proximal point
cg between the particle path and the plane occurs when
cg
cg V(t) dot N = 0 = (V(0) dot N) + (A dot N) * t
cg
cg or everywhere on the path if (A dot N) = 0.
cg
cg The point on the plane nearest the particle is at
cg
cg Q' = P(t) + ((Q - P(t)) dot N / |N|) * N
cg
cg The intersection between the particle path and a
cg quadric surface is obtained by substituting the
cg time-dependent coordinates of the particle into the
cg equation of the quadric surface, solving the
cg resulting quartic equation for any real time of
cg intersection, and calculating the particle
cg coordinates at that time.
cg
cg See command "accelerate".
cg acceptable An input line is acceptable if recognized as a comment
cg or a command. An input argument is acceptable if
cg recognized as a command argument, is in the correct
cg mode, and if an integer or floating point number, is
cg within the allowed numerical range.
cg accuracy See "precision", "TOL", command "tol", command "big",
cg "error estimate", "significant figures".
cc acos An option in command "variable", argument FUNCTION,
cc to indicate the trigonometric inverse cosine
cc function. A acos B means A * acos (B).
cf acos The trigonometric inverse cosine function.
cf Example: y = acos (x) means y is the angle whose
cf cosine is x, and x = cos (y). The result is in
cf radians, between 0 and pi.
cc acosh An option in command "variable", argument FUNCTION,
cc to indicate the inverse hyperbolic cosine function.
cc A acosh B means A * acosh (B).
cf acosh The inverse hyperbolic cosine function.
cf Example: y = acosh (x) means y is the argument for
cf which the hyperbolic cosine is x, and x = cosh (y).
cf The range of x is x >= 1.
cf
cf acosh (x) = ln (x + sqrt (x^2 - 1)) (principal val)
cf acosh (x) = ln (x - sqrt (x^2 - 1)) (secondary val)
cg add See "add vectors".
cg add To add real or integer numbers, see commands
cg "variable, "big", "icalc".
cc add A synonym for sum in commands "quadric", "vector.
cc See commands "icalc", "variable", argument
cc FUNCTION, and command "big"..
cc add Following command "output", if the specified output
cc file already exists, and the current input is from
cc the user's terminal, the user must respond "add" to
cc allow GEOM to append to the existing output file.
cc This is the default if the current input is not from
cc the user's terminal. To write over the existing
cc output file, the response must be "yes".
cc
cc Synonyms: [add, a].
cg add See "add vectors".
cg add vectors See "vector sum". See option "move" in commands:
cg axisym, cone, cylinder, ellipsoid, plane, point,
cg quadric, sphere.
cc al A synonym for alias.
cg alias An alias may be used to replace all or part of a
cg frequently used long command line with a much shorter
cg substitute, for easier input.
cg
cg An alias is a delimited word up to 24 characters
c long, including any subscripts.
cg Its replacement is any character string up to 72
cg characters long or whatever will fit on the input
cg line of command "alias" (limited to 80 characters)
cg used to create the alias. In any input line, an
cg initial word that is an alias will be replaced by the
cg replacement string. This is done before symbol
cg replacement. The alias replacement may contain
cg symbols, which will be replaced.
cg Only the first word of an input line containing
cg multiple statements can be replaced by an alias.
cg The combined number of characters resulting from the
cg replacement may not exceed 80.
cg
cg See "definition".
cg Also see "symbol", "synonym", "marker", command ".".
cg
cg The replacement string, if it is a single word that
cg contains no field delimiter, may itself be aliased to
cg another replacement string, but there may be no more
cg than 10 sequential replacements to find the final
cg string. The maximum number of aliases is now 256.
cg
cg To repeat the preceding command many times, use
cg command ".", or create alias ANAME:
cg
cg alias ANAME = 'input command -1"
cg
cg Then after the command to be repeated, type
cg ANAME<return> as many times as desired.
cg
cg To repeat a single command "COMMAND ..." many times,
cg create alias ANAME (single characters near the
cg <return> key are convenient):
cg
cg alias ANAME = "COMMAND ..."
cg
cg Create alias ANAME, so that every time you
cg type "ANAME<return>", command "COMMAND ... "
cg will be executed.
cg
cg Then type ANAME<return> as many times as desired.
cg
cg To repeat a block of commands many times, execute
cg the block of commands once. Then execute command
cg "input command ?" to find the indices N1 and N2 of
cg the first and last commands of the block of commands
cg saved in memory.
cg
cg Then create alias ANAME:
cg
cg alias ANAME = 'input command N1 N2'
cg
cg Create alias ANAME, so that every time you
cg type "ANAME<return>", stored commands N1 through
cg N2 are executed.
cg
cg Then type ANAME<return> as many times as desired.
cg
cg The following commands may affect or display aliases:
cg alias, copy, delete, help, last, list, rename,
cg repack, search, sort, tables.
cg
cg Synonyms: [alias, al, a]. [command, c, cmd],
cg [input, call, i, in, r, rd, read].
cc alias An option in command "debug", to display GEOM internal
cc parameters and variables for aliases: naliasm,
cc nalias, alias1, alias2, lalias2, alias1s, lalias1s.
cc Synonyms: [alias, al, a].
cc alias Command to display one or more aliases or to create or
cc delete an alias. An alias is a delimited word up to
cc 24 characters long which, when the initial word of an
cc input line, is replaced by a specified character
cc string up to 72 characters long.
cc The combined number of characters resulting from the
cc replacement may not exceed 80.
cc Alias replacement is done before symbol replacement.
cc The alias replacement may contain symbols,
cc which will be replaced before executing the line.
cc Only the first word of an input line containing
cc multiple statements can be replaced by an alias.
cc See "do loop use".
cc
cc Note: no replacement of symbols will be done
cc in this command.
cc
cc NOTE! A warning message will be displayed if an
cc alias has the same name as a preset synonym or a
cc symbol or its replacement.
cc
cc Aliases may also be displayed with command
cc "synonymn".
cc
cc Forms include:
cc
ccin help alias
ccin alias [help]
cc
cc Display the command options.
cc
ccin alias [all,list]
cc
cc Display all alias pairs.
cc
ccin alias list ANAME1 ANAME2 ANAME3 ...
cc
cc Display the alias pairs for aliases ANAME1, ANAME2,
cc ANAME3, ..., including any aliases with subscripts
cc following the specified names.
cc
ccin alias ANAME
cc
cc Display the alias pair for alias ANAME.
cc
ccin alias ANAME = ''
cc delete alias ANAME
cc
cc Delete the alias pair for alias ANAME.
cc
ccin alias ANAME = 'STRING'
cc
cc Create alias ANAME with replacement string STRING.
cc If STRING is bracketed by single quotes, repeat any
cc internal single quotes. If STRING is bracketed by
cc double quotes, repeat any internal double quotes.
cc ANAME may not contain the current field delimiter,
cc and should not contain any field delimiter that
cc will be in use when alias ANAME is used in a
cc command. This might include any of the characters:
cc (blank) , : < > [ \ ] ^ _ ` { | }
cc STRING may contain blanks.
cc
cc Use "+" or "-" instead of ANAME to form the name
cc by incrementing or decrementing the base name for
cc aliases. See command "last", "increment names".
cc
cc Note: no replacement of symbols will be done
cc in this command.
cc
cc A warning message will be displayed if an alias has
cc the same name as a preset synonym.
cc
cc Synonyms: [", ' (in pairs)], [alias, al, a],
cc [help, h].
cc alias An option in commands "copy", "delete", "last", "list",
cc "rename", "repack" and "sort", to perform the
cc specified operation on an alias.
cc Synonyms: [alias, al, a].
cg alias arrays Aliases may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cg aliases Some suggested aliases, to shorten long "mesh" and
cg "plot" commands, are:
cg
cg alias dma = "mesh - all"
cg alias dmbl = "mesh - block"
cg alias dmcl = "mesh - cluster"
cg alias dmp = "mesh - point"
cg alias mbla = "mesh block all"
cg alias mexbl = "mesh exchange block"
cg alias mins = "mesh insert"
cg alias minv = "mesh invert"
cg alias mlin = "mesh linear"
cg alias mlst = "mesh list"
cg alias mmv = "mesh move"
cg alias mrx = "mesh relax"
cg alias msz = "mesh size"
cg alias mtst = "mesh test"
cg alias pla = "plot array"
cg alias plax = "plot axis"
cg alias plcen = "plot center"
cg alias dpla = "plot delete all"
cg alias dpli = "plot delete index"
cg alias dplm = "plot delete marker"
cg alias plim = "plot limits"
cg alias plma = "plot marker all"
cg alias plm = "plot marker"
cg alias plpa = "plot point all"
cg alias plpi = "plot point index"
cg alias plpm = "plot point marker"
cg alias plsz = "plot size"
cg alias plst = "plot status"
cg alias plt = "plot title"
cg alias zoom = "plot zoom"
cg alias prpa = "project point all"
cg alias whpa = "where point all"
cg align To move a quadric surface of type QTYPE (plane, sphere,
cg cylinder, cone, ellipsoid, axisym, quadric, hyperb),
cg with name QNAME, to the origin, and/or align its
cg symmetry axes with the major axes, execute the
cg following:
cg
cg point pcen QTYPE QNAME
cg
cg Create point pcen, the center of QNAME.
cg
cg vector vmove QTYPE QNAME
cg
cg Create vector vmove, pointing from the center of
cg QNAME to the origin.
cg
cg operator oprot QTYPE QNAME
cg
cg Create rotation operator oprot, to rotate the
cg symmetry axes of QNAME to the major axes.
cg
cg Move QNAME to the origin, then align it:
cg
cg move QTYPE QNAME vmove
cg
cg Translate QNAME to the origin.
cg
cg rotate QTYPE QNAME oprot
cg
cg Rotate QNAME (around the origin) to align its axes
cg with the major axes.
cg
cg Or, without first moving QNAME to the origin:
cg
cg rotate QTYPE QNAME oprot pcen
cg
cg Rotate QNAME (around point pcen) to align its axes
cg with the major axes.
cg
cg move QTYPE QNAME vmove
cg
cg Translate QNAME to the origin.
cg
cg See "center".
cc all An option in command "help", to display all help
cc messages.
cc all An option in commands, in place of an object name, to
cc indicate that all of the specified type of object are
cc to be processed.
cc
cc Do not name any object "all", but if you do, use
cc command "rename" to rename it, or command "delete"
cc to delete it.
cc
cc Commands that may affect all named objects include:
cc delete, last, list, repack, search, sort.
cc all An option in command "plot", to indicate that the
cc plot axis limits will include all plot points.
cc ALNAME The name of a line between two points. May have up to
cc 24 characters, and may be ASCII, integer or floating
cc point. No line name may be "+", "-", "all", "h",
cc "help", "list" or "thru", begin with "!" or contain
cc ";".
cc Also referred to as ALNAME1, ALNAME2, ALNAME3, ...
cc Specified with command "line".
cc
cc Lines may appear in commands:
cc accelerate, cone, copy, delete, distance, help, last,
cc line, list, rename, repack, search, sort, track,
cc vector.
cc alph A synonym for commands.
cc alph An option in command "help", to display an alphabetic
cc list of command words, including synonyms.
cg alphabetic See "alphabetic order".
cg alphabetic order To list all commands and their synonyms in alphabetic
cg order, use commands "commands" and "synonyms".
cg altitude An altitude of a triangle is a line from a vertex
cg perpendicular to the opposite edge. The three
cg altitudes intersect at the orthocenter.
cg See "median", "bisector", "trig".
cc AMNAME In commands "marker" and "plot", any single character,
cc except that no marker name may be "!", ";", "+",
cc "-" or "h".
cc Also referred to as AMNAME1, AMNAME2, AMNAME3, ...
cc May include numbers, upper and lower case letters,
cc control characters, tabs, etc, but not the current
cc field delimiter.
cg amu Atomic mass units.
cg 1 amu = 9.3149432E8 eV (+/- 0.3 ppm).
cc ANAME In command "alias", any delimited string up to
cc 24 characters long, except that no alias name may be
cc "+", "-", "all", "h", "help", "list" or "thru",
cc begin with "!" or contain ";".
cc Also referred to as ANAME1, ANAME2, ANAME3, ...
cc May include numbers, upper and lower case letters,
cc control characters, tabs, etc, but not the current
cc field delimiter.
cg and The and or ampersand character, "&".
cc ang A synonym for angle.
cc ang A synonym for angles in command "angles".
cc ANG1 See "ANG1, ANG2".
cc ANG1, ANG2 In command "cone", the first and last vertex
cc half-angles of a family of nested cones with the same
cc vertex point and axis.
cc ANG1, ANG2 In command "vector", option "angle", the angles between
cc the unit vector being created and vectors VNAME1
cc and VNAME2, respectively, in the current angle units.
cc ANG2 See "ANG1", ANG2.
cc ANGLE In command "angles", an angle, specified in degrees,
cc radians or grads.
cc Also referred to as ANGLE1, ANGLE2, ANGLE3, ...,
cc ANGLEN.
cc May be integer, floating point or a variable.
cc Absolute value in degrees may not exceed the largest
cc machine integer.
cc ANGLE In command "cone", the half-angle of the cone at
cc the vertex.
cc See "angles", "DANGLE".
cc ANGLE In command "operator", option "axial", the angle
cc (counterclockwise, with the axis pointed at the
cc observer) of rotation around the axis vector VAXIS.
cc See "angles", "DANGLE".
cc Note: angle ANGLE may be sampled randomly.
cc ANGLE In command "vector", options "random" and "angle",
cc the fixed scattering angle from a specified axis.
cc May be integer, floating point or a variable.
cc Specified in the current angle units.
cc See "angles", "DANGLE".
cc Note: angle ANGLE may be sampled randomly.
cc angle A synonym for angles in command "angles".
cc angle An option in command "trig", indicating that the next
cc argument is a positive vertex angle of a triangle,
cc in the current angle units, and less than 180
cc degrees or pi radians.
cc Synonyms: [angle, ang].
cc angle An option in command "variable", to find the angle
cc between two vectors, in the current angle units.
cc Synonyms: [angle, ang].
cc angle An option in command "vector", to create a unit vector
cc at specified angles from two specified vectors.
cc
cc Given a tetrahedron with the three vertex points P1,
cc P2 and P3, to find the fourth vertex point P4 such
cc that the edge from P1 to P4 makes angle ANG12 with
cc the edge from P1 to P2, makes angle ANG13 with the
cc edge from P1 to P3, and has length EDGE14, use the
cc following commands:
cc
cc vector V12 point P1 P2
cc vector V13 point P1 P3
cc vector V14 angle ANG12 V12 ANG13 V13
cc copy point P1 P4
cc move point P4 V14 EDGE14
cc angle An option in command "vector", to have the vector
cc randomly sampled from a uniform distribution of
cc azimuth angles around a specified axis vector VAXIS,
cc at a fixed angle ANGLE from VAXIS.
cc Note: angle ANGLE itself may be sampled randomly.
cg angle See "angle of incidence", "angle of rotation",
cg "angle units", "angle, central", "angle, dihedral",
cg "angles", "scatter angle".
cg angle To find the angle between two vectors, use command
cg "variable", option "angle". The angle is that
cg measured from one vector to the other, at the vertex
cg formed by placing the tails (the initial points) of
cg the two vectors together, so is always between 0 and
cg 180 degrees (between 0 and pi radians.)
cg angle of incidence
cg The angle of incidence between a linear track and a
cg line is the angle between the track and the line at
cg the point of intersection.
cg The angle of incidence between a linear track and a
cg surface is the angle between the track and the vector
cg normal to the surface at the point of intersection.
cg angle of rotation
cg A rotation operator OPNAME, specified with command
cg "operator", has associated with it an angle
cg of rotation around a particular axis, and three
cg sequential angles of rotation around the x, y and z
cg axes. These may be displayed with command
cg "operator OPNAME".
cg angle units See "angles".
cg angle, central The central angle is the angle between the two lines
cg from a central point to any other two points.
cg angle, dihedral The dihedral angle is the angle between two
cg intersecting planes.
cc angles An option in command "debug", to display GEOM internal
cc variables for the coordinate system and angles:
cc asys, acoordu, acoordv, acoordw, angunit.
cc Synonyms: [angles, angle, ang].
cc angles Command to display or specify the units for angles,
cc degrees (default) or radians or to convert angles
cc from one unit to another.
cc Display of point coordinates and vector components
cc will be in the specified angle units, unless
cc specifically labeled otherwise.
cc See "coordinate conversion", "vector conversion".
cc Note: variables are not affected by changes
cc in the angle units, so their values and units remain
cc as intended by the user when originally specified.
cc Variables may be assigned a descriptive tag to
cc specify the units or other data.
cc See command "variable", option "tag".
cc
cc Command "angles" relates to objects: symbol,
cc variable.
cc
cc Forms include:
cc
ccin help angles
ccin angles help
cc
cc Display the command options.
cc
ccin angles
cc
cc Display the current angle units, and
cc display the command options.
cc
ccin angles [degrees,radians]
cc
cc Set the angle units to [degrees, radians].
cc
ccin angles UNIT1 UNIT2 ANGLE1 ANGLE2 ANGLE3 ...
cc
cc Convert from UNIT1 ("degrees", "grads" or
cc "radians") to UNIT2 ("degrees", "grads", "radians"
cc or "dms"): ANGLE1, ANGLE2, ANGLE3, ...
cc The absolute value of ANGLE1, ANGLE2 or ANGLE3, ...
cc in degrees must not exceed the largest machine
cc integer.
cc
ccin angles dms UNIT2 DEGREES MINUTES SECONDS
cc
cc Convert from degrees, minutes, seconds to UNIT2
cc ("degrees", "grads" or "radians").
cc The absolute values of DEGREES, MINUTES and SECONDS
cc in degrees must not exceed the largest machine
cc integer.
cc
ccin angles UNIT1 UNIT2 ANGLE1 thru ANGLEN
cc
cc Convert from UNIT1 ("degrees", "grads" or
cc "radians) to UNIT2 ("degrees", "grads", "radians"
cc or "dms"): all stored variables with names in the
cc range from ANGLE1 thru ANGLEN.
cc The absolute values of ANGLE1 thru ANGLEN
cc in degrees must not exceed the largest machine
cc integer.
cc
cc Conversion between degrees and radians:
cc degrees = radians * 180 / pi
cc radians = degrees * pi / 180
cc See "deg/rad", "pi", "rad/deg".
cc
cc See command "coordinate" to specify the coordinate
cc system.
cc
cc Synonyms: [angles, angle, ang],
cc [degrees, deg, degree], [grads, grad].
cc [help, h], [radians, rad, radian].
cc ANGUNIT The name of the unit for measuring angles, degrees
cc (default) or radians. Specified with command
cc "angles".
cg annular See "annulus", "annular disk", "disk".
cg annular disk See "disk".
cg annulus An annulus is the space between two surfaces at
cg different radii from a central point or an axis.
cg See "disk".
cg To create zones consisting of cylindrical or
cg spherical annuli, use command "cylinder" or "sphere",
cg option "concentric" or "scale", and command "zone".
cg appended See "appended comment".
cg appended comment To append a comment to any input line, precede the
cg comment with the field delimiter and the character
cg "!". Do not begin the name of any alias, marker or
cg other object with the character "!".
cg approximation A good approximation to the decimal part of a number
cg may be obtained by finding the first few terms of
cg the continued fraction for the number (see
cg "continued fraction", command "contfr"), or the first
cg few terms of the number expressed as a series of
cg reciprocals of integers (see "reciprocal series",
cg command "iris").
cg APT The All-Particle Tracking subroutine library.
cg APT subroutines currently called directly by GEOM:
cg aptaxis, aptbang, aptbite, aptbrkn, aptbrkp, aptbrks,
cg aptbrkv, aptcang, aptchai, aptchap, aptchfp, aptchfs,
cg aptchia, aptchin, aptchmv, aptchrn, aptchrp, aptchsq,
cg aptcinc, aptcirc, aptcirk, aptcirp, aptclis, aptcris,
cg aptcsys, aptcsyv, aptcube, aptcubs, aptcycy, aptdode,
cg aptetrn, aptetrp, aptetru, aptetrw, aptexpl, aptffip,
cg aptgrat,
cg apticos, aptintq, aptlnlc, aptlnln, aptlnpl, aptlocd,
cg aptlocs, aptmaxw, aptmopv, aptnewt, aptnint, aptnorm,
cg aptocta, aptparb, aptparh, aptparl, aptparp, aptparq,
cg aptpars, aptpart, aptparx, aptpers, aptpfit, aptplcy,
cg aptplis, aptplpl, aptplqu, aptplsp, aptpolf, aptpoly,
cg aptprcy, aptprop, aptprsp, aptptln, aptptpl, aptqexc,
cg aptqext, aptqexv, aptqfit, aptqhyp, aptqnor, aptqper,
cg aptqprr, aptqprt, aptqrts, aptquar, aptqupr, aptrabc,
cg aptradv, aptrcut, aptrefq, aptrefs, aptrext, aptrich,
cg aptrins, aptripl, aptripq, aptrips, aptripv, aptrkis,
cg aptrlop, aptrois, aptrota, aptrotq, aptrots, aptrott,
cg aptrotv, aptscan, aptscat, aptscav, aptsciz, aptscll,
cg aptsclr, aptslid, aptsolv, aptspcy, aptspha, aptsphk,
cg aptsphp, aptspod, aptspsp, aptsver, apttetd, apttetr,
cg apttlod,
cg apttran, apttrig, apttrip, apttris, aptvadd, aptvang,
cg aptvaxb, aptvdis, aptvdot, aptvpln, aptvplp, aptvsum,
cg aptvunb, aptvunz, aptvusz, aptvxun, aptwhis, aptwirl,
cg aptwist, aptxnup, ranf.
cg
cg Many others are called by these. See file apt.link
cg in directory ~edwards/work/apt/doc .
cg See files geom_apt_calls, geom_apt_called_by .
cn apt.link A file listing all links between APT subroutines.
cn In directory ~edwards/work/apt/doc .
cn aptflibe The TAR library of APT subroutine source files.
cn in ~edwards/work/apt/src on the open YANA Cluster.
cn in /users/u47/edwards/apt/src on FAST archive.
cn See "libapt.a".
cc AQU See "AQU, AQV, AQW".
cc AQU, AQV, AQW In command "zone", the name of the initial quadric
cc surface in a family of quadric surfaces.
cc AQV See "AQU, AQV, AQW".
cc AQW See "AQU, AQV, AQW".
cc arc Command to find, at a point on one of a family of
cc quadric surfaces, the normal vector; the number of
cc curves passing through the point, and lying in the
cc surface, and in a plane containing the normal vector,
cc having zero or extreme curvature; and for each such
cc curve, the corresponding radius of curvature, center
cc of curvature, and unit direction vector along the
cc curve u = (ux, uy, uz). See "vector field",
cc "principal radius", command "extrema".
cc
cc Command "arc" relates to objects: axisym, cone,
cc cylinder, ellipsoid, hyperb, plane, point, quadric,
cc sphere, symbol.
cc
cc Forms include:
cc
ccin help arc
ccin arc [help]
cc
cc Display the command options.
cc
ccin arc PNAME QNAME
cc
cc Find, at point PNAME on a member of the family of
cc quadric surfaces represented by quadric surface
cc QNAME: the normal vector; the number of curves
cc passing through point PNAME, and in a plane
cc containing the normal vector, having zero or
cc extreme curvature; and for each such curve,
cc the corresponding radius of curvature, center of
cc curvature, and unit direction vector along the
cc curve through point PNAME.
cc If any of the surface curves has zero curvature,
cc the surface is a ruled surface.
cc If QNAME is a plane, four straight lines, at 45
cc degree intervals, will be returned.
cc
cc Synonyms: [help, h]
cg Archimedean See "archimedean spiral".
cg Archimedean spiral
eg An Archimedean spiral is a curve in a plane
cg perpendicular to an axis, with its radial distance
cg from the axis a linear function of the angular
cg coordinate around the axis, with the angle ranging
cg continuously from zero to infinity.
cg To generate a family of points arrayed along an
cg Archimedean spiral, use command "point ... move" to
cg create a family of points along a straight line
cg perpendicular to the axis, then use command "cluster"
cg to create a cluster consisting of the points, and
cg then operate on the cluster with command "twist",
cg option "radial".
cn archive A file containing a list of all files last saved in
cn the archives.
cg area See "area of brick", "area of disk", "area of polygon",
cg "area of quadric", "area of revolution", "area units".
cc area Command to find the projected area of a general or
cc regular polygon, the average edge length, and the
cc average of the vertex points.
cc
cc Command "area" relates to objects: cluster, point,
cc symbol, vector.
cc
cc Forms include:
cc
ccin help area
ccin area [help]
cc
cc Display the command options.
cc
ccin area VNORM point PNAME1 PNAME2 PNAME3 ...
cc
cc Find the area projected perpendicularly onto a
cc plane with normal vector VNORM, of the general
cc polygon with three or more vertex points PNAME1,
cc PNAME2, PNAME3, ..., which need not be coplanar.
cc Also display the average of the vertex points, and
cc the average edge length.
cc
ccin area VNORM cluster CLNAME
cc
cc Find the area projected perpendicularly onto a
cc plane with normal vector VNORM, of the general
cc polygon formed by the points in the cluster CLNAME,
cc which need not be coplanar. Also display the
cc average of the vertex points, and the average edge
cc length.
cc
cc Synonyms: [cluster, cl], [help, h],
cc [point, p, pnt, pt].
cg area To find the area of the parallelogram or triangle
cg between two vectors, use command "cross".
cg The parallelogram or triangle is that formed by
cg placing the tails (the initial points) of the two
cg vectors together, and completing the figure.
cg To find the area of the triangle specified by three
cg points, use command "triangle".
cg To find the area of the triangle specified by three
cg of its parts (three edges and three angles), use
cg command "trig".
cg To find the area of a regular polygon, use command
cg "polygon".
cg To find the projected area of a regular or general
cg polygon, use command "area".
cg To find the area of a circle, use command "circle",
cg "disk" or "intcirc".
cg To find the area of an annular disk, use command
cg "disk".
cg To find the surface area of a sphere or the cross
cg section area of a circular cylinder, use command
cg "cylinder" or "sphere".
cg To find the areas of the faces of a "brick", use
cg command "brick".
cg To find the area of the faces of a regular
cg polyhedron, use command "polyhedron".
cg
cg To find other areas, use command "area".
cg area of brick The area AREA(u) of a surface with a fixed value of one
cg of the coordinates u of an orthogonal coordinate
cg system (u, v, w), and bounded by two fixed values of
cg each of the other two coordinates v and w, is given
cg below.
cg Cartesian coordinates (x, y, z):
cg AREA(x) = (Y2 - Y1) * (Z2 - Z1)
cg AREA(y) = (Z2 - Z1) * (X2 - X1)
cg AREA(z) = (X2 - X1) * (Y2 - Y1)
cg Cylindrical coordinates (rcyl, theta, z)
cg (cylindrical radius, azimuthal angle, z axis)
cg (rcyl => 0, 0 <= theta <= 2*pi):
cg AREA(rcyl) = rcyl * (Z2 - Z1) * (theta2 - theta1)
cg AREA(theta) = (rcyl2 - rcyl1) * (Z2 - Z1)
cg AREA(z) = (rcyl2^2 - rcyl1^2) *
cg (theta2 - theta1) / 2
cg Angle theta = arctan (y / x), in radians, and
cg pi = 3.141592653589793...
cg Spherical coordinates (rsph, theta, phi)
cg (spherical radius, azimuthal angle, polar angle)
cg (rsph => 0, 0 <= theta <= 2*pi, 0 <= phi <= pi):
cg AREA(rsph) = rsph^2 * (cos (phi1) - cos (phi2)) *
cg (theta2 - theta1)
cg AREA(theta) = (rsph2^2 - rsph1^2) *
cg (phi2 - phi1) / 2
cg AREA(phi) = (rsph2^2 - rsph1^2) * sin (phi) *
cg (theta2 - theta1) / 2
cg
cg See "brick".
cg area of disk The annular area of an annular disk with inner radius
cg RADKIN and outer radius RADKOUT is:
cg AREADK = pi * (RADKOUT^2 - RADKIN^2)
cg The inner area (the "hole") is:
cg AREAH = pi * RADKIN^2
cg pi = 3.141592653589793...
cg area of polygon The area of a polygon in the plane z = 0, with N
cg vertices, is given by the absolute value of:
cg area = 0.5 * sum(i = 1, N) {(x(i) + x(i+1)) *
cg (y(i) - y(i+1))}, where N + 1 -> 1.
cg See command "area".
cg
cg The area of any plane figure, projected onto a plane,
cg is equal to the original area multiplied by the
cg cosine of the angle between the normal vectors of the
cg two planes. See commands "dot" and "variable".
cg
cg To find the area of the faces of a regular
cg polyhedron, use command "polyhedron".
cg area of quadric See "ellipsoid", "sphere".
cg area of revolution
cg An area of revolution, formed by rotating the line
cg with end points (rcyl1, z1) and (rcyl2, z2) around
cg the z axis from azimuthal angle theta1 to azimuthal
cg angle theta2:
cg AREA = ((rcyl1 + rcyl2) / 2) *
cg (z2 - z1) * (theta2 - theta1)
cg area units See "conv.mac", "conversion factors".
cc ARGUMENT An argument in an input line. Always delimited on the
cc left by the beginning of the line or a field
cc delimiter, and on the right by a field delimiter or
cc the end of the line (80 characters). If the field
cc delimiter is a blank character, initial and trailing
cc blanks are ignored, and multiple blanks are treated
cc as a single blank. If the field delimiter is not a
cc blank character, trailing null fields are ignored,
cc but an initial null field is an error. Do not begin
cc an input line with a non-blank field delimiter.
cc The field delimiter is initially a blank character,
cc but may be changed with command "delimiter".
cc The argument may be ASCII, integer, floating point,
cc a variable whose value has the same mode as the
cc argument, or a symbolic word which, after symbol
cc replacement, has the same mode as the argument.
cc See command "variable".
cg arguments Command arguments are displayed in lower case for
cg arguments to be typed literally as shown, and in
cg UPPER CASE for arguments for which the user must
cg provide a value, which may be ASCII, an integer or
cg floating point variable name, an integer or floating
cg point value, or a word which when modified by symbol
cg replacement, is one of the above.
cg The first argument of a command, the command word
cg itself, is always in lower case.
cg
cg With certain exceptions (see "symbol"), any argument,
cg may be replaced by a symbolic word which, after
cg symbol replacement, must be an acceptable value for
cg the argument, including the name of an integer or
cg floating point variable or a literal argument.
cg
cg Any argument which allows a floating point value may
cg also be replaced by the name of an integer or
cg floating point variable, or by a symbolic word which,
cg after symbol replacement, is an integer or floating
cg point value. See "VARNAME".
cg
cg Any argument which only allows an integer value may
cg also be replaced by an integer variable, or by a
cg symbolic word which, after following symbol
cg replacement, is an integer value, except for the
cg argument LINE in command "indo" or "redo".
cg
cg With certain exceptions, arguments are always
cg delimited from other arguments by the current
cg field delimiter (see command "delimiter"), so cannot
cg contain internal field delimiters. The exceptions
cg are the argument STRING in command "alias",
cg the argument TEXT in command "marker", and the
cg argument ENTRY in command "define", which must also
cg be bracketed by single or double quotes.
cc arguments Numerical values that are arguments in commands, and
cc may be replaced by a variable or a symbolic word
cc which, after symbol replacement, is a variable,
cc include:
cc
cc Integer only Commands
cc -------------- --------
cc I1, I2, I3 indo
cc INC variable, vector, point, plane
cc INC sphere, cylinder, cone, ellipsoid
cc INC axisym, quadric, brick, tetrahedron
cc INC zone, increment
cc INCR symbol
cc INT1, INT2, ... big
cc IP1,IP2,IP3,IP4 tetrahedron
cc IQ1, IQ2, ... zone
cc IQU,IQV,IQW zone
cc IVAR variable
cc IZU,IZV,IZW zone
cc K, L, M mesh, variable
cc K1, K2 mesh
cc KMAX,LMAX,MMAX mesh
cc KMOVE,LMOVE mesh
cc L1, L2 mesh
cc M1, M2 mesh
cc M1, M2, M3 factor
cc MINUTES angles
cc MMOVE mesh
cc N icalc, spin
cc N1, N2 mesh, plot
cc N3 plot
cc NCOLUMNS plot
cc NITMAX root
cc NLINES plot
cc NQU,NQV,NQW zone
cc NSAMP sample
cc NUMAX axisym
cc NUMBR brick
cc NUMCONE cone
cc NUMCYL cylinder
cc NUMDIR proximal
cc NUMELL ellipsoid
cc NUMLINE line
cc NUMPL plane
cc NUMPT point
cc NUMQ quadric
cc NUMSPH sphere
cc NUMSTR increment
cc NUMT ratio
cc NUMTET tetrahedron
cc NUMTR triangle
cc NUMV vector
cc NUMVAR variable
cc NUMZN zone
cc NVER polygon, polyhedron
cc
cc Integer or
cc floating point Commands
cc -------------- --------
cc A variable
cc A(0), A(1), ... root
cc A0, A1, A2, ... roots
cc ABSLEN vector
cc ANG1, ANG2 cone
cc ANGLE cone, operator, quadric
cc ANGLE1-ANGLEN angles
cc AQU, AQV, AQW zone
cc AVAR variable
cc AXQ(1), AXQ(2) axisym
cc B variable
cc BTEMP bin
cc DANGLE plane
cc DEGREES angles
cc DEV bin
cc DMAX walk
cc DMEAN walk
cc DPR bin
cc DPRL, DPRR bin
cc DT accelerate
cc DU, DV, DW vector, plane, slice
cc DX root
cc F1, F2, ..., FN variable
cc FACT quadric
cc FADD variable
cc FMULT brick, variable
cc FU, FV, FW point
cc FVAR variable
cc PATHMAX walk
cc PHI point
cc PITCH twist
cc POW bin
cc POWER bin
cc PRTOT bin
cc PTL, PTR project
cc QC to QZZ quadric
cc R1, R2, R3 redo
cc RAD1, RAD2 sphere, cylinder, kiss
cc RAD3, RAD4 kiss
cc RADIUS point, sphere, cylinder
cc RADIUS1, RADIUS2 intcirc
cc RADKIN disk
cc RADKOUT disk
cc RATIO bin, operator
cc RCYL point
cc RELLEN vector
cc RINV twist
cc RSPH point
cc SAX, SAY, SAZ ellipsoid
cc SCENH, SCENV plot
cc SECONDS angles
cc SIGMA bin
cc SMAX, SMIN plot
cc SUM ratio
cc T1, T2, T3 accelerate
cc TERM1 ratio
cc THETA point, vector, plane
cc TMAX, TMIN accelerate
cc TOL tol
cc U, V, W vector, plane, intcirc
cc U1, U2 intcirc
cc UANGLE operator
cc UMAX, UMIN brick
cc V1, V2 intcirc
cc VACC accelerate
cc VAL quadric
cc VALUE variable
cc VANGLE operator
cc VINIT accelerate
cc VMAX, VMIN brick
cc VMULT move
cc VMULT1, VMULT2 vector
cc VNORM area, disk, plane, project
cc VRAN bin
cc VRANL, VRANR bin
cc W1,W2,W3,W4 point
cc WANGLE operator
cc WMAX, WMIN brick
cc X(1), X(2), ... root
cc X, Y, Z point
cc X1,X2,X3,X4 roots (real part)
cc XMAX, XMIN root
cc XROOT rootf
cc Y1,Y2,Y3,Y4 roots (imaginary part)
cc ZOOMULT plot
cc ZVOL zone
cc arith A synonym for arithmetic.
cc arithmetic An option in command "debug", to display GEOM internal
cc parameters and variables for integer and floating
cc point arithmetic: idmax, amode, abind, iemax, tol.
cc These include the maximum size of integers and
cc floating point machine words, the number base for
cc input to command "icalc", and the option for display
cc of the binary form of output from command "icalc".
cc See commands "icalc", "tol", "big".
cc Synonyms: [arithmetic, arith].
cg arithmetic See "arithmetic series".
cg arithmetic Arithmetic may be done on floating point and integer
cg values with command "variable".
cg Arithmetic may be done on integer values with
cg commands "icalc", "big".
cg
cg The real and/or complex roots of a quadratic, cubic
cg or quartic polynomial equation with real coefficients
cg may be found with command "roots".
cg
cg The real coefficients of a polynomial equation with
cg from two to four specified real and/or complex roots
cg may be found with command "roots", option "=".
cg
cg The real coefficients of an Nth-order polynomial
cg equation with N specified real roots may be found
cg with command "root", option "=".
cg
cg To search for real roots, extrema and inflection
cg points of a polynomial equation using Newtonian
cg iteration, use command "root".
cg
cg The value of a quadratic, cubic or quartic polynomial
cg equation with real coefficients may be found for any
cg real or complex argument with command "roots",
cg option "?".
cg
cg The value of a polynomial with specified coefficients
cg and a specified argument may be found with command
cg "variable", option "polynomial".
cg
cg The ratio for a geometric series with a given sum
cg first term and number of terms may be found using
cg command "ratio".
cg
cg To find the continued fraction for a decimal number,
cg or vice versa, use command "contfr".
cg
cg To find the equivalent of a decimal number, expressed
cg as an integer plus a sum of reciprocals of integers,
cg use command "iris".
cg arithmetic series
cg An arithmetic series is one in which the value of each
cg term after the first term differs from the preceding
cg term by an additive constant. To create a family of
cg variables whose values form an arithmetic
cg series:
cg
cg variable VAR(1) = VALUE
cg
cg Create variable VAR(1), with the value of the
cg first term.
cg
cg variable VAR(2) series NUMVAR INC VAR(1) FADD 1
cg
cg Create a series of NUMVAR variables VAR(2),
cg ..., with names incremented by INC characters
cg (or INC digits, if an integer name or a name with
cg one or more integer subscripts), each equal to the
cg preceding variable plus FADD, starting from
cg variable VAR(1).
cg See "increment names".
cg
cg Alternately, using subscripts and a do loop:
cg
cg variable VAR(1) = VALUE
cg do NL 2 NUMVAR
cg variable NLM = NL - 1
cg variable VAR(NL) = VAR(NLM) + FADD
cg enddo
cg
cg To create a family of points, planes or quadric
cg surfaces in which the distance of each from an
cg invariant point, axis or plane forms an arithmetic
cg series, use option "move" of commands "point",
cg "sphere", "cylinder", "cone", "ellipsoid", "axisym"
cg or "quadric", or use command "plane", option
cg "parallel".
cg array See "array shape", 'array sizes".
cc array An option in command "rename", to replace the stem name
cc of all members of an array with a new stem name. A
cc stem name without a subscript will also be replaced.
cc array An option in command "plot", to display the plot array,
cc and all of the plot parameters.
cg array An object with a name of the form OBJNAME(N),
cg OBJNAME_N. or OBJNAME.N, where N may have more than
cg one value, is a member of an array.
cg The form using parentheses, with a variable name
cg for N, may be used for any object.
cg array shape A two-dimensional array x(i,j), i = 1, imax,
cg j = 1, jmax, is equivalent to a one-dimensional
cg array y(n), n = 1, kmax,
cg kmax = imax * jmax,
cg n = j + jmax * (i - 1),
cg i = 1 + (n - 1) / jmax,
cg j = 1 + mod (n - 1, jmax).
cg
cg A three-dimensional array x(i,j,k), i = 1, imax,
cg j = 1, jmax, k = 1, kmax, is equivalent to a
cg one-dimensional array y(n), n = 1, nmax, where
cg nmax = imax * jmax * kmax,
cg n = k + kmax * (j - 1) + kmax * jmax * (i - 1),
cg i = 1 + (n - 1) / (jmax * kmax),
cg j = 1 + mod ((n - 1) / kmax, jmax),
cg k = 1 + mod ((n - 1), kmax).
cg
cg See "shape".
cg array sizes See "maximum number", commands "tables", "mesh".
cg arrays See "subscript", "subscripted names", "do loops",
cg commands "do" and "enddo".
cg ASCII See "ASCII variable", "ASCII word".
cg ASCII When used to describe arguments in commands, ASCII
cg means symbolic, i.e., not explicitly integer or
cg floating point. See "integer input",
cg "floating point".
cg
cg ASCII characters are The set of characters used for
cg data of type character.
cg
cg The order of available keyboard characters is:
cg
cg (blank) ! " # $ % & ' ( ) * + , -
cg . / 0-9 : ; < = > ? @ A-Z [ \ ] ^
cg _ ` a-z { | } ~
cg
cg See "character set".
cg
cg Objects may be sorted into ASCII order of their
cg names, using command "sort", with options to sort
cg into increasing, decreasing or random order.
cg
cg For the order of entries in this file, case is
cg ignored.
cg ASCII variable See "symbol", command "symbol".
cg ASCII word See "ASCII", "commands", "key words".
cc asin An option in command "variable", argument FUNCTION,
cc to indicate the trigonometric inverse sine
cc function. A asin B means A * asin (B).
cf asin The trigonometric inverse sine function.
cf Example: y = asin (x) means y is the angle whose
cf sine is x, and x = sin (y). The result is in
cf radians, between -pi and pi.
cc asinh An option in command "variable", argument FUNCTION,
cc to indicate the inverse hyperbolic sine function.
cc A asinh B means A * asinh (B).
cf asinh The inverse hyperbolic sine function.
cf Example: y = asinh (x) means y is the argument for
cf which the hyperbolic sine is x, and x = sinh (y).
cf
cf asinh (x) = ln ( x + sqrt (x^2 + 1)), x >= 0,
cf asinh (x) = -ln (-x + sqrt (x^2 + 1)), x <= 0.
cg ASSIGNED In the display for a point, indicates a mesh point,
cg assigned a set of mesh indices (k, l, m).
cg asymptotes The asymptotes of a hyperbola, a hyperbolic cylinder,
cg or a hyperboloid are the intersecting lines,
cg intersecting planes, or the cone, respectively,
cg resulting from changing the constant term in the
cg equation of the quadric curve or surface to zero.
cg at symbol The "at" symbol, "@".
cc atan An option in command "variable", argument FUNCTION,
cc to indicate the trigonometric inverse tangent
cc function. A atan B means A * atan (B).
cf atan The trigonometric inverse tangent function.
cf Example: y = atan (x) means y is the angle whose
cf tangent is x, and x = tan (y). The result is in
cf radians, between -pi and pi.
cc atan2 An option in command "variable", argument FUNCTION,
cc to indicate the trigonometric inverse tangent
cc function. A atan2 B means atan2 (A, B)
cf atan2 The trigonometric inverse tangent function, with two
cf arguments. Example: z = atan2 (x, y) means z is the
cf angle whose tangent is x / y, or tan (z) = x / y.
cf The result is in radians, between -pi and pi, in the
cf quadrant for which sin (z) = x, cos (z) = y.
cc atanh An option in command "variable", argument FUNCTION,
cc to indicate the inverse hyperbolic tangent function.
cc A atanh B means A * atanh (B).
cf atanh The inverse hyperbolic tangent function.
cf Example: y = atanh (x) means y is the argument for
cf which the hyperbolic tangent is x, and x = tanh (y).
cf The range of x is -1 < x < 1.
cf
cf atanh (x) = 0.5 * ln ((1 + x) / (1 - x)).
cc avg An option in command "variable", argument FUNCTION,
cc to indicate the average function.
cc A avg B means (A + B) / 2.
cg axial See "axial symmetry".
cc axial An option in command "operator", to specify a rotation
cc by an angle ANGLE (counterclockwise, with the axis
cc pointed at the observer) around an axis VNAME.
cc See "planar", "serial", "triple", "vector".
cc axial An option in command "twist", to specify a rotation of
cc one or more points around an axis in proportion to
cc the axial distance of each point from a fixed point
cc on the axis.
cg axial symmetry Axial symmetry exists when an object may be rotated
cg by any amount around a particular geometric axis,
cg without changing shape. Any section through the
cg object in a plane perpendicular to the symmetry axis
cg must contain only circles concentric around the axis.
cg Any section through the object in a plane containing
cg the symmetry axis must be the same for all such
cg planes. See "axisymmetric".
cg axially See "axially symmetric".
cg axially symmetric
cg See "axisymmetric".
cg axis See "axis of rotation", "axis of symmetry",
cg "principal axis".
cg axis An axis is a direction in 3-D space, usually associated
cg with a point through which the axis passes.
cg In Cartesian or rectangular coordinates, the major
cg axes are the x, y and z axes, passing through the
cg origin, and forming a right-hand orthogonal triple,
cg parallel to the thumb, first and middle fingers,
cg respectively. In any other coordinate system, the
cg principal axes may be specified relative to the x, y
cg and z axes of a Cartesian or rectangular coordinate
cg system.
cg
cg A vector specifies an axis in 3-D space, if bound to
cg a point, or an infinite set of parallel axes, if not.
cg A vector and a point specify an axis in 3-D space.
cg
cg Any quadric surface has a symmetry with respect to
cg a central point, and three orthogonal axes, one, two
cg or three of which may be arbitrary. The principal
cg axis transformation rotates these three axes, the x',
cg y' and z' axes, to the x, y and z axes,
cg and translates the central point to the origin.
cg The direction of the axis vector at a point on the
cg axis is parallel to the normal vector of the quadric
cg surface at that point.
cg
cg To find the axis associated with a scaling,
cg reflection or rotation operator, use command
cg "operator".
cg
cg See "transverse", "conjugate".
cc axis An option in command "plot", to display the plot axis
cc coordinates and labels [and specify the horizontal or
cc vertical axis coordinate and label].
cg axis of rotation A rotation operator OPNAME, specified with command
cg "operator", has associated with it an axis
cg and angle of rotation, which may be displayed with
cg command "operator OPNAME".
cg axis of symmetry A geometric object has an axis of symmetry if the
cg projection of the object in any plane through that
cg axis is the same. In cylindrical coordinates, with
cg the z axis the axis of symmetry, the description of
cg the object is independent of the theta coordinate.
cg See "axisymmetric".
cg axisym See "axisymmetric", "quadric surface",
cg "axisym zone".
cc axisym In a command, means an axially symmetric quadric
cc surface (except in command "axisym", option "scale",
cc when the scaling operator is linear or radial, with
cc an axis not through the center of the base sphere, or
cc not parallel to that of the base axially symmetric
cc quadric surface).
cc Axially symmetric quadric surfaces include all types
cc of planes, spheres, circular cylinders, circular
cc cones, circular ellipsoids (oblate and prolate
cc spheroids), circular paraboloids, and circular
cc hyperboloids of one or two sheets.
cc See "axisymmetric", "axisym zone".
cc axisym Command to display or create one or more axially
cc symmetric quadric surfaces (except that linear or
cc radial scaling may create axially unsymmetric quadric
cc surfaces). The normal vectors will be radially
cc outward. Creating a quadric surfaces replaces any
cc existing quadric surface having the same name.
cc See "quadric" for other options.
cc See "do loop use".
cc
cc Command "axisym" relates to objects: axisym, cone,
cc cylinder, ellipsoid, operator, plane, point, quadric,
cc sphere, symbol, variable, vector.
cc
cc Forms include:
cc
ccin help axisym
ccin axisym [help]
cc
cc Display the command options.
cc
ccin axisym [all,list]
cc
cc Display all axially symmetric quadric surfaces
cc (short display).
cc
ccin axisym list AXNAME1 AXNAME2 AXNAME3 ...
cc
cc Display axially symmetric quadric surfaces AXNAME1,
cc AXNAME2, ..., including any with the specified
cc names followed by one or more subscripts (short
cc display).
cc
ccin axisym AXNAME
cc
cc Display axially symmetric quadric surface AXNAME
cc (long display).
cc
cc In the following commands, use "+" or "-" instead of
cc AXNAME or AXQ(2) to form the name by incrementing or
cc decrementing the base name for axially symmetric
cc quadric surfaces.
cc See command "last", "increment names".
cc
ccin axisym AXNAME fit PCEN VAXIS PNAME2 PNAME3
cc
cc Create axially symmetric quadric surface AXNAME,
cc centered at point PCEN, with axis vector VAXIS, and
cc passing through the two points PNAME2 and PNAME3.
cc
ccin axisym AXNAME focus PFOC VAXIS PNAME2 PNAME3
cc
cc Create axially symmetric quadric surface AXNAME,
cc with focus at point PFOC, with axis vector VAXIS,
cc and passing through the two points PNAME2 and
cc PNAME3.
cc See "planetary orbits".
cc
ccin axisym AXQ(2) move NUMAX INC AXQ(1) VMOVE
cc
cc Create a family of NUMAX axially symmetric quadric
cc surfaces AXQ(2), ..., with names incremented by INC
cc characters or digits, and spaced at intervals of
cc vector VMOVE, starting from axially symmetric
cc quadric AXQ(1). See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin axisym AXQ(2) rotate NUMAX INC AXQ(1) OPNAME PINV
cc
cc Create a family of NUMAX axially symmetric quadric
cc surfaces AXQ(2), ..., with names incremented by INC
cc characters, by rotating the preceding axially
cc symmetric quadric surface with operator OPNAME and
cc invariant point PINV, starting from axially
cc symmetric quadric surface AXQ(1).
cc See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin axisym AXQ(2) scale NUMAX INC AXQ(1) OPNAME PINV
cc
cc Create a family of NUMAX quadrics AXQ(2), ..., with
cc names incremented by INC characters, by scaling the
cc preceding quadric surface with operator OPNAME and
cc invariant point PINV, starting from axially
cc symmetric quadric surface AXQ(1).
cc WARNING: a linear or radial scaling axis not
cc parallel to that of AXQ(1) will produce axially
cc unsymmetric quadric surfaces; a linear or radial
cc scaling will change spheres to ellipsoids.
cc See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
cc Synonyms: [help, h], [move, mv, trans, translate],
cc [rotate, rot].
cc axisym An option in commands "copy", "delete", "last", "list",
cc "rename", "repack" and "sort", to perform the
cc specified operation on an axially symmetric quadric
cc surface.
cg axisym zone A zone is axially symmetric if it is bounded by
cg surfaces that are all axially symmetric around the
cg same axis.
cg If all of those surfaces are planes, cylinders or
cg cones, the projection of the zone in a plane through
cg the axis is a polygon bounded entirely by straight
cg lines, and the volume of the zone and the area of the
cg projected polygon can be calculated. See commands
cg "volume" and "area". If the vertices of the polygon
cg are known, the bounding surfaces can be specified
cg with commands "plane", "cylinder" and "cone", and
cg the zone specified with command "zone".
cg
cg To find the volume of a body of revolution with a
cg polygonal cross section, use command "volume".
cg axisymmetric A surface or volume is axially symmetric if it is a
cg surface or body of revolution around a specified
cg axis, or the same for all angles around the axis.
cg Real quadric surfaces that are axially symmetric
cg include the following, in their standard forms (each
cg coefficient must have the preceding sign):
cg
cg Simple plane: x = 0
cg Coincident planes: x^2 = 0
cg Real parallel planes: - 1 + QXX*x^2 = 0
cg Sphere: - 1 + QXX * (x^2 + y^2 + z^2) = 0
cg Circular cylinder: - 1 + QXX * (x^2 + y^2) = 0
cg Circular cone: x^2 + y^2 - |QZZ| * z^2 = 0
cg Circular ellipsoid:
cg - 1 + QXX * (x^2 + y^2) + QZZ * z^2 = 0
cg Circular paraboloid: - |QZ| * z + x^2 + y^2 = 0
cg Circular hyperboloid of 1 sheet:
cg - 1 + QXX * (x^2 + y^2) - |QZZ| * z^2 = 0
cg Circular hyperboloid of 2 sheets:
cg 1 + QXX * (x^2 + y^2) - |QZZ| * z^2 = 0
cg
cg See command "quadric".
cg
cg The following commands relate to
cg axisymmetric quadric surfaces:
cg accelerate, arc, axisym, cone, copy, cylinder,
cg debug, delete, distance, ellipsoid, extrema, help,
cg invert, last, list, move, operator, plane, point,
cg project, proximal, quadric, reflect, rename, repack,
cg rotate, scale, search, side, slice, sort, sphere,
cg symbol, synonym, tables, track, triple, vector, zone.
cg axisymmetric arrays
cg Axisymmetri quadric surfaces may be created as array
cg with subscripted names. See "subscript",
cg "subscripted names", commands "do" and "enddo".
cg axisymmetrics A family of axially symmetric quadric surfaces may be
cg created with command "axisymmetric", options "move",
cg "rotate" or "scale" or as follows:
cg
cg p pinv (options)
cg
cg Create an invariant point, if needed.
cg
cg axisym AXQ(1) (options)
cg
cg Create a base axially symmetric quadric surface.
cg
cg op opr (options)
cg
cg Create a tensor operator, to reflect, rotate,
cg invert or scale, if needed.
cg
cg v vmove (options)
cg
cg Create a vector for use as a translation operator,
cg if needed.
cg
cg cp AXQ(1) AXQ(2)
cg
cg Copy axially symmetric quadric surface AXQ(1) to
cg the first axially symmetric quadric surface.
cg
cg Repeat the following commands as needed:
cg
cg mv axisym AXQ(1) vmove
cg
cg Move the base axially symmetric quadric surface by
cg amount vmove, if needed.
cg
cg [inv, refl, rot, scale] axisym AXQ(1) opr [pinv]
cg
cg Invert, reflect, rotate or scale the base axially
cg symmetric quadric surface with tensor operator opr,
cg if needed.
cg
cg cp axisym AXQ(1) +
cg
cg Copy the base axially symmetric quadric surface to
cg the next axially symmetric quadric surface.
cc AXNAME The name of an axially symmetric quadric surface.
cc May have up to 24 characters, including any
cc subscripts, and may be ASCII, integer or floating
cc point.
cc No axially symmetric quadric name may be "+", '-',
cc "all", "h", "help", "list" or "thru" or begin with
cc "!".
cc May not be the same as any other quadric surface
cc name QNAME. Also referred to as AXNAME1, AXNAME2,
cc ..., AXQ(1), AXQ(2). Specified with command "axisym"
cc or "quadric".
cc
cc Quadric surfaces may appear in commands:
cc accelerate, axisym, cone, copy, cylinder, delete,
cc distance, ellipsoid, extrema, invert, move, name,
cc operator, plane, point, proximal, quadric, reflect,
cc rename, rotate, scale, side, slice, sphere, surface,
cc track, vector.
cc Also see commands: last, list, repack, search, sort.
cc AXQ(1) In command "axisym", the name of a base axially
cc symmetric quadric surface, used to create a family of
cc axially symmetric quadric surfaces.
cc AXQ(2) In command "axisym", the name of the first of a family
cc of axially symmetric quadric surfaces to create.
cg azimuth The azimuth angle, theta, of a point is the angle of
cg the line from the origin to the point around the z
cg axis, measured counterclockwise from the y plane,
cg and limited to the range (in different applications)
cg from 0 to 360 degrees (0 to 2 * pi radians), or
cg from -180 to 180 degrees (-pi to pi radians).
cg See "polar", "phi".
cg
cg The azimuthal angle around any axis is the angle
cg measured in a plane perpendicular to the axis, and
cg counterclockwise looking in the negative direction
cg along the axis. The zero point must be specified.
B-------------------------------------------------------------------------------
cg back See "back up". cg back up There are several ways to recover from an error. cg Commands may be undone or may be redone with cg modified arguments. cg See commands "undo", "redo", "indo". cg If an object is copied before modifying it, and an cg error is made in the modification, the copy may be cg used to replace the original object. cg backslash The backslash or escape character, "\". cg backup If an object is copied before modifying it, and an cg error is made in the modification, the copy may be cg used to replace the original object. cg ballistic See "accelerate", "trajectory". cg bang The exclamation point, "!". cg base An integer or non-integer floating point value may be cg specified in any number base. For value x and base cg n, the digits of x are the coefficients k(m) in the cg expression: cg cg x = k(m) * n^m + k(m-1) * n^(m-1) + ... + k(0) * n^0 cg + k(-1) * n^(-1) + k(-2) * n^(-2) + ... cg + k(-j) * n^(-j) cg cg where the coefficients k(m) through k(0) define the cg integer part of x, and the coefficients k(-1) through cg k(-j) define the fractional part of x. cg See command "base". cg base See "base axisym", "base brick", "base cone", cg "base cylinder", "base ellipsoid", "base line", cg "base name", "base plane", "base point", cg "base quadric", "base sphere", "base tetrahedron", cg "base variable", "base vector", "base zone", cg command "base". cc base Command to convert a decimal integer or floating point cc number to a specified number base. cc See commands "icalc", "big", "base". cc cc Forms include: cc ccin help base ccin basew [help] cc cc Display the command options. cc ccin base NBASE VALUE1 VALUE2 VALUE3 ... cc cc Convert to number base NBASE, an integer, the cc decimal integer or non-integer floating point cc values VALUE1, VALUE2, VALUE3, .... cg base axisym A base axially symmetric quadric surface is an axially cg symmetric quadric surface specified in command cg "axisym", to serve as the initial axially symmetric cg quadric surface for creating a family of axially cg symmetric quadric surfaces translated, rotated or cg scaled from the preceding axially symmetric quadric cg surface. cg base brick A base brick is a brick specified in command "brick", cg to serve as the initial brick for creating a family cg of bricks adjacent to a specified face of the cg preceding brick, with thicknesses scaled from that of cg the preceding brick. cg base cone A base cone is a cone specified in command "cone", to cg serve as the initial cone for creating a family of cg cones with the same vertex and axis, but translated, cg rotated or scaled from the preceding cone. cg base cylinder A base cylinder is a cylinder specified with command cg "cylinder", to serve as the initial cylinder for cg creating a family of cylinders translated, rotated or cg scaled from the preceding cylinder. cg base ellipsoid A base ellipsoid is a ellipsoid specified with command cg "ellipsoid", to serve as the initial ellipsoid for cg creating a family of ellipsoids translated, rotated cg or scaled from the preceding ellipsoid. cg base line A base line is a line specified in command "line", to cg serve as the initial line for creating a family of cg lines with vertex point names incremented by a cg specified numbers of characters from those of the cg preceding line. cg base name The base name for naming objects of a given type is the cg last name used for creating or renaming an object of cg that type, or the name specified with command "last", cg whichever occurs later. All base names may cg be displayed with command "last". cg The next name after or before the base name, in a cg limited ASCII sequence may be used in a command to cg create, copy, or rename an object of the same type, cg by using the character "+" or "-" in place of the cg new object name, but not in command "rename" with cg option "array". cg See "+", "-", "increment names", command "last". cg base plane A base plane is a plane specified in command "plane", cg to serve as the initial plane for creating a family cg of planes at specified vector displacements, or a cg family of planes rotated at specified angular cg increments around an axis, or a family of planes cg scaled from the preceding plane by a specified scale cg factor. cg base point A base point is a point specified in command "point", cg to serve as the initial point for creating a family cg of points translated, rotated or scaled from the cg preceding point. cg base quadric A base quadric surface is a quadric surface specified cg with command "quadric", to serve as the initial cg quadric surface for creating a family of concentric cg quadric surfaces translated, rotated or scaled from cg the preceding quadric surface. cg base sphere A base sphere is a sphere specified in command cg "sphere", to serve as the initial sphere for creating cg a family of spheres rotated, scaled or translated cg from the preceding sphere. cg base tetrahedron A base tetrahedron is a tetrahedron specified in cg command "tetrahedron", to serve as the initial cg tetrahedron for creating a family of tetrahedrons cg with vertex point names incremented by specified cg numbers of characters from those of the preceding cg tetrahedron. cg base variable A base variable is a variable specified in command cg "variable", to serve as the initial variable for cg creating a family of variables forming a series by cg incrementing and/or multiplying the preceding cg variable. cg base vector A base vector is a vector specified in command cg "vector", to serve as the initial vector for creating cg a family of vectors rotated from the preceding cg vector. cg base zone A base zone is a zone specified in command "zone", to cg served as the initial zone for creating a family of cg zones with the names of the bounding surfaces cg incremented by specified numbers of characters from cg those of the preceding zone. cg basic See "basic commands". cg basic commands See "starting up". cg BETA The random variable in a relativistic Maxwellian cg probability distribution function is BETA, the ratio cg of the particle velocity, v, to the velocity of cg light, c = 299,792,458 m / s. cg A related variable is the relativistic function cg GAMMA = 1 / sqrt (1 - BETA^2). cg For RATIO << 1, where RATIO is the dimensionless cg ratio of gas temperature to particle rest mass cg energy, the expected value of BETA is approximately cg 1.60 * sqrt (RATIO), with a standard deviation of cg approximately 0.67 * sqrt (RATIO), and the expected cg value of BETA^2 is 3 * RATIO. cg For RATIO >> 1, the expected value of BETA is cg approximately 1 - 0.23 / RATIO^2, with a standard cg deviation of approximately 1.26 / RATIO^2, cg the expected value of BETA^2 is approximately cg 1 - 0.46 / RATIO^2, the expected value of GAMMA is cg 3 * RATIO, with a standard deviation of approximately cg 1.73 * RATIO, and the expected value of GAMMA^2 is cg 12 * RATIO^2. cc big An option in command "debug", to display GEOM internal cc parameters and variables for big integers: cc abig, abigtag, idig, nbigm, ndig, ndigm. cc big Command to display or create big integers, with up to cc 1001 digits, and with names a single capital letter cc from "A" to "Z". cc Big integers may be used in calculations related to cc cryptography and combinatorial mathematics. cc See commands "icalc" and "variable". cc cc Forms include: cc ccin help big ccin big [help] cc cc Display the command options. cc ccin big all cc cc Display all big integers that are not zero. cc ccin big all zero cc cc Zero out all big integers. cc ccin big BIGNAME cc cc Display big integer BIGNAME. BIGNAME must be a cc single upper case alphabetic character, from "A" to cc "Z". cc Included in the display will be the one-word cc integer and floating point values of BIGNAME, if cc possible, and the log of BIGNAME to the base 10. cc ccin big BIGNAME [binary,octal,hex] cc cc Display big integer BIGNAME in number base cc [2, 8, 16]. cc ccin big BIGNAME base NBASE cc cc Display big integer BIGNAME in number base NBASE. cc The stored value of BIGNAME will not be changed. cc ccin big BIGNAME = 0 cc cc Set big integer BIGNAME to zero. cc ccin big BIGNAME [N|1] = INT1 INT2 INT3 ... cc Replace the digits in BIGNAME, starting with the cc N'th digit (N defaults to 1 if unspecifed, or if cc BIGNAME is initially zero), with the digits of the cc successive integer groups INT1, INT2, INT3, ..., cc which may be positive integers or integer cc variables, or ASCII strings containing only the cc digits 0-9, but may not be the names of big cc integers. If N is not specified, BIGNAME will cc initially be set to 0. cc If BIGNAME is not zero, and N exceeds the initial cc length of BIGNAME, all digits in between will be cc zero. Any leading zeros in BIGNAME will be cc ignored. cc cc For example, the commands: cc variable n = 77777 cc big Q = 000123 n 000456 789000 cc define big integer Q = 12377777000456789000 cc ccin big BIGNAME tag 'BIGTAG' cc cc Give big integer BIGNAME the label or tag BIGTAG cc (up to 32 characters), which may be used to define cc or describe BIGNAME. This tag will be changed by cc GEOM if BIGNAME is recalculated using one of the cc available functions described below. cc ccin big BIGNAME = big BIGNAME2 cc cc Replace big integer BIGNAME with big integer cc BIGNAME2. cc ccin big BIGNAME = INT1 [+,-,*,/] INT2 cc cc Replace big integer BIGNAME with the cc [sum, difference, product, quotient] of integers cc INT1 and INT2, which, in this and the following cc commands, may be positive integers or integer cc variables or big integers. cc The quotient is rounded to an integer. cc See "reciprocal". cc cc Integer INT1 or INT2 or both may be the result of cc multiplying a number with digits after the decimal cc point by a sufficiently large power of ten to cc shift the deciml point to the right of those cc digits. cc cc Numbers to be added or subtracted must be cc multiplied by the same power of ten. cc Numbers to be multiplied may each be multiplied by cc a different power of tem. cc When dividing, the numerator may be multiplied by cc a much larger power of ten than the denomenator, cc to produce more significant figures in the result. cc cc The correct placement of the decimal point in the cc result should be obvious. If necessary, the same cc calculation may be done with ordinary floating cc point variables as a check. ccin big BIGNAME = INT1 mod INT2 cc cc Replace big integer BIGNAME with the modulus of cc integer INT1 with respect to integer INT2, with cc INT1 and INT2 specified as above. cc This is the remainder or residual of the division cc in the preceding command. cc ccin big BIGNAME = INT1 // INT2 cc cc Replace big integer BIGNAME with the result of cc dividing INT1 by the highest possible power of cc INT2, if the latter is an exact factor of INT1. cc ccin big BIGNAME = INT1 cat INT2 cc cc Replace big integer BIGNAME with the concatenation cc of nonzero INT1 and nonzero INT2. cc ccin big BIGNAME = INT1 perm INT2 cc cc Replace big integer BIGNAME with the number of cc permutations of INT1 things taken INT2 at a time. cc The largest allowed value of INT1 is 450. cc ccin big BIGNAME = INT1 comb INT2 cc cc Replace big integer BIGNAME with the number of cc combinations of INT1 things taken INT2 at a time. cc The largest allowed value of INT1 is 450. cc ccin big BIGNAME = INT1 ^ NPOW cc cc Replace big integer BIGNAME with the NPOW'th power cc of integer INT1. If INT1 has had its decimal point cc shifted N digits to the right, then BIGNAME must cc have its decimal point shifted N * NPOW digits to cc the left. cc ccin big BIGNAME = INT1 root NROOT cc cc Replace big integer BIGNAME with the NROOT'th root cc of integer INT1, specified as above. cc i.e., BIGNAME = BIGNAME2^(1/NROOT). cc The root is rounded to the nearest integer. cc If INT1 has had its decimal point shifted N digits cc to the right, then BIGNAME must have its decimal cc point shifted N / NROOT digits to the left, so cc N must be an exact multiple of NROOT. cc ccin big BIGNAME = INT1 fact cc cc Replace big integer BIGNAME with the factorial of cc integer INT1 The largest value of INT1 that can be cc used without exceeding 1001 digits is 450. cc ccin big BIGNAME = INT1 exp cc cc Replace big integer BIGNAME with the exponential cc function of integer INT1. The largest value of cc INT1 that can be used without exceeding 1001 digits cc is 2302. Accuracy is to the nearest digit, but cc for INT1 = 35 or more, 16 or fewer significant cc figures. cc ccin big BIGNAME random N cc cc Replace big integer BIGNAME with N random digits. cc The result may have leading zeros, which may be cc removed by the command "big BIGNAME = 1 * BIGNAME". cc cc WARNING: avoid conflicts between the names of cc aliases and symbols and the names of big integers. cc cc Synonyms: [help, h], [^, **], [0, zero], cc [binary, bin], [octal, oct]. cg big integer Command "big" allows specification of up to 26 big cg integers, each with up to 1001 digits, each stored cg in a separate machine word. cg Allowed operations include zeroing, replacement, cg addition, subtraction, multiplication, division, cg modulus, powers, roots, factorials, combinations, cg permutations, and exponentiation. cg These operations may be of use in cryptographic cg applications, including encryption and decryption. cg cg The name of a big integer must be a single upper cg case letter (A to Z), in order to avoid confusion cg with the names of variables, symbols, aliases and cg synonyms. Each big integer is allowed to have up to cg 1001 digits, each stored in a separate machine word, cg and in normal order, with the units digit last. cg cg The names of big integers may be incremented or cg decremented by use of command "symbol", with option cg "increment", or by the use of "+" or "-" in place of cg the big integer name. cg cg Digits to the right of a decimal point may be cg included in calculations by moving the decimal point cg to the right of those digits, doing the calculations, cg then deciding where to put the decimal point. cg Numbers to be added or subtracted must have the cg decimal point moved by equal amounts. cg To find a root, multiply by a power of 10 which is cg a multiple of the number of the root. cf big.mac A file with 50 significant figures in the values of cf pi, the golden ratio, log_e(10), log_10(ebase), and cf ebase, and 21 for Euler's constant. cc BIGNAME In command "big", the name of a big integer. cc Must be a single upper case letter (A to Z). cc Also referred to as BIGNAME1, BIGNAME2, BIGNAME3, ... cg bin A probability bin specifies the relative probability cg of a discrete event or object, a discrete value of a cg random variable, or a range of values of a random cg variable. In the latter case, the probability may be cg a uniform, linear, power-law, exponential, normal, cg relativistic Maxwellian, Planck or Wien function of cg the random variable value. A discrete object may be cg any of the objects used in GEOM, including a cg probability distribution function (pdf). cg The maximum number of bins is now 1000. cg cg A set of probability bins may be combined to form a cg probability distribution function (pdf) over a set of cg discrete events, discrete values of a random cg variable, or a continuous or discontinuous set of cg ranges of values of a random variable. cg cg The following commands relate to bins: cg bin, copy, debug, delete, help, last, list, pdf, cg rename, repack, search, sort, symbol, synonym, cg tables. cc bin An option in command "debug", to display GEOM internal cc parameters and variables for probability bins: cc nbinm, nbins, abin, atypeb, probl, probr, cc vranl, vranr, prbin, prbint, cosbin, conbin, vexbin, cc nsampb, abins, labins. cc bin Command to display one or more probability bins or to cc create a probability bin. Creating a probability bin cc replaces any existing probability bin having the same cc name. All probabilities must be positive, and cc the bin widths VRANR - VRANL must be positive. cc cc Command "bin" relates to objects: bin, pdf, symbol, cc variable. cc cc Forms include: cc ccin help bin ccin bin [help] cc cc Display the command options. cc ccin bin [all,list] cc cc Display all bins (short display). cc ccin bin list BINAME1 BINAME2 BINAME3 ... cc cc Display bins BINAME1, BINAME2, BINAME3, ..., with cc or without subscripts (short display). cc ccin bin BINAME cc cc Display bin BINAME (long display). cc cc In the following commands, use "+" or "-" instead of cc BINAME to form the name by incrementing or cc decrementing the base name for probability bins. cc See "base name", command "last", "increment names". cc ccin bin BINAME event [PRTOT|1] cc cc Create probability bin BINAME for a discrete event cc with relative total probability PRTOT. cc ccin bin BINAME value VRAN [PRTOT|1] cc cc Create probability bin BINAME for a discrete value cc VRAN of a random variable, with relative total cc probability PRTOT. cc ccin bin BINAME uniform VRANL VRANR [DPR|1] cc cc Create probability bin BINAME with a uniform cc differential probability DPR from value VRANL to cc value VRANR of a random variable (a histogram). cc ccin bin BINAME linear VRANL VRANR [DPRL|1] [[DPRR|DPRL]] cc cc Create probability bin BINAME with linear cc differential probability, from DPRL at value cc VRANL, to DPRR at value VRANR of a random cc variable. DPRL defaults to 1. DPRR defaults cc to DPRL. cc cc For DPR a known function of VRAN, use the command cc above between commands "do" and "enddo", with cc a calculation of DPRL and DPRR for each of a range cc of values of VRANL and VRANR. cc ccin bin BINAME exp VRANL VRANR SIGMA [PRTOT|1] cc cc Create probability bin BINAME with relative total cc probability PRTOT, from value VRANL to value VRANR, cc with exponentially varying differential cc probability, with decay constant SIGMA. cc For relative differential probabilities PL at VRANL cc and PR at VRANR, DVAL = VRANR - VRANL, cc SIGMA = log (PL / PR) / DVAL, and cc PRTOT = (PL - PR) / SIGMA. cc If SIGMA = 0, PRTOT = PL * DVAL. cc See "mean free path", "decay time". cc ccin bin BINAME power VRANL VRANR POW [PRTOT|1] cc cc Create probability bin BINAME with relative total cc probability PRTOT, from value VRANL to value VRANR, cc with power-law differential probability, with power cc POW. For relative differential probabilities PL at cc VRANL and PR at VRANR, cc POW = log (PR / PL) / log (VRANR / VRANL), cc PRTOT = (VRANR * PR - VRANL * PL) / (POW + 1), or cc if POW = -1: PRTOT = PL * VRANL * log (PL / PR). cc ccin bin BINAME normal VMEAN DEV [PRTOT|1] cc cc Create probability bin BINAME with relative total cc probability PRTOT, with a normal probability cc distribution with mean value VMEAN and standard cc deviation DEV. The random variable ranges from cc minus infinity to plus infinity. cc ccin bin BINAME maxwell RATIO [PRTOT|1] cc cc Create probability bin BINAME with relative total cc probability PRTOT, for a relativistic Maxwellian cc probability distribution, with a dimensionless cc ratio RATIO of gas temperature to particle rest cc mass energy. The random variable beta is the ratio cc of particle velocity to the velocity of light, cc v / c, ranging from 0 to 1. c = 299,792,458 m / s. cc 1 K = 8.617385E-5 eV (+/- 8.5 ppm), cc 1 amu = 9.3149432E8 eV (+/- 0.3 ppm). cc ccin bin BINAME [planck,wien] BTEMP [PRTOT|1] cc cc Create probability bin BINAME with relative total cc probability PRTOT, with a probability distribution cc of a [Planck, Wien] spectrum at temperature BTEMP. cc The random variable is a frequency XNU (same units cc as BTEMP) from that spectrum, ranging from 0 to cc infinity. 1 K = 8.617385E-5 eV (+/- 8.5 ppm). cc 1 Hz = 4.1356692E-15 eV (+/- 0.3 ppm). cc cc Synonyms: [help, h], [maxwell, Maxwell], cc [normal, norm], [planck, Planck], [power, pow], cc [wien, Wien]. cc bin An option in commands "copy", "delete", "last", "list", cc "rename", "repack" and "sort", to perform the cc specified operation on one or more bins. cc bin A synonym for binary in commands "icalc", "big". cg bin arrays Bins may be created as arrays with subscripted cg names. See "subscript", "subscripted names", cg commands "do" and "enddo". cg bin types The types of probability bins currently include: cg cg Type Key word cg cg discrete event event cg discrete value value cg uniform distribution (histogram) uniform cg linear distribution linear cg power-law distribution power, pow cg exponential distribution exp cg normal (Gaussian) distribution normal, norm cg relativistic Maxwellian spectrum maxwell, Maxwell cg Planck spectrum planck, Planck cg Wien spectrum wien, Wien cc BINAME The name of a probability bin. May have up to 24 cc characters, and may be ASCII, integer or floating cc point. cc No bin name may be "+", "-", "all", "h", "help", cc "list" or "thru", begin with "!" or contain ";". cc Specified with command "bin". cc Also referred to as BINAME1, BINAME2, BINAME3, ... cc cc Probability bins may appear in commands: cc bin, copy, delete, rename, pdf. cc Also see commands: last, list, repack, search, sort. cc binary An option in command "big", to display a big integer cc in binary. cc binary An option in command "icalc", to turn on the binary cc mode display of the results. cc Synonyms: [binary, bin]. cg binary The binary form of an integer M, specified in the cg current integer mode (see commands "icalc", "big"), cg may be displayed with commands: cg cg icalc binary cg cg Turn on display of results of command "icalc" in cg binary mode. cg cg binary BIGNAME binary cg cg Display big integer BIGNAME in number base 2. cg cg icalc M cg cg Specify integer M in the current integer mode, and cg display M in decimal, hexadecimal, octal and binary cg mode. cg bisect To find the bisector of an angle, use command "bisect". cg cg To find the midpoint of a line between two points, cg PNAME1 and PNAME2: cg cg vector VNAME = PNAME1 PNAME2 cg cg Create the vector from point PNAME1 to point cg PNAME2. cg cg copy p PNAME1 PMID cg cg Create a point PMID at PNAME1. cg cg move p PMID VNAME 0.5 cg cg Move point PMID to the midpoint. To create a plane cg at the midpoint, perpendicular to the line from cg point PNAME1 to PNAME2: cg cg pl PLNAME v PMID VNAME cg cg Create a plane at the midpoint, with a normal cg vector parallel to the line from point PNAME1 to cg point PNAME2. cg cg To find one of the two planes bisecting the space cg between two other planes, use command "distance" to cg find the intersection of the two planes, then use cg command "plane" to create a plane through a point on cg the line of intersection, with a normal vector equal cg to either the sum or the difference of the normal cg vectors of the two planes. The command "vector", cg with option "sum", may used to find that sum or cg difference. cc bisect Command to bisect the angle formed by the lines cc connecting three points. cc cc Command "bisect" relates to objects: point, symbol. cc cc Forms include: cc ccin help bisect ccin bisect [help] cc Display the command options. cc ccin bisect PNAME1 PNAME2 PNAME3 cc cc Find the bisector of the angle formed by the three cc points PNAME1, PNAME2 and PNAME3, and display the cc intercept of the bisector on the line joining cc points PNAME3 and PNAME1, the vector from point cc PNAME2 to the intercept and the length of that cc vector. cc cc Synonyms: [help, h]. cg bisector The perpendicular bisectors of the three edges of a cg triangle meet at the center of the circumscribed cg circle. The bisectors of the three vertex angles of cg a triangle meet at the center of the inscribed cg circle. See "altitude", "median", "trig". cc bl A synonym for block. cg blackjack See "21". cg blank The initial field delimiter is a blank character, cg but may be changed with command "delimiter". cg If the field delimiter is a blank character, any cg number of leading and trailing blank characters will cg be ignored, and multiple blank characters between cg words are treated as a single field delimiter. cg blank See "blank line". cg blank line Blank input lines will be ignored. cg block See "mesh block". cc block An option in commands "mesh" and "cluster", to operate cc on a specified mesh block. cc Synonyms: [block, bl]. cg Boolean Boolean operations are on individual bits of one or cg two machine words. For each bit or pair of bits, cg the various Boolean operations available with cg commands "icalc" and "cluster", return the following cg results: cg cg Bit A: | 0 0 1 1 cg Bit B: | 0 1 0 1 cg -------------------------|-------------------- cg comp. A (complement) | 1 1 0 0 cg comp. B (complement) | 1 0 1 0 cg -------------------------|-------------------- cg A .not. B (not) | 0 0 1 0 cg B .not. A (not) | 0 1 0 0 cg -------------------------|-------------------- cg A .and. B (intersection)| 0 0 0 1 cg A .nand. B (comp. .and.) | 1 1 1 0 cg -------------------------|-------------------- cg A .or. B (union) | 0 1 1 1 cg A .nor. B (comp. .or.) | 1 0 0 0 cg -------------------------|-------------------- cg A .xor. B (exclusive or)| 0 1 1 0 cg A .xnor. B (comp. .xor.) | 1 0 0 1 cg ---------------------------------------------- cg cg To do Boolean operations on clusters of points, see cg command "cluster". cg cg To do Boolean operations on machine words, see cg command "icalc". cg bound See "bound point". cg bound point The point in 3-D space at which a vector is specified. cg Required for converting vectors between rectangular, cg cylindrical and spherical coordinates. It is only in cg rectangular coordinates that the components of all cg parallel vectors of the same magnitude are equal. cg May be specified with command "vector VNAME = ... ", cg and changed with command "vector VNAME bound PNAME". cg See "coordinate conversion", "vector conversion". cc box An option in command "sudoku", to assign up to 9 cc digits to a 3 x 3 Sudoku box. cg box To create a zone with the shape of a box, or a right cg parallelepiped, use commands "plane" and "zone", or cg command "brick". cc br A synonym for brick. cg brick See "brick (cylindrical)", "brick (rectangular)", cg "brick (spherical)". cg brick A brick is a six-faced solid geometric object in 3-D cg space, bounded by three specified pairs of coordinate cg surfaces, one pair for each of the three coordinates cg (u, v, w) of a specified orthogonal coordinate cg system, with angles measured in specified units. cg See "coordinate", "angles". cg A brick has 8 vertices, 12 edges, and 6 faces. cg The maximum number of bricks is now 1000. cg See "briquette". cg cg If one pair of coordinates are equal, the brick is cg a plane, or a section of a circular cylinder, sphere cg or circular cone, and has zero volume. cg See "tile", "sheet". cg cg If two pairs of coordinates are equal, the brick is cg a line segment or an arc of a circle, and has zero cg volume and zero areas on the faces. See "filament". cg cg If all three pairs of coordinates are equal, the cg brick is a point, and has zero volume, zero areas on cg the faces, and zero edge lengths. cg cg A brick is a convenient object for use in specifying cg a limited geometric region for carrying out other cg geometric operations. See commands "mcvol", "point", cg "plot". cg cg To create and assign mesh points uniformly cg distributed within a brick, use command cg "point PMESH brick BRNAME mesh block [volume]". cg cg See "zone (rectangular)", "zone (cylindrical)", cg "zone (spherical)". cg See "x plane", "y plane", "z plane", "rcyl cylinder", cg "rsph sphere", "theta plane", "phi cone". cg cg To create a brick containing a set of points, cg first create a cluster of the points, and then use cg the displayed minimum and maximum coordinates to cg create the brick. cg cg To find if a point is in a brick, use command cg "distance" or "where". cg cg To find the distances from a point to the six cg surfaces bounding a brick, use command "distance". cg cg To create a family of vertex points, distributed over cg the u, v and w coordinate surfaces so as to divide a cg brick BRNAME up into equal volume elements, each with cg 6 faces, 12 edges and 8 vertex points, use command: cg "point PMESH brick BRNAME mesh block volume". cg cg The following commands relate to bricks: cg brick, cluster, copy, debug, delete, distance, help, cg last, list, mcvol, point, rename, repack, search, cg sort, symbol, synonym, tables, where. cc brick An option in command "debug", to display GEOM internal cc parameters and variables for bricks: nbrickm, cc nbricks, abrick, asysbr, angbr, ubr, dubr, vbr, dvbr, cc wbr, dwbr, volbr, abricks, labricks. cc Synonyms: [brick, br]. cc brick An option in command "point", to create a family of cc points in a brick, at equal-volume values between cc the minimum and maximum u, v and w coordinates of cc the brick, each with a unique name. cc brick An option in commands "cluster", "copy", "delete", cc "last", "list", "rename", "repack" and "sort", to cc perform the specified operation on one or more cc bricks. cc Synonyms: [brick, br]. cc brick Command to display or create bricks. Creating a brick cc replaces any existing brick having the same name. cc The display for a brick includes the coordinate cc system, the angle units, the minimum, increment and cc maximum values of the coordinates of the bounding cc surfaces in each of the three coordinate directions, cc the edge lengths, the face areas, and the volume. cc See "do loop use". cc cc Command "brick" relates to objects: brick, symbol, cc variable. cc cc Forms include: cc ccin help brick ccin brick [help] cc cc Display the command options. cc ccin brick [all,list] cc cc Display all bricks (short display). cc ccin brick list BRNAME1 BRNAME2 BRNAME3 ... cc cc Display bricks BRNAME1, BRNAME2, BRNAME3, ..., cc with or without subscripts (short display). cc ccin brick BRNAME cc cc Display brick BRNAME (long display). cc cc In the following commands, use "+" or "-" instead of cc BRNAME or BR(2) to form the name by incrementing or cc decrementing the base name for bricks. cc See command "last", "increment names". cc ccin brick BRNAME = UMIN UMAX VMIN VMAX WMIN WMAX cc cc Create brick BRNAME, bounded by the coordinate cc surfaces at UMIN and UMAX, VMIN and VMAX, WMIN and cc WMAX, in the current coordinate system (u, v, w), cc which may be rectangular (x, y, z), cylindrical cc (rcyl, theta, z) or spherical (rsph, theta, phi), cc with the current units for angles (degrees or cc radians). One, two or three of the coordinate cc pairs may be equal, to create a surface, a segment cc of a line or arc of a circle, or a point, resp. cc This command could be inside a triple do loop cc over the U, V and W indices, to create a family cc of bricks. cc ccin brick BR(2) incr NUMBR INC BR(1) [-] CDIR [FMULT|1] cc cc Create a family of NUMBR bricks BR(2), ..., with cc names incremented by INC characters, each sharing cc a coordinate surface in the [negative] coordinate cc direction CDIR (x, y, z, rcyl, theta, rsph, phi), cc with the preceding brick, starting from brick cc BR(1), and with a thickness in direction CDIR equal cc to FMULT times the thickness of the preceding cc brick. See "increment names". cc cc This command can be replaced by using commands cc "do" and "enddo", with any of the "brick" commands, cc to create a do loop over bricks with subscripted cc names, with more general variation of properties. cc For example, creating a family of bricks with cc constant thickness increments in the U direction: cc cc variable UMIN = UMINVAL cc variable UMAX = UMAXVAL cc variable UTHICK = UMAX - UMIN cc variable NB = NBINIT cc brick BRNAME(NB) = UMIN UMAX VMIN VMAX WMIN WMAX cc do n = 1 NUMBR cc variable NB = NB + INC cc variable UMIN = UMAX cc variable UMAX = UMAX + UTHICK cc brick BRNAME(NB) = UMIN UMAX VMIN VMAX WMIN WMAX cc enddo cc cc Synonyms: [brick, br], [help, h], [increment, incr]. cg brick (cylindrical) cg A brick defined in cylindrical coordinates, bounded cg by RCYLMIN, RCYLMAX, THETAMIN, THETAMAX, ZMIN and cg ZMAX has the bounding surfaces: cg -RCYLMIN + x^2 + y^2 = 0 cg -RCYLMAX + x^2 + y^2 = 0 cg sin (THETAMIN) * x - cos (THETAMIN) * y = 0 cg sin (THETAMAX) * x - cos (THETAMAX) * y = 0 cg -ZMIN + z = 0 cg -ZMAX + z = 0 cg cg The distances D from a point P1 = (X1, Y1, Z1) to cg each of these surfaces are: cg D = RCYLMIN - sqrt (X1^2 + Y1^2) cg D = RCYLMAX - sqrt (X1^2 + Y1^2) cg D = sin (THETAMIN) * X1 - cos (THETAMIN) * Y1 cg D = sin (THETAMAX) * X1 - cos (THETAMAX) * Y1 cg D = ZMIN - Z1 cg D = ZMAX - Z1 cg cg If P1 = (RCYL, THETA, Z1), substitute cg X1 = RCYL * cos (THETA) cg Y1 = RCYL * sin (THETA) cg sqrt (X1^2 + Y1^) = RCYL cg cg See "proximal". cg brick (rectangular) cg A brick defined in rectangular coordinates, bounded cg by XMIN, XMAX, YMIN, YMAX, ZMIN and ZMAX has the cg bounding planes: cg -XMIN + x = 0 -XMAX + x = 0 cg -YMIN + y = 0 -YMAX + y = 0 cg -ZMIN + z = 0 -ZMAX + z = 0 cg cg The distances D from a point P1 = (X1, Y1, Z1) to cg each of these planes are: cg D = XMIN - X1 D = XMAX - X1 cg D = YMIN - Y1 D = YMAX - Y1 cg D = ZMIN - Z1 D = ZMAX - Z1 cg cg See "proximal". cg brick (spherical) cg A brick defined in spherical coordinates, bounded by cg RSPHMIN, RSPHMAX, THETAMIN, THETAMAX, PHIMIN and cg PHIMAX has the bounding surfaces: cg -RSPHMIN + x^2 + y^2 + z^2 = 0 cg -RSPHMAX + x^2 + y^2 + z^2 = 0 cg sin (THETAMIN) * x - cos (THETAMIN) * y = 0 cg sin (THETAMAX) * x - cos (THETAMAX) * y = 0 cg (cos (PHIMIN))^2 * (x^2 + y^2) - cg (sin (PHIMIN))^2 * z^2 = 0 cg (cos (PHIMAX))^2 * (x^2 + y^2) - cg (sin (PHIMAX))^2 * z^2 = 0 cg cg The distances D from a point P1 = (X1, Y1, Z1) to cg each of these surfaces are: cg D = RSPHMIN - sqrt (X1^2 + Y1^2 + Z1^2) cg D = RSPHMAX - sqrt (X1^2 + Y1^2 + Z1^2) cg D = sin (THETAMIN) * X1 - cos (THETAMIN) * Y1 cg D = sin (THETAMAX) * X1 - cos (THETAMAX) * Y1 cg D = -sqrt (X1^2 + Y1^2) * cos (PHIMIN) + cg abs (Z1) * sin (PHIMIN) cg D = -sqrt (X1^2 + Y1^2) * cos (PHIMAX) + cg abs (Z1) * sin (PHIMAX) cg cg If P1 = (RSPH, THETA, PHI), substitute cg X1 = RSPH * sin (PHI) * cos (THETA) cg Y1 = RSPH * sin (PHI) * sin (THETA) cg Z1 = RSPH * cos (PHI) cg sqrt (X1^2 + Y1^2 + Z1^2) = RSPH cg cg See "proximal". cg brick arrays Bricks may be created as arrays with subscripted cg names. See "subscript", "subscripted names", cg commands "do" and "enddo". cg bricks A family of bricks may be created with command "brick", cg option "increment". cg briquette A briquette is a small volume element of a brick, cg bounded by six coordinate surfaces through eight cg vertex points created by command cg "point PMESH brick BRNAME mesh block volume". cg All such briquettes have equal volume. cc BRNAME The name of a brick. May have up to 24 characters, cc including any subscripts, and may be ASCII, integer cc or floating point. cc No brick name may be "+", "-", "all", "h", "help", cc "list" or "thru", begin with "!" or contain ";". cc Specified with command "brick". cc Also referred to as BRNAME1, BRNAME2, BRNAME3, ... cc BR(1), BR(2), ... cc cc Bricks may appear in commands: cc brick, copy, delete, mcvol, plot, point, rename, cc where. cc Also see commands: last, list, repack, search, sort. cc BTEMP In command "bin", the black-body temperature of a cc Planck or Wien spectrum.
C-------------------------------------------------------------------------------
cc C A synonym for c in a comment line.
cc C In command "delimiter", a character to be used as a
cc field delimiter, which must be one of the following:
cc (blank) ( ) , : < > [ \ ] ^ _ ` { | }
cg C The musical note middle C has a frequency of
cg 523.2511306012 Hz on an equally-tempered scale.
cc c A synonym for command in command "input".
cc c The first word of a comment line.
cc See "!", "#", "*", "/".
cc Synonyms: [c, C, c...., C...., c++++, C++++, c----,
cc C----, c____, C___, !].
cc C++++ A synonym for c++++ in a comment line.
cc c++++ A synonym for c.
cc C---- A synonym for c---- in a comment line.
cc c---- A synonym for c.
cc C.... A synonym for c.... in a comment line.
cc c.... A synonym for c.
cg C1 See "C1, C2, ...".
cc C1, C2, ... In command "contfr", coefficients of a continued
cc fraction.
cg C2 See "C1, C2, ...".
cg calculate To do simple calculations with real numbers, use
cg command "variable".
cg To do simple calculations with integers, in decimal,
cg hexadecimal or octal mode, use command "icalc".
cg To do simple calculations with big integers, use
cg command "big".
cc call A synonym for input.
cg calls For subroutine calls, see files geom_link, geom_to,
cg geom_from, geom_aptcomms, geom_commapts.
cn card.mac An input file that sets up probability bins and a
cn pdf representing a deck of playing cards, to
cn demonstrate how to work with bins and pdfs.
cc cart A synonym for cartesian.
cc Cartesian A synonym for cartesian.
cg Cartesian A 3-D coordinate system using the coordinates
cg (x, y, z). A rectangular coordinate system.
cg To create a volume element bounded by surfaces of a
cg rectangular coordinate system, use command "brick".
cg To create zones partially or completely bounded by
cg planar surfaces, use command "plane", options
cg "parallel", "move", "rotate", "scale", and
cg command "zone".
cg
cg To use a Cartesian coordinate system (the default),
cg use command:
cg
cg coord rect
cg
cg Make the coordinate system Cartesian.
cc cartesian An option in command "coordinate", to use a 3-D
cc Cartesian coordinate system with x, y and z
cc coordinates.
cc Synonyms: [cartesian, cart, Cartesian,
cc rectangular, rect, xyz].
cg case The case of command arguments displayed in geom_base,
cg and in the "help" messages in GEOM, are lower case
cg for arguments to be typed literally as shown, and
cg UPPER CASE for arguments that are to be provided by
cg the user. Arguments provided by the user
cg may be either ASCII strings (using any case or
cg mixture of cases), explicit numerical values,
cg variables or symbols.
cg See commands "alias", "symbol", "variable".
cc cat An option in command "big", to create a big integer by
cc concatenating two nonzero big integers, making it
cc easy to add digits at the beginning or end of a big
cc integer.
cc CC A synonym for cc in a comment line.
cc cc In columns 1-2, the first two characters of a
cc comment line.
cc Synonyms: [cc, CC].
cg cc In columns 1-2 of geom_base, indicates a description of
cg a command or a description of a word that is part of
cg a command.
cg ccin In columns 1-4 of geom_base, indicates a command.
cg cd In columns 1-2 of geom_base, indicates a directory.
cg cell An option in command "sudoku" to assign a digit to
cg a cell, then to display all of the digits permitted
cg in each cell.
cg cen Indicates the center of a geometric object.
cg In a brick, the centroid or center of volume.
cg center The center of a quadric surface is its center of
cg symmetry. To move the center of a quadric surface of
cg type QTYPE (plane, sphere, cylinder, cone, hyperb,
cg ellipse, axisym, quadric), with name
cg QNAME, to the origin, execute the following:
cg
cg point pcen QTYPE QNAME
cg
cg Create point pcen, the center of QNAME.
cg
cg vector vmove QTYPE QNAME
cg
cg Create vector vmove, pointing from the center of
cg QNAME to the origin.
cg
cg move QTYPE QNAME vmove
cg
cg Translate QNAME to the origin. QTYPE may be
cg "quadric" for all types of simple planes and
cg quadric surfaces.
cg
cg move point pcen vmove
cg
cg Check the translation. The new pcen should be at
cg the origin.
cg
cg Vector vmove may also be used for the reverse
cg translation.
cg
cg See "align".
cg
cg Argument PCEN is the name of a point at the center of
cg an annular disk, quadric surface, regular polygon or
cg a regular polyhedron. See commands "axisym", "disk",
cg "ellipsoid", "polygon", "polyhedron", "project",
cg "sphere".
cg central See "angle, central".
cg centroid In a brick, a point at the center of volume of the
cg brick. Also refers to the distances through the
cg brick in the coordinate directions at the centroid,
cg and the areas of the coordinate surfaces through the
cg centroid.
cg centroid When a triangle is created or displayed, the centroid
cg is displayed. The coordinates of the centroid are
cg the average of the coordinates of the vertices.
cg The centroid is at the intersection of the
cg medians, the lines from each vertex to the midpoint
cg of the opposite edge.
cg See "circumscribed circle", "inscribed circle",
cg "orthocenter", commands "triangle", "trig".
cg cents A logarithmic measure of musical pitches, 1200 to an
cg octave. 100 cents corresponds to a semitone on an
cg equally-tempered scale. The difference between two
cg frequencies F1 and F2 in cents is given by:
cg cents = 1200 * log (F1/F2) / log (2).
cg See "equally-tempered".
cc cf A synonym for contfr.
cg cf In columns 1-2 of geom_base, indicates a function.
cc CFNAME1 An option in command "quadric", to specify a new value
cc CFVAL1 of an individual coefficient in the general
cc implicit equation of a specified quadric surface.
cc May be QC, QX, QY, QZ, QXY, QYZ, QZX, QXX, QYY or
cc QZZ. Likewise for CFNAME2, CFNAME3, ...
cc CFVAL1 A new value of coefficient CFNAME1 in the general
cc implicit equation of a specified quadric surface.
cc Likewise for CFVAL2, CFVAL3, ...
cg cg In columns 1-2 of geom_base, indicates a general
cg definition.
cg chance See "probability", "flip a coin", "spin the bottle".
cg change See "change name".
cg change name To change the name of an object, or an array of
cg objects, use command "rename".
cg changes To repeat a GEOM run with changes, make a new input
cg file from the output file from the GEOM run.
cg See "input file".
cg character A character is a single ASCII 8-bit symbol, included in
cg the ASCII character set. See "character set".
cg character See "character data", "character set".
cg character data Character data is data which has been assigned type
cg character in GEOM, with a specified number of
cg characters. On execution, GEOM fills all such data
cg with blanks. See "data types".
cg character set The available keyboard character set on the systems
cg that GEOM is currently running on includes the
cg ASCII characters:
cg
cg (blank) ! " # $ % & ' ( ) * + , -
cg . / 0-9 : ; < = > ? @ A-Z [ \ ] ^
cg _ ` a-z { | } ~
cg
cg Other characters may be obtained with the <Alt>
cg or <Ctrl> keys, but may produce unexpected results.
cg
cg The inline function char(n) equals the characters:
cg
cg char(0) = (null)
cg
cg char(1) to char(31) = (control)
cg
cg char(32) = (blank) char(33) = !
cg char(34) = " char(35) = # char(36) = $
cg char(37) = % char(38) = & char(39) = '
cg char(40) = ( char(41) = ) char(42) = *
cg char(43) = + char(44) = , char(45) = -
cg char(46) = . char(47) = /
cg
cg char(48) to char(57) = 0-9
cg
cg char(58) = : char(59) = ; char(60) = <
cg char(61) = = char(62) = > char(63) = ?
cg char(64) = @
cg
cg char(65) to char(90) = A-Z
cg
cg char(91) = [ char(92) = \ char(93) = ]
cg char(94) = ^ char(95) = _ char(96) = `
cg
cg char(97) to char(122) = a-z
cg
cg char(123) = { char(124) = | char(125) = }
cg char(126) = ~
cg
cg char(127) = (control)
cg
cg char(128) to char(255) = (non-ASCII)
cg characteristics Each type of quadric surface has certain unique
cg characteristics, which are displayed when the
cg quadric surface is displayed. These include:
cg
cg alignment: all types;
cg axis intercepts: all types;
cg axially symmetry: all types;
cg center(s) of symmetry: all types;
cg coefficients of implicit equation: all types;
cg distance between planes: parallel planes;
cg eccentricity: hyperbolic and elliptic cylinders,
cg hyperboloids of one or two sheets, ellipsoids;
cg extrema: all types;
cg foci: parabolic, hyperbolic and elliptic cylinders,
cg paraboloids, hyperboloids, ellipsoids;
cg general type: all types;
cg half-angles: intersecting planes, cones, hyperbolic
cg cylinders and hyperboloids;
cg invariants: all types;
cg latus rectum: parabolic and hyperbolic cylinders,
cg circular and elliptic paraboloids, hyperboloids;
cg normal vector: simple planes;
cg plane type: simple planes;
cg radius, circumference and circular area:
cg circular cylinders, spheres;
cg rotation tensor to align the major axes with the
cg coordinate axes: all types;
cg semiaxes: elliptic cylinders, ellipsoids;
cg simple planes: coincident planes, parallel planes
cg and intersecting planes;
cg surface area: sphere;
cg symmetry axis vectors: all types;
cg transverse and conjugate semiaxes:
cg hyperbolic cylinders,
cg hyperboloids of one or two sheets;
cg vertex to focus distance: parabolic cylinders.
cg circular paraboloids;
cg volume: ellipsoid, sphere.
cg charge To find the machine time charged to the problem, use
cg command "time".
cg chi.group.mac A command file for finding the number of ways to select
cg two or more groups of items with specified lengths
cg from an anagram of all the items in those groups,
cg when the sequence of items in each group is unchanged
cg in the anagram. See "chimera"
cg chimera An anagram of two or more groups of items, with the
cg sequence of items in each group unchanged in the
cg anagram. See "chi.group.mac".
cg Chimera Puzzle A word puzzle, in which a chimera is give, and the
cg puzzle solver must find the phrase for which the
cg chimera is an anagram in which the sequence of
cg letters in each word of the phrase is unchanged.
cg See "chimera", test problem "chi.test", command file
cg "chi.group.mac".
cg Chinese See "Chinese Remainder".
cg Chinese Remainder
cg The Chinese Remainder Theorem tells how to find the
cg least integer that has a specified set of remainders,
cg when divided by a specified set of divisors:
cg
cg REM1 = mod (I, IDIV1)
cg REM2 = mod (I, IDIV2)
cg REM3 = mod (I, IDIV3)
cg ...
cg REMN = mod (I, IDIVN)
cg
cg No pair of divisors may have a common factor, which
cg is easily satisfied with only prime divisors.
cg
cg Let IP = IDIV1 * IDIV2 * IDIV3 * ... * IDIVN.
cg There is a unique solution I (modulo IP), found as
cg follows:
cg
cg Let M1 = IP / IDIV1
cg Let M2 = IP / IDIV2
cg ...
cg Let MN = IP / IDIVN
cg
cg Let K1 be defined such that K1*M1 mod IDIV1 = 1
cg K1 = mod (M1^(IDIV1 - 2), IDIV1)
cg
cg Let K2 be defined such that K2*M2 mod IDIV2 = 1
cg K2 = mod (M2^(IDIV2 - 2), IDIV2)
cg ...
cg Let KN be defined such that KN*MN mod IDIVN = 1
cg KN = mod (MN^(IDIVN - 2), IDIVN)
cg
cg The K1, K2, ..., KN values may also be found just by
cg trying all of the integers until one works.
cg This avoids generating very large integers, as may
cg happen using the equations above.
cg
cg Then the solution is given by:
cg
cg I = K1*M1*IREM1 + K2*M2*IREM2 + ... + KN*MN*IREMN
cg I (minimum) = mod (I, IP)
cg
cg Other larger solutions are I + K * IP, where K is
cg any positive integer.
cg
cg See command "crt".
cg choose randomly See commands "bin", "pdf", "sample".
cg See "spin the bottle".
cc circ A synonym for circle.
cg circle A circle is a curve in a plane, everywhere equidistant
cg from a central point. For a radius R, the
cg circumference is 2 * pi * R, and the area is
cg pi * R^2.
cg To find a circle through three points, use command
cg "circle".
cg To find two circles, each tangent to three mutually
cg tangent circles with specified radii, use command
cg "kiss". See "tangent circles".
cg To find any intersection between two circles, use
cg command "intcirc".
cg To find the circular intersection between a plane
cg and a sphere or between two spheres, use command
cg "distance".
cc circle Command to find a circle through three specified
cc points or to find two circles each tangent to three
cc tangent circles with specified radii.
cc
cc Command "circle" relates to objects: point, symbol.
cc
cc Forms include:
cc
ccin help circle
ccin circle [help]
cc
cc Display the command options.
cc
ccin circle point PNAME1 PNAME2 PNAME3
cc
cc Find the circle through the three points PNAME1,
cc PNAME2 and PNAME3, and display the radius, center,
cc unit normal vector, and area.
cc
cc Use command "disk" to create circular or annular
cc disks representing the circles. Use command
cc "cylinder" to create cylinders parallel to the z
cc axis and through the circles.
cc Use commands "move" and "rotate", to move and orient
cc the disks or cylinders anywhere in 3-D space.
cc Use command "kiss" to find the center coordinates
cc of three tangent circles with specified radii, and
cc the radii and center coordinates of two additional
cc circles tangent to the first three.
cc
cc Synonyms: [circle, circ], [help, h].
cg circular See "circular cone", "circular cylinder",
cg "circular ellipsoid", "circular paraboloid".
cg circular cone A circular cone is an axially symmetric quadric surface
cg for which the standard equation is:
cg x^2 + y^2 - |QZZ|*z^2 = 0 (QZZ < 0),
cg An imaginary circular cone is a quadric surface for
cg which the standard equation is:
cg x^2 + y^2 + QZZ*z^2 = 0, (QZZ > 0).
cg This last equation is also satisfied at the real
cg point (0,0,0).
cg circular cylinder
cg A circular cylinder is an axially symmetric quadric
cg surface for which the standard equation is:
cg - 1 + QXX * (x^2 + y^2) = 0
cg An imaginary circular cylinder is a quadric surface
cg for which the standard equation is:
cg 1 + QXX * (x^2 + y^2) = 0, (QXX > 0).
cg circular ellipsoid
cg A circular ellipsoid is an axially symmetric quadric
cg surface for which the standard equation is:
cg - 1 + QXX*x^2 + QYY*y^2 + QZZ*z^2 = 0,
cg (QXX => QYY => QZZ > 0),
cg with two of the coefficients QXX, QYY, QZZ equal.
cg
cg A circular ellipsoid may be either an oblate spheroid
cg (QYY = QZZ) or a prolate spheroid (QXX = QYY).
cg circular paraboloid
cg A circular paraboloid is an axially symmetric quadric
cg surface for which the standard equation is:
cg -QZ*z + x^2 + y^2 = 0.
cg This is the shape of a telescope reflector or the
cg reflector behind a beamed light source.
cg
cg To find the distance from a point to a circular
cg paraboloid, use command "distance", "proximal" or
cg "side".
cg
cg To find the distance or intersection between a plane
cg and a circular paraboloid, use command "distance".
cg circum Abbreviation for circumference.
cg circumference To find the circumference of a circle or a circular
cg cylinder, use command "circle", "cylinder", "disk"
cg or "intcirc".
cg circumscribed See "circumscribed circle", "circumscribed sphere".
cg circumscribed circle
cg When a triangle is created or displayed, the center
cg and radius of the circumscribed circle is displayed.
cg The center is at the intersection of the
cg perpendicular bisectors of the edges.
cg See "inscribed circle", "centroid", "orthocenter",
cg commands "circle", "kiss", "trig".
cg Any circumscribed circle tangent externally to each
cg of three mutually tangent circles may be found with
cg command "kiss".
cg circumscribed sphere
cg A sphere may be circumscribed outside a regular
cg polyhedron, such as a tetrahedron, a cube, an
cg octahedron, a dodecahedron or an icosahedron,
cg so that it passes through every face of the regular
cg polyhedron. See "inscribed sphere".
cg Any circumscribed sphere, tangent internally to each
cg of four mutually tangent spheres may be found with
cg command "kiss".
cc cl A synonym for cluster.
cc CLNAME The name of a cluster of points. May have up to 24
cc characters, and may be ASCII, integer or floating
cc point.
cc No cluster name may be "+", "-", "all", "h", "help",
cc "list", "point" or "thru", begin with "." or "!" or
cc contain ";".
cc Specified with command "cluster".
cc Also referred to as CLNAME1, CLNAME2, CLNAME3, ...
cc
cc Clusters may appear in commands:
cc accelerate, area, cluster, copy, delete, distance,
cc invert, mesh, move, project, reflect, rename, rotate,
cc scale, twist, where.
cc Also see commands: last, list, repack, search, sort.
cc closest See "minimum", "nearest", "proximal".
cg cluster A cluster is a named set of points. Points may be
cg added or removed by name or by the names of clusters
cg containing the points, added by mesh status, or by
cg presence in a tetrahedron, brick or zone.
cg Any duplicate point names in a cluster will be
cg deleted. Any point may be in any number of clusters.
cg The maximum number of clusters is now 100.
cg The maximum number of points assigned to clusters is
cg now 1000, counting points assigned to more than one
cg cluster.
cg Clusters may be copied, deleted, renamed, and listed.
cg Clusters may be translated, rotated, reflected,
cg inverted, scaled and projected.
cg The points in a cluster may be deleted.
cg
cg No cluster name may be "+", "-", "all", "comp.", "h",
cg "help", "list", "point" or "thru", begin with "!" or
cg contain ";".
cg
cg Clusters may be sorted by name with command "sort".
cg
cg The following commands relate to clusters:
cg accelerate, area, cluster, copy, debug, delete,
cg distance, help, invert, last, list, mesh, move,
cg point, project, reflect, rename, repack, rotate,
cg scale, search, sort, symbol, synonym, tables, twist,
cg where.
cc cluster An option in command "debug", to display GEOM internal
cc parameters and variables for clusters of points:
cc nclustm, nclusts, aclust, laclust, aclusts, laclusts,
cc npairm, npairs, apaircl, apairpt.
cc Synonyms: [cluster, cl].
cc cluster Command to display or create clusters of existing
cc points, or to modify an existing cluster by adding or
cc removing points. Creating a cluster replaces any
cc existing cluster having the same name. The display
cc will include the coordinates of each point, and the
cc minimum, maximum, average and standard deviation of
cc each of the coordinates.
cc See "do loop use".
cc
cc Command "cluster" relates to objects: brick,
cc cluster, mesh, point, symbol, tetrahedron, zone.
cc
cc Forms include:
cc
ccin help cluster
ccin cluster [help]
cc
cc Display the command options.
cc
ccin cluster [all,list]
cc
cc Display all clusters.
cc
ccin cluster list CLNAME1 CLNAME2 CLNAME3 ...
cc
cc Display clusters CLNAME1, CLNAME@, CLNAME3, ...,
cc with or without subscripts.
cc
ccin cluster CLNAME
cc
cc Display cluster CLNAME.
cc
cc In the following commands, use "+" or "-" instead of
cc CLNAME to form the name by incrementing or
cc decrementing the base name for clusters.
cc See command "last", "increment names".
cc
ccin cluster CLNAME all
cc
cc Create new cluster CLNAME, consisting of all
cc points.
cc
ccin cluster CLNAME = PNAME1 ... PNAME2 [thru] PNAME3 ...
cc
cc Create new cluster CLNAME, consisting of points
cc PNAME1, ..., PNAME2 [, through] PNAME3, ...
cc If option "thru" is used, the adjacent points need
cc not exist. Any error cancels entire command.
cc
ccin cluster CLNAME & PNAME1 ... PNAME2 [thru] PNAME3 ...
cc
cc Add to existing cluster CLNAME (do not use "+" or
cc "-"), points PNAME1, ..., PNAME2 [, through]
cc PNAME3, ...
cc If option "thru" is used, the adjacent points need
cc not exist. A warning message is displayed if the
cc cluster CLNAME does not already exist. Any error
cc cancels entire command.
cc
cc This command could be placed between commands "do"
cc and "enddo", to create a do loop over subscripted
cc point names, to add them to a cluster.
cc
ccin cluster CLNAME - PNAME1 ... PNAME2 [thru] PNAME3 ...
cc
cc Remove from existing cluster CLNAME (do not use
cc "+" or "-"), points PNAME1, ..., PNAME2 [, through]
cc PNAME3, ... If option "thru" is used, the adjacent
cc points need not exist. WARNING: an error in one
cc word does not cancel the entire command. For a
cc backup, copy the cluster before modifying.
cc
cc This command could be placed between commands "do"
cc and "enddo", to create a do loop over subscripted
cc point names, to remove them from a cluster.
cc
ccin cl CLNAME cl CLNAME1 ... CLNAME2 [thru] CLNAME3 ...
cc
cc Create new cluster CLNAME, consisting of existing
cc clusters CLNAME1, ..., CLNAME2 [, through] CLNAME3,
cc ... If option "thru" is used, the adjacent
cc clusters need not exist. Add to existing cluster
cc CLNAME if CLNAME is in the list of cluster names.
cc Any error cancels entire command.
cc Note: "cl" is a synonym for "cluster".
cc
ccin cl CLNAME cl CLNAME ... CLNAME2 [thru] CLNAME3 ...
cc
cc Add to existing cluster CLNAME, (do not use "+" or
cc "-") the existing clusters CLNAME1, ..., CLNAME2 [,
cc through] CLNAME3, ... If option "thru" is used,
cc the adjacent clusters need not exist. Any error
cc cancels entire command.
cc Note: "cl" is a synonym for "cluster".
cc
cc This command could be placed between commands "do"
cc and "enddo", to create a do loop over subscripted
cc cluster names, to add them to a cluster.
cc
ccin cl CLNAME cl - CLNAME1 ... CLNAME2 [thru] CLNAME3 ...
cc
cc Remove from existing cluster CLNAME (do not use
cc "+" or "-"), all points in existing clusters
cc CLNAME1, ..., CLNAME2 [, through] CLNAME3, ...
cc If option "thru" is used, the adjacent points need
cc not exist. A warning message is displayed if the
cc cluster CLNAME does not already exist.
cc WARNING: an error in one word does not cancel the
cc entire command. For a backup, copy the cluster
cc before modifying.
cc Note: "cl" is a synonym for "cluster".
cc
cc This command could be placed between commands "do"
cc and "enddo", to create a do loop over subscripted
cc cluster names, to remove them from a cluster.
cc
cc cluster CLNAME cluster comp. CLNAME1
cc
cc Create new cluster CLNAME, consisting of all points
cc not in cluster CLNAME1. This is the Boolean
cc "complement" of the cluster CLNAME1.
cc
cc cluster CLNAME cl CLNAME1 .and. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are in both clusters CLNAME1 and CLNAME2.
cc This is the Boolean "and" or "intersection" of
cc clusters CLNAME1 and CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
cc cluster CLNAME cl CLNAME1 .nand. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are not in both clusters CLNAME1 and CLNAME2.
cc This is the Boolean "complement" of the "and" or
cc "intersection" of clusters CLNAME1 and CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
cc cluster CLNAME cl CLNAME1 .nor. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are not in cluster CLNAME1 and not in cluster
cc CLNAME2. This is the Boolean "complement" of the
cc "intersection" of clusters CLNAME1 and CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
cc cluster CLNAME cl CLNAME1 .not. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are in cluster CLNAME1 but not in cluster
cc CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
cc cluster CLNAME cl CLNAME1 .or. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are in cluster CLNAME1 or in cluster CLNAME2.
cc This is the Boolean "or" or "union" of clusters
cc CLNAME1 and CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
cc cluster CLNAME cl CLNAME1 .xnor. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are either in both clusters or in neither
cc cluster CLNAME1 and CLNAME2. This is the Boolean
cc "complement" of the "exclusive or" of clusters
cc CLNAME1 and CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
cc cluster CLNAME cl CLNAME1 .xor. CLNAME2
cc
cc Create new cluster CLNAME, consisting of all points
cc that are in cluster CLNAME1 but not in cluster
cc CLNAME2, or in cluster CLNAME2 but not in cluster
cc CLNAME1. This is the Boolean "exclusive or" of
cc clusters CLNAME1 and CLNAME2.
cc Note: "cl" is a synonym for "cluster".
cc
ccin cluster CLNAME brick BRNAME
cc
cc Create new cluster CLNAME, consisting of all points
cc inside of brick BRNAME.
cc
ccin cluster CLNAME tetrahedron TETNAME
cc
cc Create new cluster CLNAME, consisting of all points
cc inside of tetrahedron TETNAME.
cc
ccin cluster CLNAME zone ZNAME
cc
cc Create new cluster CLNAME, consisting of all points
cc inside of zone ZNAME.
cc
ccin cluster CLNAME mesh [all]
cc
cc Create new cluster CLNAME, consisting of all mesh
cc points.
cc
ccin cluster CLNAME nomesh
cc
cc Create new cluster CLNAME, consisting of all
cc non-mesh points.
cc
ccin cluster CLNAME mesh block
cc
cc Create new cluster CLNAME, consisting of all mesh
cc points in the mesh block.
cc
ccin cluster CLNAME mesh vacuum
cc
cc Create new cluster CLNAME, consisting of all mesh
cc points with x, y, z coordinates of -10^99 or less.
cc
cc Synonyms: [.and., .int.], [.or., .un.],
cc [.xnor., .eqv.], [block, bl],
cc [brick, br], [cluster, cl], [help, h],
cc [tetrahedron, tet, tetra], [zone, z, zn].
cc cluster An option in commands "accelerate", "area", "cluster",
cc "copy", "delete", "distance", "invert", "last",
cc "list", "mesh", "move", "project", "reflect",
cc "rename", "repack", "rotate", "scale", "sort",
cc "twist" and "where", to perform the specified
cc operation on one or more clusters of points.
cc Synonyms: [cluster, cl].
cg cluster arrays Clusters may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cc cmd A synonym for command in command "input".
cn cmd Indicates a command summary file.
cn The command summary file from GEOM is geom_cmd.
cg cn In columns 1-2 of geom_base, indicates a file name.
cc CNNAME The name of a circular cone. May have up to 24
cc characters, and may be ASCII, integer or floating
cc point. May not be the same as any other quadric
cc surface name QNAME. Also referred to as CNNAME1,
cc CNNAME2, ..., CONE(1), CONE(2). Specified with
cc commands "cone", "quadric" or "axisym".
cc No cone name may be "+", "-", "all", "h", "help",
cc "list", "point" or "thru", begin with "!" or contain
cc ";".
cc
cc Cones may appear in commands:
cc accelerate, arc, axisym, cone, copy, delete,
cc distance, extrema, help, invert, last, list, move,
cc operator, point, project, proximal, quadric, reflect,
cc rename, repack, rotate, scale, search, side, slice,
cc sort, track, triple, vector.
cg code The code name is GEOM.
cg coefficient To find the real coefficients of a polynomial equation
cg with from two to four specified real and/or complex
cg roots, use command "roots", option "=".
cg
cg To find the real coefficients of an Nth-order
cg polynomial equation with N specified real roots,
cg use command "root", option "=".
cg
cg To find the real and/or complex roots of a linear,
cg quadratic, cubic or quartic polynomial equation with
cg real coefficients, use command "roots".
cg
cg To search for real roots, extrema and inflection
cg points of a polynomial equation by Newtonian
cg iteration, use command "root".
cg cofactor If an integer N has an integer factor M, the cofactor
cg of M is N / M.
cg
cg coil A coil is a curve at a fixed distance from an axis,
cg with its angular coordinate around the axis a
cg linear function of its displacement parallel to the
cg axis. To generate a family of points arrayed along a
cg coil, use command "point ... move" to create a family
cg of points along a straight line parallel to the coil
cg axis, then use command "cluster" to create a cluster
cg consisting of the points, and then operate on the
cg cluster with command "twist", option "axial".
cg coincident Two geometric objects are coincident if they have the
cg same size, shape, position and orientation, or the
cg difference between them is no more than the
cg estimated error in calculating that difference, based
cg on the tolerance limit TOL.
cg
cg To test points, lines, triangle, planes, spheres or
cg circular cylinders for coincidence, use command
cg "distance".
cg
cg To test two spheres for coincidence of their centers
cg or their surfaces, or to test two circular cylinders
cg for coincidence of their axes or their surfaces,
cg use command "distance".
cg coincident See "coincident planes".
cg coincident planes
cg A pair of coincident planes may be represented by a
cg single quadric surface for which the standard
cg equation is x^2 = 0.
cg This factors into the two equations:
cg x = 0 (a simple plane),
cg x = 0 (a simple plane, coincident with the first).
cg
cg The general implicit quadric equation for coincident
cg planes is the square of the implicit quadric equation
cg for a simple plane:
cg (QC + QX * x + QY * y + QZ * z)^2 = 0.
cg
cg This is a limiting case of parallel planes or
cg intersecting planes.
cg See "non-simple planes".
cg
cg To create such a quadric surface, use command
cg "quadric", option "plane".
cc col An option in command "sudoku", to assign up to 9
cc digits to a Sudoku column.
cg collision See "mean free path".
cg colon The colon character, ":".
cg column In an input line, the character position counting from
cg the first (leftmost) character, including blank
cg characters. Control characters displayed as two
cg characters count as only one column. Tab characters
cg may be any number of columns.
cg column See "family of objects", "move", "scale".
cc comb An option in command "big", to find the number of
cc combinations of M things taken N at a time.
cc
cc big BIGNAME = M comb N
cc comb An option in command "icalc", to find the number of
cc combinations of M things taken N at a time.
cc
cc icalc M comb N
cg combinations The number of combinations of M things taken N at a
cg time is C(M,N) = M! / (N! * (M - N)!).
cg Use command "icalc M comb N" or
cg "big BIGNAME = INT1 comb INT2".
cg . See "permutations".
cc comm A synonym for commands.
cc comma The comma character, ",".
cc COMMAND In command "help COMMAND" or "COMMAND help", any
cc command name or the word "all".
cc See "commands", "help".
cc COMMAND In any command, the command key word. See "commands".
cc
cc Forms include:
cc
ccin COMMAND
cc
cc For most commands, display forms and options.
cc Exceptions include commands "angles", "coordinate",
cc "input", "output", "time", "title", and "when",
cc which display other information, and
cc commands "delimiter", "endif", "indo", "redo",
cc "return" and "undo" which perform some operation.
cc
ccin help COMMAND
ccin COMMAND help
cc
cc For all commands, display forms and options.
cc
ccin COMMAND ...
cc
cc See the description for each command in geom_base.
cc
ccin COMMAND ... ! COMMENT
cc
cc Command COMMAND with appended comment COMMENT.
cc
ccin COMMAND1 ...;COMMAND2 ... ; COMMAND3 ...
cc
cc Multiple commands COMMAND1, COMAND2 and COMMAND3 on
cc the same line. The ";" needs no delimiter.
cc
ccin COMMAND1 ... ! COMMENT1 ; COMMAND2 ... ! COMMENT2
cc
cc Multiple commands COMMAND1 and COMMAND2, with
cc appended comments COMMENT1 and COMMENT2,
cc respectively.
cc
cc Synonyms: [help, h].
cc command An option in command "input", used in place of a
cc file name, to indicate that one or more lines from
cc the input lines saved in memory are to be
cc executed or displayed.
cg command See "command form", "command list", "command summary".
cg command form Commands begin with a command word or one of its
cg synonyms, and may have additional arguments, and
cg must always be ended by typing the <return> key, or
cg with certain exceptions, by the command separator
cg character ";" if followed by another command on the
cg same input line, or by the comment separator
cg character "!" if followed by a comment on the same
cg input line.
cg The default field delimiter is a blank character,
cg but may be changed with command "delimiter".
cg Arguments are separated by the field delimiter.
cg Any argument beginning with "!" is the beginning of
cg an appended comment.
cg The <return> key must be typed at the end of every
cg input line typed at the user's terminal.
cg
cg Command arguments are displayed in lower case for
cg arguments to be typed literally as shown, and in
cg UPPER CASE for arguments for which the user
cg must provide an ASCII name (using any case), an
cg integer or floating point value, an integer or
cg floating point variable or a symbol.
cg
cg Any argument which allows a floating point value may
cg be replaced by the name of an integer or floating
cg point variable.
cg
cg Except for the argument LINE in command "indo" or
cg "redo", any argument which only allows an integer
cg value may be replaced by an integer variable.
cg
cg With certain exceptions (see "symbol"), any argument,
cg may be replaced by a symbolic word which, after
cg symbol replacement, is an acceptable value for that
cg argument.
cg
cg The first word of a command, and additional words if
cg desired, may be replaced by a previously defined
cg alias (see command "alias").
cg
cg See "commands", "key words", "arguments", "help".
cg command list See "input", "macro".
cg A list of commands from the current session is saved
cg in file geom_cmd, and may be displayed or executed
cg again with command "input geom_hsp [options]".
cg Another such list is saved internally, and may be
cg displayed or executed again with command
cg "input command [options]".
cg command summary See "geom_cmd", command "input command".
cg command use See the entries in this file for each object type.
cc commands Command to display an alphabetic list of command words,
cc including synonyms.
cc
cc Forms include:
cc
ccin help commands
ccin commands [help]
cc
cc Display an alphabetic list of command words,
cc including synonyms.
cc
cc Synonyms: [commands, alph, comm], [help, h].
cc commands The currently implemented commands are listed below,
cc with their synonyms. See the entry for each command,
cc for a description of required and optional arguments.
cc Also see "key words", "help", "command form",
cc "arguments". Also see files geom_commands and
cc geom_input.
cc Use command "alias" to create your own command names,
cc with or without additional arguments.
cc Use command "alph" to display an alphabetic list of
cc all commands and their synonyms.
cc Use command "synonym" to find any synonym for a
cc given command or any command with a given synonym.
cc
cc .
cc accelerate accel
cc alias al a
cc alph commands comm
cc angles angle ang
cc arc
cc area
cc axisym
cc base
cc big
cc bin
cc bisect
cc brick br
cc circle circ
cc cluster cl
cc commands comm alph
cc cone
cc contfr cf
cc coordinate coord cs system sys
cc copy cp duplicate dup
cc cross outer
cc crt
cc cut slice
cc cute
cc cuts
cc cylinder cyl
cc define def
cc debug
cc delete del remove rm
cc delimiter delimit delim
cc disk dk
cc distance dist intersect inter int
cc do
cc dot inner
cc duplicate dup copy cp
cc ellipsoid ellipse ell el
cc end exit split quit
cc enddo
cc endif
cc environment env setup
cc error err
cc exit end quit split
cc extrema extr
cc factor totient
cc goto
cc help h
cc hex
cc hyperb saddle
cc icalc
cc id title
cc if
cc increment incr
cc indo
cc inner dot
cc input in i read rd r
cc input call
cc intcirc
cc intersect inter int distance dist
cc invert inv
cc iris
cc kiss
cc last
cc line ln l
cc list print
cc lock zzz
cc marker mark m
cc math
cc mcvol
cc mesh
cc misc
cc move mv translate trans
cc object obj
cc operator oper op
cc outer cross
cc output out o write wr w
cc page
cc parse
cc pdf
cc plane pl
cc plot
cc point pnt pt p
cc polygon polyg pg
cc polyhedron polyh ph
cc project proj
cc prompt
cc proximal prox
cc quadric quad q
cc quit end exit split
cc random ?
cc ratio rat
cc read rd r input in i
cc redo
cc reflect refl
cc remove rm delete del
cc rename switch sw
cc repack
cc return rtn
cc root
cc rootf
cc roots
cc rotate rot
cc saddle hyperb
cc sample
cc search find
cc scale
cc set s variable var
cc setup environment env
cc side
cc sizes tables
cc slice cut
cc solve
cc sort
cc sphere sph
cc spin
cc split end exit quit
cc status stat
cc steiner stein
cc sudoku su
cc switch sw rename
cc symbol symb sym
cc synonym syn
cc system sys coordinate coord cs
cc tables sizes
cc tetrahedron tetra tet
cc time t
cc title id
cc tol
cc trace
cc track trk
cc translate trans move mv
cc triangle tri
cc trig
cc triple
cc twist tw
cc undo u
cc variable var set s
cc vector vect v
cc vi
cc volume vol
cc walk
cc when
cc where
cc write wr w output out o
cc zone zn z
cc comment A comment line is any input line with one of the
cc following forms, where COMMENT is any desired
cc comment, which may include leading blanks:
cc
ccin !COMMENT (starting in column 1)
ccin #COMMENT (starting in column 1)
ccin *COMMENT (starting in column 1)
ccin /COMMENT (starting in column 1)
ccin C COMMENT (starting in any column)
ccin c COMMENT (starting in any column)
ccin C++++ COMMENT (starting in any column)
ccin c++++ COMMENT (starting in any column)
ccin C---- COMMENT (starting in any column)
ccin c---- COMMENT (starting in any column)
ccin C.... COMMENT (starting in any column)
ccin c.... COMMENT (starting in any column)
ccin CCCOMMENT (starting in column 1)
ccin ccCOMMENT (starting in column 1)
cc
cc Comment lines are echoed in the output file.
cc
cc An appended comment is any character "!" following
cc a command and a field delimiter, and the rest of the
cc input line after the "!":
cc
cc COMMAND !COMMENT
cc
cc You may create your own comment corresponding to any
cc single character you desire, with command "marker".
cc See "definition", "alias".
cc
cc You may create your own comment corresponding to any
cc object name or other word you desire, with
cc command "alias". See "definition", "marker".
cg Comments See "comment".
cg Common See "Common factors".
cg common See "common divisor", "common multiplier".
cg common divisor A common divisor divides two or more numbers without
cg remainder. A greatest common divisor (gcd) is the
cg largest such number, and must contain only those
cg prime factors common to all of the numbers, with
cg each such prime factor to the least power of that
cg factor in any of the numbers.
cg If the gcd of a set of numbers is 1, the numbers are
cg all relatively prime.
cg See command "icalc", option "gcm".
cg Common factors In the display for command "factor", the number of
cg integers in the set (1, ..., N - 1), where N is the
cg integer being factored, that have common factors
cg with N.
cg The value "Totient function" is the number of
cg integers in the set (1, ..., N - 1) that are
cg relatively prime to N (have no common factor other
cg than 1).
cg common multiplier
cg A common multiplier is divisible by two or more numbers
cg without remainder. A least common multiplier (lcm)
cg is the smallest such number, and must contain all of
cg the prime factors found any any of the numbers, with
cg each such prime factor to the greatest power of that
cg factor in any of the numbers.
cg See commands "icalc" and "variable", option "lcm".
cc comp. An option in command 'icalc", to multiply an integer
cc by the Boolean complement of another integer.
cc M comp. N means M times the complement of N.
cc comp. N: replace 0 with 1 and 1 with 0.
cc See "Boolean".
cc comp. An option in command "cluster", to create a cluster
cc consisting of all of the points not in a specified
cc cluster. This is the Boolean "complement" of the
cc specified cluster.
cg complement See "Boolean".
cg complex Complex numbers are not allowed as input, except in
cg command "roots", options "=" and "?".
cg Complex roots displayed by command "roots" are the
cg only complex numbers displayed in the output data.
cg
cg A complex variable may be written in various forms:
cg z = x + i*y = r*exp(i*a) = r*cos(a) + i*r*sin(a),
cg where r = sqrt(x^2 + y^2), a = arctan (y / x),
cg x = r*cos(a), y = r*sin(a).
cg Complex roots of polynomial equations with real
cg coefficients only occur in the conjugate pairs
cg z = x + i * y and z' = x - i * y.
cg Alternate forms for z' are:
cg z' = x - i*y = r*exp(-i*a) = r*cos(a) - i*r*sin(a).
cg Also, z * z' = r^2, z + z' = 2*x, z - z' = 2*y*i.
cg component A vector has a component in each of the 3 coordinate
cg directions. See "coordinate system", "vector".
cg See "coordinate conversion", "vector conversion".
cg
cg A tensor operator has nine components, in a 3 by 3
cg matrix. See "operator".
cg composite See "composite number".
cg composite number A composite number is a positive non-prime integer.
cg Every known positive composite (non-prime) integer
cg N can be expressed as the product of a unique
cg collection of positive primes. These are the prime
cg factors of N. If N has the prime factors P1, P2,
cg ..., PN, then N = P1^a1 * P2^a2 * ... * PN^aN, where
cg a1, a2, ..., aN are positive integer exponents.
cg compress Output files may be compressed by editing them.
cg Some examples, using UNIX text editor VI, follow:
cg
cg :%s/ *$//
cg
cg Remove all trailing blanks.
cg
cg :%s/ */ /g
cg
cg Reduce all multiple blanks to single.
cg
cg :%s/00*E/E/g
cg
cg Remove all trailing zeros on floating point output.
cg
cg :%s/E+00/g
cg
cg Remove all zero exponents on floating point output.
cg
cg :%s/.......E/E/y
cg
cg Remove the final seven (for example) significant
cg figures after the decimal point of floating point
cg output.
cg
cg :g/^$/d
cg
cg Remove blank lines.
cc conc A synonym for concentric.
cc concatenation A new integer may be created by concatenating two
cc integers, e.g., 111 and 33333 may be concatenated to
cc form 11133333. See command "big".
cc This is a convenient way to add digits at the
cc beginning or end of a big integer.
cc concentric An option in command "cylinder", to create a family of
cc concentric circular cylinders with a specified axis
cc point, axis direction, and equally spaced between two
cc radii.
cc See "move", "nest", "parallel", "rotate", "scale".
cc
cc This command option can be replaced, using a do loop.
cc See "do loop use", commands "do", "enddo".
cc concentric An option in command "sphere", to create a family of
cc concentric spheres with a specified center point,
cc inner radius, outer radius, and equally spaced
cc between two radii.
cc See "move", "nest", "parallel", "rotate", "scale".
cc
cc This command option can be replaced, using a do loop.
cc See "do loop use", commands "do", "enddo".
cg concentric Two spheres are concentric if they share the same
cg center. Two circular cylinders are concentric if
cg they share the same axis. To see if two spheres are
cg concentric, use command "distance". To see if two
cg circular cylinders are concentric, use command
cg "distance".
cg conditional The execution of a block of input lines may be made
cg conditional by preceding the block with command
cg "if ...", and following the block with command
cg "endif ...". Command "if ..." specifies the
cg condition for executing the block of input lines.
cg cone A cone is a surface in 3-D space described by an
cg implicit quadric equation, and is a limit case of a
cg hyperboloid of one or two sheets. A conical surface
cg includes both sheets, on opposite sides of the vertex
cg point. At any point in the surface, a straight line
cg drawn through that point and through the vertex point
cg lies entirely within the surface. Along with planes,
cg cylinders, hyperbolic paraboloids and hyperboloids
cg of one sheet, a cone is a ruled surface.
cg
cg The standard forms of the implicit equations for
cg conical quadric surfaces are as follows (each
cg coefficient must have the preceding sign):
cg
cg Real elliptic cone:
cg x^2 + QYY*y^2 - |QZZ|*z^2 = 0
cg Real circular cone:
cg x^2 + y^2 - |QZZ|*z^2 = 0
cg or x^2 + y^2 = K^2 * z^2
cg Imaginary elliptic cone:
cg x^2 + QYY*y^2 + QZZ*z^2 = 0
cg Imaginary circular cone:
cg x^2 + y^2 + QZZ*z^2 = 0
cg or x^2 + y^2 = -K^2 * z^2
cg where K = tan (ALPHA), and ALPHA is the half-angle
cg at the vertex. K = sqrt (QZZ/QXX).
cg
cg Given a cone on the z axis, through the points
cg (R1, Z1), (R2, Z2), where R1^2 = X1^2 + Y1^2, and
cg R2^2 = X2^2 + Y2^2, the equation of the cone is
cg (Z2-Z1)^2*(x^2+y^2) - (R2-R1)^2*(z-ZVER)^2 = 0,
cg where ZVER = (Z1 * R2 - Z2 * R1) / (R2 - R1).
cg
cg See "half-angle". Also see "phi cone".
cg
cg The word "cone" in a command means a real circular
cg cone. Otherwise, use "quadric".
cg
cg To find the distance from a point to a cone, use
cg command "distance", "proximal" or "side".
cg
cg To find the distance or intersection between a plane
cg and a cone, use command "distance".
cg
cg The following commands relate to circular
cg cones:
cg accelerate, arc, axisym, cone, copy, debug, delete,
cg distance, extrema, help, invert, last, list, move,
cg operator, point, proximal, quadric, reflect, rename,
cg repack, rotate, scale, search, side, slice, sort,
cg symbol, synonym, tables, track, triple, vector, zone.
cg
cg A family of nested cones, with the same vertex and
cg axis, but with equally spaced vertex half-angles,
cg may be created with command "cone", option "nest".
cg See "parallel planes", "rotated planes",
cg "concentric".
cg
cg Also see "phi cone".
cc cone In a command, means a circular cone, except in
cc command "cone", option "scale", when the scaling
cc operator is linear or radial with an axis not
cc parallel to that of the base cone, elliptic cones
cc are created.
cc cone Command to display or create circular cones (except
cc that linear or radial scaling may create elliptic
cc cones). Creating a cone replaces any existing
cc quadric surface having the same name.
cc The normal vectors will be pointed radially outward.
cc See "quadric" for other options.
cc See "do loop use".
cc
cc Command "cone" relates to objects: axisym, cone,
cc line, operator, point, quadric, symbol, variable
vv vector.
cc
cc Forms include:
cc
ccin help cone
ccin cone [help]
cc
cc Display the command options.
cc
ccin cone [all,list]
cc
cc Display all circular cones (short display).
cc
ccin cone list CNNAME1 CNNAME2 CNNAME3 ...
cc
cc Display circular cones CNNAME1, CNNAME2, CNNAME3,
cc ..., with or without subscripts (short display).
cc
ccin cone CNNAME
cc
cc Display circular cone CNNAME (long display).
cc
cc In the following commands, use "+" or "-" instead of
cc CNNAME or CONE(2) to form the name by incrementing or
cc decrementing the base name for circular cones.
cc See command "last", "increment names".
cc
ccin cone CNNAME line PAXIS VAXIS ALNAME
cc
cc Create circular cone CNNAME on the axis specified
cc by point PAXIS and vector VAXIS, and passing
cc through the end points of line ALNAME. This is the
cc best way to specify the bounding surfaces of an
cc axially symmetric zone whose projected area is a
cc polygon.
cc
ccin cone CNNAME fit PVER VAXIS PNAME2
cc
cc Create circular cone CNNAME with vertex point PVER,
cc axis vector VAXIS, and passing through the point
cc PNAME2.
cc
ccin cone CNNAME angle PVER VAXIS ANGLE
cc
cc Create circular cone CNNAME with vertex point PVER,
cc axis vector VAXIS, and vertex half-angle ANGLE.
cc
ccin cone CNNAME nest NUMCONE INC PVER VAXIS ANG1 ANG2
cc
cc Create a family of NUMCONE nested circular cones
cc CNNAME, ..., with names incremented by INC
cc characters, with the same vertex point PVER and
cc axis vector VAXIS, and with vertex half-angles
cc equally spaced from ANG1 to ANG2.
cc See "increment names".
cc
cc This command can be replaced, by using commands
cc "do" and "enddo" to create a do loop over any of
cc the "cone" commands, using cones with subscripted
cc names, with more general specification of
cc properties.
cc
ccin cone CONE(2) move NUMCONE INC CONE(1) VMOVE
cc
cc Create a family of NUMCONE circular cones CONE(2),
cc ..., with names incremented by INC characters, and
cc spaced at intervals of vector VMOVE, starting from
cc circular cone CONE(1). See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin cone CONE(2) rotate NUMCONE INC CONE(1) OPNAME PINV
cc
cc Create a family of NUMCONE circular cones CONE(2),
cc ..., with names incremented by INC characters, by
cc rotating the preceding circular cone with operator
cc OPNAME and invariant point PINV, starting from
cc circular cone CONE(1). See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin cone CONE(2) scale NUMCONE INC CONE(1) OPNAME PINV
cc
cc Create a family of NUMCONE cones CONE(2), ..., with
cc names incremented by INC characters, by scaling the
cc preceding cone with operator OPNAME and invariant
cc point PINV, starting from circular cone CONE(1).
cc See "increment names". WARNING: a linear or
cc radial scaling axis not parallel to that of CONE(1)
cc will produce elliptic cones.
cc See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
cc Synonyms: [help, h], [line, l, ln],
cc [move, mv, trans, translate], [point, p, pnt, pt],
cc [rotate, rot].
cc cone An option in commands "copy", "delete", "last", "list",
cc "rename", "repack" and "sort", to perform the
cc specified operation on one or more circular cones.
cg cone See "cone, circular", "cone, elliptic".
cg cone arrays Cones may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cc CONE(1) In command "cone", the name of a base cone, used to
cc create a family of cones.
cg cone, circular For the circular cone:
cg QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QXX = QYY > 0, QZZ < 0),
cg the center and vertex are at x = y = z = 0,
cg the main axis is the z axis, and
cg the half-angle from the z axis is
cg atan (sqrt (-QZZ/QXX)).
cg cone, elliptic For the elliptic cone:
cg QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QXX => QYY > 0, QZZ < 0),
cg the center and vertex are at x = y = z = 0,
cg the main axis is the z axis,
cg the eccentricity is sqrt (1 - QYY / QXX) < 1,
cg the half-angle from the z axis toward the x axis is
cg atan (sqrt (-QZZ/QXX)), and
cg the half-angle from the z axis toward the y axis is
cg atan (sqrt (-QZZ/QYY).
cg cones A family of circular cones may be created with
cg command "cone", options "concentric", "move",
cg "rotate" or "scale" (with restrictions) or as
cg follows:
cg
cg p pinv ...
cg
cg Create an invariant point, if needed.
cg
cg cone CONE(1) (options)
cg
cg Create a base cone.
cg
cg op opr (options)
cg
cg Create a tensor operator, to reflect, rotate,
cg invert or scale, if needed.
cg
cg v vmove (options)
cg
cg Create a vector for use as a translation operator,
cg if needed.
cg
cg cp CONE(1) CONE(2)
cg
cg Copy cone CONE(1) to the first cone.
cg
cg Repeat the following block of commands as many times
cg as needed to create the rest of the family of cones.
cg See "shortcuts", "saved input lines".
cg
cg move cone CONE(1) vmove
cg
cg Move the base cone by amount vmove, if needed.
cg
cg [invert,reflect,rotate,scale] cone CONE(1) opr [pinv]
cg
cg Invert, reflect, rotate or scale the base cone with
cg tensor operator opr, if needed.
cg
cg copy cone CONE(1) +
cg
cg Copy the base cone to the next cone.
cg conflicts Tests are made for conflicts between the names of
cg preset synonyms, symbols and aliases created by
cg the user. If any are found, a warning message is
cg displayed, and the objects are displayed.
cg congruent Two geometric objects are congruent if they have the
cg same size and shape, and may be translated or rotated
cg to have the same position and orientation, such that
cg the difference between them is no more than the
cg estimated error in calculating that difference, based
cg on the tolerance limit TOL.
cg Objects that are mirror images, and can not be
cg superimposed, are not congruent.
cg conic See "conic sections".
cg conic sections The conic sections are the curves resulting from the
cg intersection of a plane with a circular cone.
cg The type of curve depends on the angle THETA of the
cg plane relative to the axis of the cone, and the
cg half-angle THHALF of the cone:
cg
cg hyperbola: THETA = 0.
cg
cg parabola: 0 < THETA < THHALF.
cg
cg ellipse: THHALF < THETA < 90 degrees.
cg
cg circle: THETA = 90 degrees.
cg conjugate Conjugate complex numbers are pairs of complex numbers
cg of the form x + i*y and x - i*y, where i is the
cg square root of -1.
cg z = x + i*y = r*exp( i*a) = r*cos(a) + i*r*sin(a),
cg z' = x - i*y = r*exp(-i*a) = r*cos(a) - i*r*sin(a).
cg where r = sqrt(x^2 + y^2), a = arctan(y / x),
cg x = r*cos(a), y = r*sin(a).
cg Note that the sum of the two conjugate complex
cg numbers is 2*x, while the product is x^2 + y^2.
cg conjugate In modular arithmetic, two numbers are conjugate if
cg they have the same value modulo the modulus. That
cg is, they only differ by a multiple of the modulus.
cg conjugate On a hyperbola or hyperbolic cylinder, the conjugate
cg semiaxis is the line perpendicular to the transverse
cg semiaxis, from either of the two vertices to either
cg of the asymptotes of the hyperbola. Its length is
cg half the distance between the asymptotes at the
cg vertex, in the direction of a tangent to the vertex.
cg See "transverse".
cg
cg For the hyperbola or hyperbolic cylinder,
cg QC + QXX * x^2 + QYY * y^2 = 0,
cg (QXX > 0, QYY < 0),
cg the length of the conjugate semiaxis is:
cg sqrt (QC / QXX), if QC > 0, and
cg sqrt (QC / QYY), if QC < 0.
cg
cg For the hyperboloid of one sheet,
cg QC + QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QC < 0, QXX => QYY > 0, QZZ < 0),
cg the length of the conjugate semiaxis is:
cg sqrt (QC / QZZ).
cg
cg For the hyperboloid of two sheets,
cg QC + QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QC > 0, QXX => QYY > 0, QZZ < 0),
cg the length of the conjugate semiaxis is:
cg sqrt (QC / QYY), in the plane x = 0, and
cg sqrt (QC / QXX), in the plane y = 0.
cg constant See "variable".
cg constant In data displayed for a quadric surface, the notation
cg "x const", "y const" or "z const" describes a plane
cg parallel to a major plane. In data displayed for a
cg quadric curve, those notations describe a line
cg line perpendicular to a major axis.
cg constants See "internal" for GEOM internal numerical constants.
cg construct See "create".
cc contfr Command to find the integer coefficients of the
cc continued fraction for a specified value, and to
cc find the value of a continued fraction given the
cc coefficients (in any mode).
cc See "continued fraction".
cc
cc Command "contfr" relates to objects: symbol,
cc variable.
cc
cc Forms include:
cc
ccin help contfr
ccin contfr [help]
cc
cc Display the command options.
cc
ccin contfr = VALUE
cc
cc Find the integer coefficients kc1, kc2, kc3, ...
cc of the continued fraction with value VALUE:
cc VALUE = kc1 + 1/(kc2 + 1/(kc3 + 1/(kc4 + ...))),
cc and the successive partial sums for VALUE, and
cc the integer numerators and denominators of the
cc corresponding rational fraction convergents.
cc If VALUE < 1, kc1 = 0. Otherwise kc1 > 0.
cc All other coefficients > 0.
cc The coefficients of the continued fraction for 1/x
cc will differ from those of x only by a leading zero.
cc
cc The series will terminate when the relative
cc difference between successive partial sums is less
cc than TOL. A very large final coefficient may
cc sometimes be ignored.
cc
ccin contfr C1 C2 C3 ... CN
cc
cc Find the value x of a continued fraction,
cc x = C1 + 1/(C2 + 1/(C3 + 1/(C4 + ...))), given
cc the coefficients C1, C2, C3, ... CN, which may be
cc integer or floating point, positive, zero or
cc negative. Also find
cc the numerators and denominators of the rational
cc fraction convergents (when all coefficients are
cc integers) equivalent to the successive partial sums
cc of the continued fraction.
cc The method will fail if an infinity occurs.
cc Final coefficients of 0 will cause the values of
cc successive partial sums to oscillate, if they have
cc not already converged.
cc A final coefficient of 1 may be added to the
cc preceding coefficient.
cc
cc
cc See "continued fraction".
cc
cc Synonyms [contfr, cf], [help, h].
cg continue See "restart".
cg continued See "continued fraction".
cg continued fraction
cg An expression of the form
cg x = C1 + 1/(C2 + 1/(C3 + 1/(C4 + ... 1/(CN))))...
cg where x > 0, and the coefficients are all positive
cg integers, except for C1, which is zero if x < 1.
cg If x is a rational number (an integer or a ratio of
cg two integers) the continued fraction terminates.
cg If x is an irrational number (a root of a polynomial
cg equation) the coefficients repeat in groups.
cg If x is a transcendental number (neither rational or
cg irrational, such as pi or e) the coefficients do not
cg repeat in groups, but may still form a predictable
cg pattern.
cg
cg To find the integer coefficients, start with the
cg integer part of x, find the reciprocal of the
cg remainder, and repeat. See command "contfr".
cg
cg To evaluate a continued fraction, see "convergent",
cg "partial sum", command "contfr".
cg
cg If the first coefficient is zero, x is the reciprocal
cg of the x evaluated from the remaining coefficients.
cg
cg The final N coefficients may be replaced by a single
cg coefficient equal to the value x (not necessarily an
cg integer) of the continued fraction consisting of just
cg those N coefficients.
cg
cg Final coefficients of K, 1 may be replaced by K + 1.
cg
cg Golden Mean (n = 1) and Silver Means (n > 1):
cg the coefficients of the continued fraction with value
cg (n + sqrt (n^2 + 4)) / 2 are (n, n, n, n, ...)
cg for n = 1, 2, 3, ...
cg
cg A continued fraction solution for a root of the
cg quadratic equation P(x) = a + a*b * x - b * x^2 is
cg r1 = CF {a, b, a, b, a, b, ...}.
cg
cg See files cf.root and cf.size in ~edwards/geom/test
cg contour See "slice", "profile".
cg control See "control errors".
cg control errors To control typing errors, use command "undo", "redo"
cg or "indo", and see "input file".
cg To control numerical truncation errors, see "tol",
cg "error estimate".
cn conv.mac A macro file containing selected metric conversion
cn factors. In directory ~edwards/work/geom/test .
cn To view or to read in conversion factors, use command
cn
cn input ~edwards/work/geom/test/conv.mac [options]
cn
cn See command "input" for options.
cg conventions See "command form", "default arguments", "key word",
cg converge See "convergence".
cg convergence Convergence of the iterative procedures used by
cg commands "side", "distance" and "proximal" is
cg determined by TOL.
cg The final relative change in distance must be no
cg greater than TOL, and the final angle between the
cg line from the specified point to the proximal point
cg and the normal vector of the quadric surface at the
cg proximal point must have a cosine within TOL of -1.0
cg or 1.0.
cg convergent The n'th convergent of a continued fraction is the
cg ratio of integers obtained by evaluating only the
cg first n coefficients of the continued fraction.
cg The value of the n'th convergent is the n'th
cg partial sum.
cg
cg To find the n'th convergent P(n) / Q(n), and the
cg n'th partial sum x(n), given the coefficients
cg C(n), n = 1, N:
cg P(0) = 1, P(1) = C(1),
cg P(n) = C(n) * P(n-1) + P(n-2), n = 2, N,
cg Q(0) = 0, Q(1) = 1,
cg Q(n) = C(n) * Q(n-1) + Q(n-2), n = 2, N,
cg x(n) = P(n) / Q(n), n = 2, N.
cg
cg These values are found and displayed when command
cg "contfr" is used.
cg conversion See "conversion factors", "coordinate conversion",
cg "convert output", "unit conversion",
cg "vector conversion".
cg conversion factors
cg Selected metric conversion factors are in macro file
cg conv.mac in directory ~edwards/work/geom/test .
cg convert See "conversion factors", "coordinate conversion",
cg "convert output", "unit conversion",
cg "vector conversion".
cg convert output To convert the output file(s) (geom_hsp or the file(s)
cg specified by the user with command "output") to an
cg input file, see "input file".
cc COORD In command "plot", option "axis", the coordinate to be
cc plotted on the horizontal or vertical axis. Must be
cc x, y, z, rcyl, rsph, theta or phi. See commands
cc "coordinate", "angles".
cc coord A synonym for coordinate.
cg coordinate A value used to locate a mesh point in the mesh or
cg to locate a physical point in a physical space.
cg See "coordinate system", command "search".
cc coordinate An option in command "debug", to display GEOM internal
cc variables for the coordinate system and angles:
cc asys, acoordu, acoordv, acoordw, angunit.
cc Synonyms: [coordinate, coord, cs, sys, system],
cc coordinate Command to display or specify the coordinate system of
cc the physical space. See "coordinate conversion",
cc "coordinate system", "vector conversion", "angle".
cc Display of point coordinates and vector components
cc will be in the specified coordinate system, unless
cc specifically labeled otherwise, e.g., xyz.
cc Specification of point coordinates and vector
cc components must be in the specified coordinate
cc system.
cc Note: variables are not affected by changes
cc in the coordinate system or angle units, so their
cc values and units remain as intended by the user when
cc originally specified. Variables may be assigned a
cc descriptive tag to specify the units or to provide
cc other information. See command "variable", option
cc "tag".
cc
cc Forms include:
cc
ccin help coordinate
ccin coordinate help
cc
cc Display the command options.
cc
ccin coordinate
cc
cc Display the coordinate system.
cc
ccin coordinate cartesian
cc
cc Set the coordinate system to rectangular (x, y, z).
cc
ccin coordinate cylindrical
cc
cc Set the coordinate system to cylindrical (rcyl,
cc theta, z).
cc
ccin coordinate spherical
cc
cc Set the coordinate system to spherical (rsph,
cc theta, phi).
cc
cc See command "angles" to specify the angle units.
cc
cc Synonyms: [coordinate, coord, cs, sys, system],
cc [cartesian, Cartesian, cart, rectangular, rect, xyz],
cc [cylindrical, cyl], [help, h], [spherical, sph].
cg coordinate See "coordinate conversion", "coordinate surface",
cg "coordinate system", "surface of coord".
cg coordinate conversion
cg To convert the coordinate system of existing points
cg and/or vectors, use commands "coordinate" and
cg "angles" to specify a new coordinate system, and
cg display the points and/or vectors with commands
cg "point" and "vector". See "coordinate system",
cg "vector conversion".
cg Angles may be in degrees or radians. See "angle".
cg
cg To convert the coordinate system of points and/or
cg vectors that appear in a data display, but are not
cg saved, see "(xyz)".
cg
cg rectangular (x, y, z):
cg x = rcyl * cos (theta),
cg x = rsph * cos (theta) * sin (phi),
cg y = rcyl * sin (theta),
cg y = rsph * sin (theta) * sin (phi),
cg z = rsph * cos (phi).
cg
cg cylindrical (rcyl, theta, z):
cg rcyl^2 = x^2 + y^2,
cg rcyl = rsph * sin (phi),
cg theta = arctan (y / x) (azimuth angle),
cg sin (theta) = y / sqrt (x^2 + y^2),
cg cos (theta) = x / sqrt (x^2 + y^2),
cg tan (theta) = y / x.
cg
cg spherical (rsph, theta, phi):
cg rsph^2 = x^2 + y^2 + z^2,
cg = rcyl^2 + z^2,
cg theta = arctan (y / x) (azimuth angle),
cg cos (theta) = x / sqrt (x^2 + y^2),
cg sin (theta) = y / sqrt (x^2 + y^2),
cg phi = arccos (z / rsph) (polar angle
cg = arctan (rcyl / z) from z axis),
cg sin (phi) = sqrt (x^2 + y^2) /
cg sqrt (x^2 + y^2 + z^2),
cg sin (phi) = rcyl / sqrt (rcyl^2 + z^2),
cg cos (phi) = z / sqrt (x^2 + y^2 + z^2),
cg cos (phi) = z / sqrt (rcyl^2 + z^2),
cg tan (phi) = sqrt (x^2 + y^2) / z,
cg tan (phi) = rcyl / z.
cg
cg Note: to avoid numerical error and insure that
cg all conversion are reversible, add 10^99 to x,
cg rcyl and rs, replace all sines and cosines less
cg than TOL with zero, and replace any results with
cg an estimated relative error less than TOL with zero.
cg coordinate surface
cg A coordinate surface is a surface at a constant value
cg of one of the three coordinates of an orthogonal
cg coordinate system, such as rectangular (x, y z),
cg cylindrical (rcyl, theta, z) or spherical (rsph,
cg theta, phi). To create a coordinate surface,
cg see "x plane", "y plane", "z plane", "rcyl cylinder",
cg "theta plane", "rsph sphere", "phi cone".
cg
cg To specify the coordinate system and the angle units,
cg use commands "coordinate" and "angles".
cg
cg To create a volume element bounded by coordinate
cg surfaces, use command "brick".
cg
cg To create a 3-D array of points on a specified family
cg of coordinate surfaces, use command "brick", followed
cg by command
cg "point PMESH brick BRNAME mesh block [volume]".
cg See "briquette".
cg
cg To create a family of variables whose values
cg are an arithmetic or geometric series, for use in
cg specifying coordinates, use command "variable",
cg option "series".
cg coordinate system
cg The coordinate system used to specify the coordinates
cg of points is specified with command "coordinate",
cg and may be one of the following:
cg
cg Rectangular (x, y, z):
cg x = rcyl * cos (theta),
cg x = rsph * cos (theta) * sin (phi),
cg y = rcyl * sin (theta),
cg y = rsph * sin (theta) * sin (phi),
cg z = rsph * cos (phi).
cg
cg Cylindrical (rcyl, theta, z):
cg rcyl^2 = x^2 + y^2,
cg rcyl = rsph * sin (phi),
cg theta = arctan (y / x),
cg (azimuth angle around z axis, measured
cg counterclockwise from x axis).
cg
cg Spherical (rsph, theta, phi):
cg rsph^2 = x^2 + y^2 + z^2,
cg = rcyl^2 + z^2,
cg theta = arctan (y / x),
cg phi = arccos (z / rsph),
cg = arctan (rcyl / z),
cg (polar angle from positive z axis).
cg
cg For practical reasons, the coefficients of the
cg implicit equations for quadric surfaces are always
cg based on a rectangular (x, y, z) coordinate system.
cg
cg See "coordinate conversion", "vector conversion".
cg coordinates See "coordinate conversion", "coordinate",
cg "vector conversion".
cg copy See "copy objects".
cc copy Command to copy an alias, marker, variable, vector,
cc tensor operator, point, cluster, line, triangle,
cc regular polygon, annular disk, quadric surface
cc (including a plane, sphere, circular cylinder,
cc circular cone, hyperbolic paraboloid, ellipsoid,
cc axially symmetric quadric surface or general quadric
cc surface), regular polyhedron, tetrahedron, brick,
cc zone, probability bin, probability distribution
cc function (pdf), symbol or big integer.
cc You can not copy over an existing object.
cc The copy must not have the same name as the original.
cc This is an excellent way to create a backup before
cc modifying an object, in case of an error.
cc Note: no replacement of symbols will be done
cc in the command "copy symbol ...".
cc
cc Command "copy" relates to objects: alias, axisym
cc big, bin, brick, cluster, cone, cylinder, disk,
cc ellipsoid, hyperb, line, marker, operator, pdf,
cc plane, point, polygon, polyhedron, quadric, sphere,
cc symbol, tetrahedron, triangle, variable, vector,
cc zone.
cc
cc Forms include:
cc
ccin help copy
ccin copy [help]
cc
cc Display the command options.
cc
cc In the following command, use "+" or "-" instead of
cc OBJNAME2 to form the name by incrementing or
cc decrementing the base name for objects of type
cc OBJTYPE (which may not be OBJNAME).
cc See command "last", "increment names".
cc
ccin copy OBJTYPE OBJNAME OBJNAME2
cc
cc Copy object type OBJTYPE (alias, axisym, big, bin,
cc brick, cluster, cone, cylinder, disk, ellipsoid,
cc hyperb, line, marker, operator, pdf, plane, point,
cc polygon, polyhedron, quadric, sphere, symbol,
cc tetrahedron, triangle, variable, vector, zone)
cc with name OBJNAME to the same object type with name
cc OBJNAME2.
cc No copy will be made if OBJTYPE is symbol or alias.
cc
cc The command above may be placed between commands "do"
cc and "enddo", to create a do loop over subscripted
cc object names, to copy all of them to new names.
cc
cc Synonyms: [alias, al, a,], [brick, br],
cc [cluster, cl], [copy, cp, dup, duplicate],
cc [cylinder, cyl], [disk, disc, dk],
cc [ellipsoid, el, ell, ellipse], [help, h],
cc [hyperb, saddle], [line, l, ln], [marker, mark, m],
cc [operator, oper, op], [plane, pl],
cc [point, pnt, pt, p], [polygon, polyg, pg],
cc [polyhedron, polyh, ph], [quadric, quad, q],
cc [sphere, sph], [symbol, sym, symb],
cc [tetrahedron, tetra, tet], [triangle, tri],
cc [variable, var, set, s], [vector, v, vect],
cc [zone, z, zn].
cg copy objects See command "copy". See "cones", "cylinders",
cg "planes", "quadric families", "quadric surfaces",
cg "spheres".
cg To copy the output from a command for use in a new
cg command, see "cut and paste".
cc cos A synonym for cosine, in commands "project" and
cc "vector".
cc cos An option in command "project", when projecting onto
cc the surface of a circular cylinder, to make the axial
cc distance of each point from point PCEN on the axis
cc equal to the cosine of the original polar angle phi
cc of the point, as measured relative to point PCEN,
cc in the positive direction along the axis.
cc cos An option in command "variable", argument FUNCTION,
cc to indicate the trigonometric cosine function.
cc A cos B means A * cos (B).
cf cos The trigonometric cosine function.
cf Example: y = cos (x) means y is the cosine of x.
cf x must be in radians.
cc cosh An option in command "variable", argument FUNCTION,
cc to indicate the hyperbolic cosine function.
cc A cosh B means A * cosh (B).
cf cosh The hyperbolic cosine function. Example: y = cosh (x)
cf means y = (1/2) * (e^x + e^(-x)).
cc cosine An option in command "vector", to create a vector by
cc randomly sampling from a cosine-power distribution
cc around a specified axis vector VAXIS, with a
cc specified power POWER.
cc
cc An option in command "project", to project onto the
cc surface of a circular cylinder by replacing the axial
cc distance of a point from the center of the cylinder
cc with the cosine of the polar angle phi of the
cc point, to preserve relative areas determined from
cc points projected from a spherical surface centered
cc at the center of the cylinder. A special projection
cc used in cartography.
cc
cc Synonyms: [cosine, cos].
cg cosine To find the cosine of the angle between two vectors,
cg use command "dot".
cg Also see "cosine-power", "Law of Cosines".
cg cosine-power A cosine-power distribution is one in which a power
cg of the cosine of the angle from a specified axis
cg is uniformly distributed from 0 to 1, and all angles
cg are within 90 degrees of the positive axial
cg direction.
cg
cg For an isotropic distribution the power must be zero.
cg
cg For a cosine distribution, the power must be 1.
cg
cg For distributions more strongly peaked toward the
cg axis, the power must be larger than 1.
cg
cg For a unit vector randomly sampled from a general
cg cosine-power distribution, with a power POWER from
cg zero to infinity, the relationship between POWER and
cg the expected value <ua> of the axial component of the
cg vector is as follows:
cg
cg <ua> = 1 - 1 / (POWER + 2)
cg POWER = 1 / (1 - <ua>) - 2
cg
cg <ua> POWER angle (degrees)
cg 0.5 0 60.00
cg 2/3 1 48.19
cg 0.8 3 36.87
cg 0.9 8 25.84
cg 0.99 98 8.11
cg 0.999 998 2.56
cg 0.9999 9998 0.81
cg 0.99999 99998 0.26
cg count If you need to count the number of times a command is
cg repeated, initialize a variable to zero, then
cg increment it each time the command is repeated.
cg
cg variable ntot [=] 0
cg
cg Initialize ntot to zero.
cg
cg alias t = "variable ntot = ntot + 1 ; COMMAND"
cg
cg Create alias "t" to increment ntot and do COMMAND.
cg
cg t
cg
cg Increment ntot and do command COMMAND.
cg
cg Any block of commands such as those above may be
cg executed together in several ways. See "alias",
cg "macro", "saved input lines", "shortcuts".
cc cp A synonym for copy.
cg cpar In columns 1-4 of geom_base, indicates a parameter.
cg CPU Central processing unit. In the time summary at the
cg end of the run, a component of machine time use,
cg separate from input/output (I/O) and system (SYS)
cg time.
cn craps.mac A macro file to create a pdf representing rolling two
cn dice, to demonstrate how to work with bins and pdfs.
cn In ~/work/geom/test .
cg create To describe an environmental, operational, geometric,
cg or Monte Carlo object, using a command.
cg See "create objects", "create environment",
cg "create operators".
cg create See "create environment", "create Monte Carlo",
cg "create objects", "create operators".
cg create environment
cg The commands for modifying the default values of
cg certain environmental parameters are:
cg alias, marker, angles, coordinate, delimiter, icalc,
cg input, output, plot, tol.
cg create Monte Carlo
cg The commands for creating Monte Carlo objects are:
cg bin (probability bins) and pdf (probability
cg distribution functions).
cg Also see "random", "sample", "spin".
cg create objects Geometric objects are created with commands:
cg point, cluster, line, vector, triangle, polygon,
cg disk, plane, sphere, cylinder, cone, hyperb,
cg ellipsoid, axisym, quadric, polyhedron, tetrahedron,
cg brick, zone.
cg
cg Other objects are created with commands "alias",
cg "bin", "marker", "operator", "pdf", "symbol",
cg "variable".
cg
cg The commands for creating objects have the general
cg forms:
cg
cg OBJTYPE [OBJNAME,+,-] [various specifications]
cg
cg Create one or more objects of type OBJTYPE with
cg initial name [OBJNAME, or the name incremented or
cg decremented from the base name for this object
cg type], with various specifications.
cg Names of objects after the first object will be
cg incremented in ASCII sequence.
cg
cg copy OBJTYPE OBJNAME [OBJNAME2,+,-]
cg
cg Copy the object of object type OBJTYPE with name
cg OBJNAME to object [OBJNAME2, or the name
cg incremented or decremented from the last name
cg specified for an object of this type].
cg
cg rename OBJTYPE OBJNAME [OBJNAME2,+,-]
cg
cg Rename the object of object type OBJTYPE with name
cg OBJNAME to object [OBJNAME2, or the name
cg incremented or decremented from the last name
cg specified for an object of this type].
cg
cg rename OBJTYPE OBJNAME OBJNAME2 array
cg
cg Rename the object of object type OBJTYPE by
cg replacing the subscripted stem name OBJNAME with
cc the subscripted stem name OBJNAME2.
cg
cg delete OBJTYPE [OBJNAME,all]
cg
cg Delete the object of object type OBJTYPE [with name
cg OBJNAME, or all such objects].
cg
cg See "OBJTYPE", "OBJNAME".
cg create operators Operators are created with commands: variable, vector,
cg operator.
cg cross See "cross product", command "cross".
cc cross Command to find the cross (outer) product of two
cc vectors, which has a magnitude equal to the area of
cc the parallelogram specified by the two vectors, or
cc twice the area of the triangle specified by the two
cc vectors.
cc
cc Command "cross" relates to objects: symbol, vector.
cc
cc Forms include:
cc
ccin help cross
ccin cross [help]
cc
cc Display the command options.
cc
ccin cross VNAME1 VNAME2
cc
cc Find the vector which is the cross (outer) product
cc of vectors VNAME1 and VNAME2.
cc
cc The cross product may be saved as another vector:
cc
cc vector VNAME cross VNAME1 VNAME2
cc
cc Create vector VNAME, the cross (outer) product of
cc vectors VNAME1 and VNAME2.
cc
cc Synonyms: [cross, outer], [help, h].
cc cross An option in command "vector", to create a vector which
cc is the cross product of two vectors.
cg cross product The cross (or outer or vector) product of two vectors
cg A = (AX, AY, AZ) and B = (BX, BY, BZ) is the vector
cg C = A cross B = (CX, CY, CZ), where
cg C = (AY*BZ - AZ*BY, AZ*BX - AX*BZ, AX*BY - AY*BX).
cg |C| = |A| * |B| * sin (THETA), where THETA is the
cg angle between vectors A and B.
cg Note that B cross A = -(A cross B), and that the
cg cross product of two parallel vectors is zero.
cc crt Command to solve the Chinese Remainder Theorem for
cc a specified set of integer divisors and remainders,
cc or to find the remainders for a specified integer
cc value, using the first few prime numbers as divisors,
cc or with a specified set of relatively prime
cc divisors. See command "factor".
cc
cc Command "crt" relates to objects: symbol, variable.
cc
cc Forms include:
cc
ccin help crt
ccin crt [help]
cc
cc Display the command options.
cc
ccin crt IDIV1 IREM1 IDIV2 IREM2 ... IDIVN IREMN
cc
cc Find the least integer value that has the
cc remainders IREM1, IREM2, ..., IREMN when divided
cc by the integer divisors IDIV1, IDIV2, ..., IDIVN,
cc respectively, where the integer divisors are 2 or
cc more, and have no common factor. Also display the
cc next four higher integer values with the same
cc remainders, if less than 10^18.
cc
ccin crt = IVAL
cc
cc Find the remainders resulting from dividing the
cc integer IVAL by the first few prime numbers
cc (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...),
cc using the minimum set of prime numbers for which
cc IVAL is the least integer with the same remainders.
cc IVAL must be 2 or more.
cc
ccin crt = IVAL IDIV1 IDIV2 ... IDIVN
cc
cc Find the remainders resulting from dividing the
cc integer IVAL by the integers IDIV1, IDIV2, ...,
cc IDIVN, which must be 2 or more, and have no common
cc factors. IVAL must be 2 or more.
cc
cc Synonyms: [help, h].
cg cryptography See command "big".
cc cs A synonym for coordinate.
cg cube A cube is a regular polyhedron with 8 vertices,
cg 12 edges and 6 square faces.
cg The edge length, face area, volume, radius of
cg inscribed sphere, dihedral angle and central edge
cg angle, for a circumscribed sphere radius of 1.0 are:
cg
cg edge = 2.0 / sqrt (3.0) = 1.154700538379
cg area = 4.0 / 3.0 = 1.333333333333
cg volume = 8.0 * sqrt (3.0) / 9.0 = 1.539600717839
cg rinsc = 1.0 / sqrt (3.0) = 0.5773502691896
cg angdih = acos (0.0) = 90.00000000000
cg angcent = acos (1.0 / 3.0) = 70.52877936551
cg
cg See "polyhedron", "brick".
cg cubic See command "roots".
cg cubic A cubic polynomial equation in z = x + i*y, where z is
cg real or complex, x and y are real, and i = sqrt (-1):
cg P(z) = a0 + a1*z + a2*z^2 + a3*z^3 = 0,
cg with real coefficients a0, a1, a2 and a3 = 1, has
cg three roots r1, r2, r3, of which one or three are
cg real, has two extrema (maxima and minima) e1, e2 of
cg which either zero or two are real, and has one real
cg inversion point v1.
cg The roots satisfy P(z) = 0. The extrema satisfy
cg P'(z) = 0. The inversion points satisfy P''(z) = 0.
cg P' and P'' are the first and second derivatives of
cg P with respect to z.
cg Some interesting relationships between the
cg coefficients and the properties of the polynomial
cg are as follows:
cg -a0 = r1*r2*r3
cg a1 / 3 = (1/3)*(r1*r2 + r2*r3 + r3*r1)
cg = e1*e2
cg -a2 / 3 = (1/3)*(r1 + r2 + r3)
cg = (1/2)*(e1 + e2)
cg = v1
cg a3 = 1
cg
cg Note that the inversion point v1 is at the average z
cg value of the roots and the extrema, and that the
cg average value of the products of pairs of roots and
cg extrema are the same.
cg
cg See command "roots".
cg curly bracket The left or right curly bracket, "{" or "}".
cc curt An option in command "variable", argument FUNCTION,
cc to indicate the real cube root function.
cc A curt B means A * B^(1/3).
cf curt The cube root function. Example: y = curt (x) means
cf y = x^(1/3) (real value only).
cf
cf To find the real and complex cube roots of any
cf real nonzero number B, use command:
cf
cf roots B 0 0 -1
cg curvature The curvature of a curve is the inverse of its radius
cg of curvature. See "radius of curvature",
cg "principal radius".
cg See commands "arc", "extrema".
cg curve See "quadric curve", "intersection curve", outline.
cc cut A synonym for slice.
cg cut See "cut and paste", "triangle cutting".
cg cut and paste If you have a mouse with cut and paste capability, you
cg can create variables, points, vectors, etc., by
cg cutting and pasting the output from previous commands
cg for use as the arguments of the new commands.
cg Note that the precision variable TOL should not be
cg less than the precision of command arguments.
cc cute Command to find all triangles formed by extending any
cc two sides of a specified triangle, to add a section
cc with the same perimeter and area as the specified
cc triangle. See "cutting line", "triangle cutting",
cc and commands "cuts", "trig" and "triangle".
cc
cc Command "cute" relates to objects: symbol, variable.
cc
cc Forms include:
cc
ccin help cute
ccin cute [help]
cc
cc Display the command options.
cc
ccin cute VA VB VC
cc
cc Find each triangle that can be formed by extending
cc any two edges of the triangle with edges VA, VB and
cc VC, to add a section with the same perimeter and
cc area as the original triangle. This is the inverse
cc of command "cuts".
cc
cc Synonyms: [help, h].
cc cuts Command to find each straight line that cuts a triangle
cc into two parts with equal perimeters and areas.
cc See "cutting line", "triangle cutting", and commands
cc "cute", "trig" and "triangle".
cc
cc Command "cuts" relates to objects: symbol, variable.
cc
cc Forms include:
cc
ccin help cuts
ccin cuts [help]
cc
cc Display the command options.
cc
ccin cuts VA VB VC
cc
cc Find each straight line that cuts the triangle with
cc edges VA, VB and VC into two sections with equal
cc perimeters and areas, and display the edges cut,
cc the fractional and absolute distances of the ends
cc of the cutting line along the edges from their
cc common vertex, and the length of the cutting line.
cc There may be 1, 2 or 3 such cutting lines.
cc This is the inverse of command "cute".
cc
cc Synonyms: [help, h].
cg cutting See "cutting line", "triangle cutting".
cg cutting line To partition a triangle into two parts of equal area
cg and equal perimeter with straight line cuts, see
cg "triangle cutting", commands "cute", "cuts",
cg "triangle", and "trig".
cg The cutting lines will be displayed whenever a
cg triangle is created or displayed.
cg cx In columns 1-2 of geom_base, indicates an executable
cg program.
cc cyl A synonym for cylinder.
cc cyl A synonym for cylindrical in command "project".
cc CYL(1) In command "cylinder", the name of a base cylinder,
cc used to create a family of cylinders.
cg cylinder A cylinder is a surface in 3-D space described by an
cg implicit quadric equation, and is a limit case of a
cg hyperboloid of one sheet or an ellipsoid.
cg At any point in the surface, any line drawn parallel
cg to the cylindrical axis and perpendicular to the
cg normal vector, lies entirely within the surface.
cg Along with planes, cones, hyperbolic paraboloids and
cg hyperboloids of one sheet, a cylinder is a ruled
cg surface.
cg
cg The standard forms of the implicit equations for
cg cylinders are as follows (each coefficient must have
cg the preceding sign):
cg
cg Parabolic cylinder: -QY*y + x^2 = 0
cg Hyperbolic cylinder:
cg 1 + QXX*x^2 - |QYY|*y^2 = 0
cg Real elliptic cylinder:
cg - 1 + QXX*x^2 + QYY*y^2 = 0
cg Real circular cylinder:
cg - 1 + QXX * (x^2 + y^2) = 0
cg or x^2 + y^2 = rcyl^2
cg Imaginary elliptic cylinder:
cg 1 + QXX*x^2 + QYY*y^2 = 0
cg Imaginary circular cylinder:
cg 1 + QXX * (x^2 + y^2) = 0
cg or x^2 + y^2 = -rcyl^2
cg
cg The word "cylinder" in a command means a real
cg circular cylinder. Otherwise, use "quadric".
cg
cg To find the distance from a cylinder to a point, use
cg command "distance", "proximal" or "side".
cg
cg To find the distance from a circular cylinder to a
cg point, use command "distance".
cg To find the distance and proximal point, and/or the
cg intersections of a circular cylinder and a line,
cg a triangle, plane, a sphere or another circular
cg cylinder, use command "distance".
cg
cg To find the distance or intersection between a plane
cg and a general cylinder, use command "distance".
cg
cg The following commands relate to circular
cg cylinders:
cg accelerate, arc, axisym, copy, cylinder, debug,
cg delete, distance, extrema, help, invert, last, list,
cg move, operator, point, project, proximal, quadric,
cg reflect, rename, repack, rotate, scale, search, side,
cg slice, sort, symbol, synonym, tables, track, triple,
cg vector, zone.
cg
cg Also see "rcyl cylinder".
cc cylinder In a command, means a circular cylinder, except in
cc command "cylinder", option "scale", when a linear or
cc radial scaling operator with an axis not parallel to
cc that of the base cylinder can create an elliptic
cc cylinder.
cc cylinder Command to display or create circular cylinders (except
cc that linear or radial scaling may create elliptic
cc cylinders). Creating a cylinder replaces any
cc existing quadric surface having the same name.
cc The normal vectors will be pointed radially outward.
cc See "quadric" for other options.
cc See "do loop use".
cc
cc Command "cylinder" relates to objects: axisym,
cc cylinder, operator, point, quadric, symbol, variable,
cc vector.
cc
cc Forms include:
cc
ccin help cylinder
ccin cylinder [help]
cc
cc Display the command options.
cc
ccin cylinder [all,list]
cc
cc Display all circular cylinders (short display).
cc
ccin cylinder list CYLNAME1 CYLNAME2 CYLNAME3 ...
cc
cc Display circular cylinders CYLNAME1, CYLNAME2,
cc CYLNAME3, ..., with or without subscripts (short
cc display).
cc
ccin cylinder CYLNAME
cc Display circular cylinder CYLNAME (long display.
cc
cc In the following commands, use "+" or "-" instead of
cc CYLNAME or CYL(2) to form the name by incrementing or
cc decrementing the base name for circular cylinders.
cc See command "last", "increment names".
cc
ccin cylinder CYLNAME = PAXIS VAXIS RADIUS
cc
cc Create circular cylinder CYLNAME, with an axis
cc through point PAXIS in the direction of vector
cc VAXIS, and radius RADIUS.
cc
ccin cylinder CYLNAME fit VAXIS PNAME1 PNAME2 PNAME3
cc
cc Create circular cylinder CYLNAME with axis vector
cc VAXIS, through the three points PNAME1, PNAME2 and
cc PNAME3, which must not be coincident or collinear.
cc
ccin cyl CYLNAME conc NUMCYL INC PAXIS VAXIS RAD1 RAD2
cc
cc Create a family of NUMCYL concentric circular
cc cylinders CYLNAME, ..., with names incremented by
cc INC characters, with an axis through point PAXIS in
cc the direction of vector VAXIS, and with radii
cc equally spaced from radius RAD1 to radius RAD2.
cc See "increment names".
cc Note: "cyl" is a synonym for "cylinder".
cc Note: "conc" is a synonym for "concentric".
cc
cc This command can be replaced by using commands
cc "do" and "enddo" to create a do loop over any
cc of the "cyl" commands, using subscripted cylinder
cc names, with more general specifications.
cc
ccin cylinder CYL(2) move NUMCYL INC CYL(1) VMOVE
cc
cc Create a family of NUMCYL circular cylinders
cc CYL(2), ..., with names incremented by INC
cc characters, and spaced at intervals of vector
cc VMOVE, starting from circular cylinder CYL(1).
cc See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
cc
ccin cylinder CYL(2) rotate NUMCYL INC CYL(1) OPNAME PINV
cc
cc Create a family of NUMCYL circular cylinders
cc CYL(2), ..., with names incremented by INC
cc characters, by rotating the preceding cylinder with
cc operator OPNAME and invariant point PINV, starting
cc from circular cylinder CYL(1).
cc See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin cylinder CYL(2) scale NUMCYL INC CYL(1) OPNAME PINV
cc
cc Create a family of NUMCYL cylinders CYL(2), ...,
cc with names incremented by INC characters, by
cc scaling the preceding cylinder with operator OPNAME
cc and invariant point PINV, starting from circular
cc cylinder CYL(1). WARNING: a linear or radial
cc scaling axis not parallel to that of CYL(1) will
cc produce elliptic cylinders. See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
cc Synonyms: [help, h], [concentric, conc],
cc [cylinder, cyl], [move, mv, trans, translate],
cc [rotate, rot].
cc cylinder An option in commands "copy", "delete", "last", "list",
cc "rename", "repack" and "sort", to perform the
cc specified operation on one or more circular
cc cylinders.
cc Synonyms: [cylinder, cyl].
cc cylinder An option in command "project", to project onto the
cc surface of a circular cylinder.
cg cylinder See "cylinder, circular", "cylinder, elliptic",
cg "cylinder, hyperbolic", "cylinder, parabolic".
cg cylinder arrays Cylinders may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cg cylinder, circular
cg For the circle or circular cylinder:
cg QC + QXX * x^2 + QYY * y^2 = 0, for all z,
cg (QC < 0, QXX = QYY > 0),
cg the center is at x = 0, y = 0,
cg the main axis is the z axis, and
cg the radius is RCYL = sqrt (-QC / QXX).
cg
cg The standard equation for the circle or circular
cg cylinder is x^2 + y^2 = RCYL^2.
cg cylinder, elliptic
cg For the ellipse or elliptic cylinder:
cg QC + QXX * x^2 + QYY * y^2 = 0, for all z,
cg (QC < 0, QXX => QYY > 0),
cg the center is at x = 0, y = 0,
cg the main axis is the z axis,
cg the major semiaxis is A = sqrt (-QC / QYY),
cg the minor semiaxis is B = sqrt (-QC / QXX),
cg the eccentricity is sqrt (1 - QYY / QXX) < 1,
cg or sqrt (1 - (B / A)^2) < 1,
cg the two foci are at:
cg x = 0, y = (+/-)sqrt (QC / QXX - QC / QYY),
cg or y + (+/-)sqrt (B^2 - A^2),
cg the distance from the center to a focus is
cg sqrt (QC / QXX - QC / QYY), or sqrt (B^2 - A^2), and
cg the length of the latus rectum (width at focus) is
cg 2 * sqrt (-QC * QYY) / QXX or 2 * B^2 / A.
cg
cg The standard equation for the ellipse or elliptic
cg cylinder is (x / B)^2 + (y / A)^2 = 1, for all z.
cg cylinder, hyperbolic
cg For the hyperbola or hyperbolic cylinder:
cg QC + QXX * x^2 + QYY * y^2 = 0, for all z,
cg (QXX > 0, QYY < 0),
cg the center is at x = 0, y = 0,
cg the length of the transverse semiaxis is
cg A = sqrt (-QC / QYY), if QC > 0, and
cg A = sqrt (-QC / QXX), if QC < 0.
cg the length of the conjugate semiaxis is
cg B = sqrt (QC / QXX), if QC > 0, and
cg B = sqrt (QC / QYY), if QC < 0.
cg the main axis is the z axis,
cg the eccentricity is
cg sqrt (1 - QYY / QXX) > 1, if QC > 0, or
cg sqrt (1 - QXX / QYY) > 1, if QC < 0, or
cg sqrt (1 + (B / A)^2),
cg the two foci are at
cg x = 0, y = (+/-)sqrt (QC / QXX - QC / QYY),
cg or y = (+/-)sqrt (A^2 + B^2), (QC > 0),
cg y = 0, x = (+/-)sqrt (QC / QYY - QC / QXX),
cg or x = (+/-)sqrt (A^2 + B^2), (QC < 0),
cg the distance from the center to a focus is
cg sqrt (abs (QC / QXX - QC / QYY)), or
cg sqrt (A^2 + B^2), and
cg the length of the latus rectum (width at focus) is
cg 2 * sqrt (-QC * QYY) / QXX, (QC > 0), or
cg -2 * sqrt (-QC * QXX) / QYY, (QC < 0), or
cg 2 * B^2 / A.
cg The standard equation for the hyperbola or hyperbolic
cg cylinder is
cg (x / B)^2 - (y / A)^2 = 1, (QC < 0), or
cg (y / A)^2 - (x / B)^2 = 1, (QC > 0), for all z.
cg cylinder arrays Cylinders may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cg cylinder, parabolic
cg For the parabola or parabolic cylinder:
cg QY * y + QXX * x^2 = 0, for all z,
cg the center is the vertex at x = 0, z = 0,
cg the focus is at x = 0, y = -0.25 * QY / QXX,
cg the distance from the vertex to the focus is
cg P = 0.25 * abs (QY / QXX), and
cg the length of the latus rectum (width at focus) is
cg abs (QY / QXX) = 4 * P.
cg
cg The standard equation for the parabola or parabolic
cg cylinder is
cg y = -x^2 / (4 * P), QY > 0, or
cg y = x^2 / (4 * P), QY < 0.
cg cylinders A family of circular cylinders may be created with
cg command "cylinder", options "concentric", "move",
cg "rotate" or "scale" (with restrictions) or as
cg follows:
cg
cg p pinv (options)
cg
cg Create an invariant point, if needed.
cg
cg cyl CYL(1) (options)
cg
cg Create a base cylinder.
cg
cg op opr (options)
cg
cg Create a tensor operator, to reflect, rotate,
cg invert or scale, if needed.
cg
cg v vmove (options)
cg
cg Create a vector for use as a translation operator,
cg if needed.
cg
cg cp CYL(1) CYL(2)
cg
cg Copy cylinder CYL(1) to the first cylinder.
cg
cg Repeat the following block of commands as many times
cg as needed to create the rest of the cylinders.
cg See "shortcuts".
cg
cg mv cyl CYL(1) vmove
cg
cg Move the base cylinder by amount vmove, if needed.
cg
cg [invert,reflect,rotate,scale] cyl CYL(1) opr [pinv]
cg
cg Invert, reflect, rotate or scale the base cylinder
cg with tensor operator opr, if needed.
cg
cg cp cyl CYL(1) +
cg
cg Copy the base cylinder to the next cylinder.
cc cylindrical An option in command "coordinate", to use a 3-D
cc coordinate system with the radial, azimuthal and
cc axial coordinates (rcyl, theta, z).
cc Synonyms: [cylindrical, cyl].
cg cylindrical To create volume elements bounded by surfaces of a
cg cylindrical coordinate system, use command "brick".
cg To create zones partially or completely bounded by
cg concentric cylindrical surfaces, use command
cg "cylinder", options "concentric", "scale", and
cg command "zone".
cg
cg To create arrays of points on surfaces of a
cg cylindrical coordinate system, see command
cg "point PMESH brick BRNAME mesh block [volume]".
cg
cg To find the volume of revolution of a polygonal area
cg rotated around an axis, use command "volume".
cc CYLNAME The name of a circular cylinder. May have up to 24
cc characters, and may be ASCII, integer or floating
cc point. May not be the same as any other quadric
cc surface name QNAME. Also referred to as CYLNAME1,
cc CYLNAME2, ..., CYL(1), CYL(2), ...
cc No cylinder name may be "+", "-", "all", "h", "help",
cc "list" or "thru", begin with "!" or contain ";".
cc Specified with command "cylinder".
cc
cc Circular cylinders may appear in commands:
cc accelerate, axisym, copy, cylinder, delete,
cc distance, invert, move, operator, point, proximal,
cc quadric, reflect, rename, rotate, scale, side, track,
cc vector.
cc Also see commands: last, list, repack, search, sort.
cc C____ A synonym for c____ in a comment line.
cc c____ A synonym for c.
D-------------------------------------------------------------------------------
cc D In command "delimiter", a character to be used as a
cc field delimiter, which must be one of the following:
cc (blank) ( ) , : < > [ \ ] ^ _ ` { | }
cc D In command "solve", the vector of the constants on
cc the right-hand side of the three equations.
cc DANGLE In command "plane" with option "rotate",
cc the angular increment (counterclockwise, with the
cc axis pointed at the observer) around the axis vector
cc VAXIS, between the normal vectors of successive
cc planes.
cc May be integer, floating point or a variable.
cc Specified in the current angle units.
cc See "ANGLE", "angles".
cc data An optionin command "variable", to specify more than
cc one variable, with values specified in tabular form.
cc See "enddata".
cg data Each time a geometric or operational object is
cg specified or used, its name and some associated data
cg is displayed. For some objects, more data is
cg displayed when the object is specified or when it
cg is listed by itself. All data is labeled in a way
cg intended to be self-explanatory or to make it
cg possible to find a description in geom_base.
cg data See "data types", "output data".
cg data types Data entered into or displayed by GEOM can be any of
cg three types - character, integer or real:
cg
cg character - a delimited character string consisting
cg of any of the allowed ASCII keyboard
cg characters. See "character set".
cg All command names and command arguments
cg shown in lower case are of type
cg character.
cg
cg integer - a delimited character string specifying a
cg positive or negative whole number, in
cg binary, octal, decimal or hexadecimal
cg integer format. See "integer".
cg Any command argument shown in upper case
cg which allows a numerical value may be of
cg type integer.
cg
cg real - a delimited character string specifying a
cg positive or negative number, in decimal
cg or hexadecimal floating point format.
cg See "floating point".
cg Any command argument shown in upper case
cg which allows a non-integer numerical
cg value may be of type real.
cc DATAGRP In command "debug", a data group for which GEOM
cc internal parameters and variables will be displayed.
cc Also referred to as DATAGRP1, DATAGRP2, ...
cc Defined in file geom_internal. May be any of the
cc following: angles, alias, arithmetic, bin, brick,
cc cluster, coordinates, disk, i/o, line, marker, mesh,
cc operator, parameter, parse, pdf, plot, point
cc polygon, polyhedron, proximal, quadric, symbol,
cc synonym, temp, tetrahedron, triangle, variable,
cc vector, zone.
cc Synonyms: [alias, al, a], [angles, angle, ang],
cc [arithmetic, arith], [brick, br], [cluster, cl],
cc [coordinate, coord, cs, system, sys],
cc [disk, disc, dk], [environment, env, setup],
cc [help, h], [line, l, ln], [marker, mark, m],
cc [operator, oper, op], [parameter, param],
cc [point, pnt, pt, p], [polygon, polyg, pg],
cc [polyhedron, polyh, ph], [proximal, prox],
cc [quadric, quad, q], [symbol, sym, symb],
cc [synonym, syn], [tetrahedron, tetra, tet],
cc [triangle, tri], [variable, var, set, s],
cc [vector, vec, v], [zone, zn, z].
cg date Dates that may be displayed include the date the code
cg was made, and the date of the current run.
cg See command "when".
cg NOT CURRENTLY AVAILABLE ON THE OPEN YANA CLUSTER.
cg dbl See "dbl max", "dbl min".
cg dbl max In output from commands "root" and "roots", indicates
cg a root of order 2 of a polynomial equation, at a
cg maximum of the equation.
cg dbl min In output from commands "root" and "roots", indicates
cg a root of order 2 of a polynomial equation, at a
cg minimum of the equation.
cc debug Command to display the values of GEOM internal
cc parameters and variables defined in file store.h.
cc Most GEOM subroutines contain the command
cc "include 'store.h'". These parameters and variables
cc are also listed and defined in file geom_internal,
cc in the same directory as the GEOM subroutines.
cc
cc Forms include:
cc
ccin help debug
ccin define [debug]
cc
cc Display the command options.
cc
ccin debug VARINT1 [VARINT2 ...]
cc
cc Display the current values of the GEOM internal
cc variables VARINT1 [, VARINT2, ...], which are
cc defined in file store.h, in the appropriate format
cc for their data type. Do not use subscripts.
cc All values of arrays will be displayed.
cc
cc
ccin debug DATAGRP1 [DATAGRP2 ...]
cc
cc Display the current values of the GEOM internal
cc variables defined in file store.h, for data
cc group[s] DATAGRP1 [, DATAGRP2, ...], where DATAGRPn
cc may be any of the following:
cc angles, alias, arithmetic, big, bin, brick,
cc cluster, coordinates, disk, i/o, line, marker,
cc mesh, operator, parameter, parse, pdf, plot, point,
cc polygon, polyhedron, proximal, quadric, subscript,
cc symbol, synonym, temp, tetrahedron, triangle,
cc variable, vector, zone.
cc
cc Synonyms: [alias, al, a], [angles, angle, ang],
cc [arithmetic, arith], [brick, br], [cluster, cl],
cc [coordinate, coord, cs, system, sys],
cc [disk, disc, dk], [environment, env, setup],
cc [help, h], [line, l, ln], [marker, mark, m],
cc [operator, oper, op], [parameter, param],
cc [point, pnt, pt, p], [polygon, polyg, pg],
cc [polyhedron, polyh, ph], [proximal, prox],
cc [quadric, quad, q], [symbol, sym, symb],
cc [synonym, syn], [tetrahedron, tetra, tet],
cc [triangle, tri], [variable, var, set, s],
cc [vector, vec, v], [zone, zn, z].
cc dec An option in command "icalc", to set the input mode for
cc integers in command "icalc" to decimal.
cg decay See "decay constant", "decay time".
cg decay constant In an exponential probability bin, the decay constant
cg is SIGMA in the relative differential probability
cg function exp (-SIGMA * v), where v is the random
cg variable, which ranges from VRANL to VRANR,
cg as specified in command "bin". Note the minus
cg sign preceding SIGMA.
cg decay time To randomly sample decay times for an event with a
cg specified half-life T:
cg
cg bin BINAME 1 0 VRANR exp SIGMA
cg
cg Create a probability bin BINAME with an
cg exponentially decaying probability with decay
cg constant SIGMA = ln(2)/T, and VRANR = 100*T (which
cg has negligible probability).
cg
cg pdf PDFNAME = BINAME
cg
cg Create a probability distribution function (pdf)
cg PDFNAME, consisting only of the probability bin
cg BINAME.
cg
cg sample PDFNAME [NSAMP|1]
cg
cg Sample from pdf PDFNAME NSAMP times.
cg decimal The decimal form of an integer M, specified in the
cg current integer mode (see command "icalc"),
cg may be displayed with command:
cg
cg icalc M
cg
cg Display M in decimal, hexadecimal, octal and
cg (optionally) in binary mode.
cg decrement See "decrement names".
cg decrement names See "increment names", command "increment".
cg decryption Decryption is the process of making encrypted data or
cg text readable, using special knowlege intended to
cg be available only to certain recipients.
cg See command "big".
cc def A synonym for define.
cg default See "default arguments", "default values".
cc default arguments
cc In commands, optional arguments are shown as follows:
cc
cc [argument]
cc
cc The literal argument is optional, and there is no
cc default value, unless specified in the description
cc of the command.
cc
cc [ARGUMENT|VALUE]
cc
cc The value of ARGUMENT is optional. If omitted, the
cc argument defaults to VALUE.
cc
cc [OBJNAME,all]
cc
cc The object name OBJNAME or the literal "all" must
cc be specified. No default is allowed.
cc
cc [arg1,arg2,arg3|arg1]
cc
cc The literal arguments arg1, arg2 or arg3 are
cc optional. If omitted, the argument defaults to
cc arg1.
cc
cc arg1 [arg2|<]
cc
cc If arg2 is not specified, it defaults to arg1.
cc
cc Other defaults may be defined in the descriptions of
cc the commands.
cg default values A number of objects are assigned default values at the
cg beginning of each GEOM run.
cg
cg The input medium is the user's terminal
cg (do NOT use "<" or ">" on the GEOM execution line).
cg Change with command "input" or "return".
cg See "redirect input".
cg The output medium (in addition to the standard
cg output, normally to the user's terminal) is
cg file geom_hsp. Change with command "output".
cg See "redirect output".
cg The field delimiter is a blank character.
cg Change with command "delimiter".
cg The numerical tolerance limit TOL = 10^(-11).
cg Change with command "tol".
cg The coordinate system is Cartesian (x, y, z).
cg Change with command "coordinate".
cg The unit for input and display of angles is degrees.
cg Change with command "angles".
cg The mode for integer input in command "icalc" is
cg decimal. Change with command "icalc".
cg The mode for integer display in command "icalc" is
cg octal, decimal and hexadecimal.
cg Turn an added binary display on and off with
cg commands "icalc binary" and "icalc nobin".
cg
cg symbol pi = 3.141592653589793
cg symbol deg/rad = 57.29577951308232
cg symbol rad/deg = 0.01745329251994330
cg symbol ebase = 2.718281828459045
cg symbol rgold = 1.618033988749894
cg symbol euler = 0.577215664901533861
cg
cg Change or reinstate any of the five preceding
cg symbols with command "symbol".
cg define See "create", commands "define", "alias", "marker".
cc define Command to display an entry in file geom_base, which is
cc assumed to be in one of the locations:
cc geom_base (local)
cc ~edwards/work/geom/doc/geom_base (YANA Cluster)
cc A list of all such entries is in file geom_define.
cc
cc Note: no replacement of symbols will be done
cc in this command.
cc
cc See "character set" for the ASCII characters which
cc may be used in command "define".
cc
cc Forms include:
cc
ccin help define
ccin define [help]
cc
cc Display the command options.
cc
ccin define 'ENTRY'
cc
cc Display entry ENTRY of geom_base. Case is ignored.
cc The first 19 characters of ENTRY must match columns
cc 7-25 of the first line of entries in this file,
cc ignoring any trailing blanks.
cc If ENTRY is bracketed by single quotes, repeat any
cc internal single quote. If ENTRY is bracketed by
cc double quotes, repeat any internal double quote.
cc
cc define 'X'
cc
cc Display the first line of all entries in geom.base
cc that begin with the letter "X". Case is ignored.
cc
cc Synonyms: [", ' (in pairs)], [define, def],
cc [help, h].
cc
cc See "help", "definition", "geom_define".
cg definition You can store and display your own comment, description
cg or definition of any object or word you desire,
cg OBJNAME, with command "alias", as follows:
cg
cg alias OBJNAME = "# DEFINITION"
cg
cg Assign alias OBJNAME to the comment line
cg "# DEFINITION", where DEFINITION is any character
cg string that will fit on the input line, describing
cg the object named OBJNAME. OBJNAME should not be
cg the same as the first word of any command that you
cg might want to use.
cg
cg OBJNAME
cg
cg Display the character string for which OBJNAME is
cg the alias.
cg
cg Example:
cg
cg You type:
cg alias vnorm = "# The vector normal to plane plx."
cg
cg Any time later, you type:
cg vnorm
cg The code then displays:
cg # The vector normal to plane plx.
cg
cg You can store and display your own comment,
cg description or definition, to go with any single
cg character AMNAME you desire, with command "marker",
cg as follows:
cg
cg marker AMNAME = "TEXT"
cg
cg Assign to the 1-character marker AMNAME the text
cg "TEXT", where TEXT is any character string that
cg will fit on the input line.
cg
cg marker AMNAME
cg
cg Display the TEXT assigned to marker AMNAME.
cg
cg Example:
cg
cg You type:
cg marker a = "Note: coordinates are in millimeters."
cg
cg Any time later, you type:
cg marker a
cg The code then displays:
cg mark a Note: coordinates are in millimeters.
cc deg A synonym for degrees in command "angles".
cn deg.mac A macro file for converting from degrees, minutes and
cn seconds to decimal degrees. Type "in deg.mac ?" for
cn info. In ~/work/geom/test . See "dms.mac".
cc deg/rad An option in command "symbol", argument SYMBNAME,
cc to create symbol deg/rad with value
cc 57.29577951308232087679815481410517033240547246658
cc Store as a big integer with command "input big.mac",
cc with file big.mac in the same directory as GEOM.
cg deg/rad Symbol, degrees per radian. Generated as a
cg symbol at the beginning of the run.
cg deg/rad = 180.0 / pi.
cg deg/rad = 57.29577951308232 degrees per radian.
cg rad/deg = 0.01745329251994330 radians per degree.
cg pi = 3.141592653589793... = acos (-1).
cg
cg symbol SYMBNAME deg/rad
cg
cg Set symbol SYMBNAME to
cg 180 / pi = 57.29577951308232.
cg
cg symbol SYMBNAME rad/deg
cg
cg Set symbol SYMBNAME to
cg pi / 180 = 0.01745329251994330.
cg degenerate A quadric surface may be degenerate:
cg
cg F(x,y,z) = QC +
cg QX * x + QY * y + QZ * z +
cg QXY * x * y + QYZ * y * z + QZX * z * x +
cg QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0
cg
cg Degenerate quadric surfaces (in standard form,
cg all coefficients positive):
cg
cg Imaginary intersecting planes:
cg (a straight line) x^2 + QYY*y^2 = 0
cg Imaginary elliptic cone:
cg (a point) x^2 + QYY*y^2 + QZZ*z^2 = 0
cg Imaginary circular cone:
cg (a point) x^2 + y^2 + QZZ*z^2 = 0
cg
cg See "quadric surfaces".
cc degree A synonym for degrees in command "angles".
cc DEGREES In command "angles", the integer number of degrees of
cc an angle specified in degree, minutes and second
cc units.
cc May be integer, floating point or a variable.
cc The absolute value of DEGREES + MINUTES / 60
cc + SECONDS / 3600 must not exceed the largest machine
cc integer.
cc degrees An option in command "angles", to specify that angles
cc are to be input and displayed in degrees.
cg degrees A unit of measurement of angles. A full circle has
cg 360 degrees or 2 * pi radians.
cg One radian = 180/pi (~57.29577951308232) degrees.
cg One degree = pi/180 (~0.01745329251994330) radians.
cc del A synonym for delete.
cc delete An option in command "plot", to delete points from the
cc list of plot points. This does not delete the points
cc from the list of geometric points.
cg delete See "delete objects", command "delete".
cc delete Command to delete aliases, bricks, probability bins,
cc big integers, clusters, annular disks, lines,
cc markers, tensor operators, planes, points,
cc regular polygons, quadric surfaces (including general
cc and axisymmetric, circular cones, circular cylinders,
cc ellipsoids, hyperbolic paraboloids and spheres),
cc regular polyhedrons, probability distribution
cc function (pdfs), tetrahedrons, triangles, vectors,
cc variables and zones.
cc
cc Command "delete" relates to objects: alias, axisym,
cc big, bin, brick, cluster, cone, cylinder, disk,
cc ellipsoid, hyperb, line, marker, operator, pdf,
cc plane, point, polygon, polyhedron, quadric, sphere,
cc symbol, tetrahedron, triangle, variable, vector,
cc zone.
cc
cc Option "all" must be verified, if input is from the
cc user's terminal (do NOT use "<" on the GEOM execution
cc line).
cc
cc Fix errors with command "undo", "redo" or "indo",
cc or by cutting and pasting from the display.
cc
cc Note: no replacement of symbols will be done
cc in the commands "delete symbol ...", "delete alias".
cc
cc Markers with dependencies (plot title, plot axis
cc labels or plot point titles) will not be deleted.
cc You must respecify the dependent object first.
cc
cc Points with dependencies (line, triangle, regular
cc polygon, annular disk, regular polyhedron or a
cc tetrahedron) will not be deleted. You must delete
cc or respecify the dependent object first. A warning
cc will be displayed if a deleted point is in a cluster,
cc unless it is the cluster that is being deleted.
cc
cc A warning will be displayed if a deleted bin is in a
cc probability distribution function (pdf), unless it is
cc the pdf that is being deleted.
cc
cc Do not use "+" or "-" for object names in these
cc commands.
cc
cc Forms include:
cc
ccin help delete
ccin delete [help]
cc
cc Display the command options.
cc
ccin delete OBJTYPE all
cc
cc Delete all objects of type OBJTYPE (alias, axisym,
cc big, bin, brick, cluster, cone, cylinder, disk,
cc ellipsoid, hyperb, line, marker, operator, pdf,
cc plane, point, polygon, polyhedron, quadric, sphere,
cc symbol, tetrahedron, triangle, variable, vector,
cc zone).
cc Requires verification by the user, if input is from
cc the user's terminal (do NOT use "<" on the GEOM
cc execution line).
cc
ccin delete OBJTYPE OBJNAME all
cc
cc Delete all objects of type OBJTYPE (see above) with
cc the names OBJNAME(NSUB1,NSUB2,...), where NSUBi is
cc any subscript or null.
cc
ccin delete OBJTYPE OBJNAME
cc
cc Delete the object of type OBJTYPE (see above) with
cc the name OBJNAME.
cc
ccin delete OBJTYPE OBJNAME1 thru OBJNAME2
cc
cc Delete any objects of type OBJTYPE (see above) with
cc names from OBJNAME1 through OBJNAME2. WARNING:
cc the name comparison is with left-adjusted ASCII
cc names, except that subscripts are compared as
cc integers.
cc
cc NOTE! No object may have the name "thru".
cc
ccin delete cluster CLNAME
cc
cc Delete cluster CLNAME. The points in cluster
cc CLNAME are not deleted.
cc
ccin delete point cluster CLNAME
cc
cc Delete the points in cluster CLNAME. Delete
cc cluster CLNAME if all of its points are deleted.
cc
ccin delete bin pdf PDFNAME
cc
cc Delete the probability bins in pdf PDFNAME.
cc Delete pdf PDFNAME if all of its bins are deleted.
cc
cc Synonyms: [alias, al, a,], [brick, br],
cc [cluster, cl], [copy, cp, dup, duplicate],
cc [cylinder, cyl], [delete, del, remove, rm],
cc [disk, disc, dk],
cc [ellipsoid, ell, el, ellipse], [help, h],
cc [hyperb, saddle], [line, l, ln], [marker, mark, m],
cc [operator, oper, op], [plane, pl],
cc [point, pnt, pt, p], [polygon, polyg, pg],
cc [polyhedron, polyh, ph], [quadric, quad, q],
cc [sphere, sph], [symbol, sym, symb],
cc [tetrahedron, tetra, tet], [triangle, tri],
cc [variable, var, set, s], [vector, vect, v],
cc [zone, zn, z].
cc delete An option in command "mesh", to delete one or more
cc layers of the mesh.
cc Synonyms: [delete, del, remove, rm].
cg delete objects See command "delete".
cc delim A synonym for delimiter.
cc delimit A synonym for delimiter.
cg delimited A delimited argument or character string is delimited
cg on the left by the beginning of the line or the
cg field delimiter, and on the right by the field
cg delimiter or the end of the line (up to 80
cg characters).
cg delimiter The field delimiter (FD) is the single character used
cg to delimit fields (arguments) in the input lines.
cg
cg The FD is initially a blank character, but may be
cg changed with command "delimiter", to one of the
cg following characters:
cg , : < > [ \ ] ^ _ ` { | }
cg Do not use a character as a delimiter in a command
cg that requires the same character as input.
cg
cg All commands shown in this file, and in the help
cg messages displayed by GEOM, are shown with a blank
cg character as the FD. If the FD is not a blank
cg character, replace all blank characters or sequential
cg strings of blank characters shown in the examples
cg with the actual FD (except in the quoted strings of
cg commands "alias", "marker" and "define").
cg
cg If the FD is a blank character, any number of
cg adjacent blank characters may be used instead of a
cg single blank character, and blank characters used
cg before the first non-blank character and after the
cg last non-blank character will be ignored.
cg
cg If the FD is a blank character, do not include any
cg blank characters in any delimited argument or
cg character string, except in the quoted strings of
cg commands "alias", 'define" and "marker", or in the
cg variable tag specified in command "variable", option
cg "tag".
cg
cg If the FD is not a blank character, do not use it to
cg begin an input line, or an extra null field will be
cg produced. Trailing null fields at the end of an
cg input line will be ignored, but any other null field
cg is an error.
cg
cg Sign prefixes on variable names do not use a field
cg delimiter. See "sign".
cc delimiter Command to display or specify the field delimiter used
cc to delimit input line arguments. The field delimiter
cc must be a blank character or one of the following
cc characters:
cc , : < > [ \ ] ^ _ ` { | }
cc
cc Forms include:
cc
ccin help delimiter
ccin delimiter help
cc
cc Display the command options, when the field
cc delimiter is a blank character.
cc
ccin helpCdelimiter
ccin delimiterChelp
cc
cc Display the command options, when the field
cc delimiter is any allowed character "C".
cc
ccin delimiter
cc
cc Change the field delimiter to a blank character,
cc when it is initially any character.
cc
ccin delimiter D
cc
cc Change the field delimiter to any allowed character
cc "D", when it is initially a blank character.
cc
ccin delimiterCD
cc
cc Change the field delimiter to any allowed character
cc "D", when it is initially the character "C".
cc
cc Synonyms: [delimiter, delim, delimit], [help, h].
cg dependent Some geometric objects are dependent on points:
cg lines, triangles, regular polygons, annular disks,
cg regular polyhedrons, and tetrahedrons. A change in
cg the coordinates of a point will change the geometry
cg of the dependent object. A change in the name of a
cg point will have no effect on the dependent object,
cg except to change the name of the point in its
cg specification. A point with dependent objects may
cg not be deleted.
cg derivatives When using command "roots" to find the real and/or
cg complex roots of a polynomial equation in z:
cg P(z) = a0 + a1*z + a2*z^2 + a3*z^3 + a4*z^4 = 0,
cg the real values of z and P(z) are displayed for which
cg each of the derivatives of P(z) are zero, up to the
cg highest derivative which is still a function of z.
cg These include the maximum and minimum points, where
cg the first derivative is zero:
cg P'(z) = a1 + 2*a2*z + 3*a3*z^2 + 4*a4*z^3 = 0,
cg the inflection points, where the second derivative
cg is zero:
cg P''(z) = 2*a2 + 6*a3*z + 12*a4*z^2 = 0,
cg and the point where the third derivative is zero:
cg P'''(z) = 6*a3 + 24*a4*z = 0.
cg
cg To search for real roots, extrema and inflection
cg points of a polynomial equation using Newtonian
cg iteration, use command "root".
cg
cg See "spatial derivatives".
cg destroy To destroy an object, use command "delete".
cg det An invariant of a quadric surface, for translations and
cg rotations. See "invariants of quadric".
cg determinant The determinant of a tensor operator is displayed
cg whenever the tensor operator is displayed.
cg The determinant for a rotation operator is 1.
cg The determinant for an inversion operator is -1.
cg The determinant for a reflection operator is -1.
cg The determinant for a scaling operator is the
cg first, second or third power of the scale factor,
cg for linear, radial or 3-D (options "scale" or
cg uniform") scaling.
cg determinant To find the value of a 3 by 3 determinant:
cg
cg variable VARNAME triple VNAME1 VNAME2 VNAME3
cg
cg Create variable VARNAME with the value of the 3 by
cg 3 determinant for which the three row or column
cg vectors are the vectors VNAME1, VNAME2 and VNAME3.
cc DEV In command "bin", the standard deviation.
cg deviation See "expected value".
cg diatonic See "diatonic scale".
cg diatonic scale In music, a diatonic scale in a major key consists
cg of eight tones, with intervals from the initial (key)
cg tone of two whole tones, a semitone, three whole
cg tones, and a semitone, ending on the octave of the
cg first tone. For example, on a piano, the diatonic
cg scale for C major is entirely on the white keys,
cg consisting of C-D-E-F-G-A-B-C. The diatonic scale
cg for a minor key, e.g. A minor, A-B-C-D-E-F-G-A, has
cg semitones for the second and fifth intervals.
cg
cg See "equally-tempered".
cn dice.mac A macro file for rolling two dice, to demonstrate the
cn use of bins and pdfs. In ~/work/geom/test .
cg digits See "significant figures".
cg dihedral See "angle, dihedral".
cg direction Reverse the direction of a vector V1 with command
cg "vector V1 rel -1"
cg direction See "direction cosine", "direction vector".
cg direction cosine A direction cosine is a component of a unit direction
cg vector in the direction of one of the axes of the
cg coordinate system.
cg direction vector The direction vector of a moving object is the vector
cg in the direction of motion. A unit vector parallel
cg to the direction vector has components in the
cg directions of the axes of the coordinate system.
cg These components are called direction cosines.
cg In linear motion, the direction cosines are constant
cs in a Cartesian (xyz) coordinate system, but change
cg continuously in a cylindrical or spherical coordinate
cg system. See "coordinate conversion",
cg "vector conversion".
cg directories See "geom_summ", "geom_files".
cg disallowed See "disallowed names".
cg disallowed names Some names are disallowed for all or some object names,
cg because they make interpretation of a command
cg ambiguous.
cg No name may be "+", "-", "all", "h", "help",
cg "list" or "thru", begin with "!" or contain ";".
cg A point name must not be "cluster" or a synonym.
cg A cluster name must not be "point" or a synonym.
cg A quadric surface name must not be "types".
cc disc A synonym for disk.
cg discrete See "discrete event", "discrete object",
cg "discrete value".
cg discrete event A type of probability bin, which assigns a relative
cg total probability to a discrete event or object.
cg The discrete object may be any of the objects used
cg in GEOM, including a probability distribution
cg function (pdf).
cg See "discrete value", "uniform", "linear",
cg "power-law", "exponential".
cg See commands "bin", "pdf", "sample".
cg discrete object A type of probability bin, which assigns a relative
cg total probability to a discrete event or object.
cg The discrete object may be any of the objects used
cg in GEOM, including a probability distribution
cg function (pdf).
cg See "discrete value", "uniform", "linear",
cg "power-law", "exponential".
cg See commands "bin", "pdf", "sample".
cg discrete value A type of probability bin, which assigns a relative
cg total probability to a discrete value of a random
cg variable.
cg See "discrete event", "uniform", "linear",
cg "power-law", "exponential".
cg See commands "bin", "pdf", "sample".
cg disk An annular disk is a surface in 3-D space, lying in a
cg plane, and bounded by two circles having a common
cg center in the same plane. For a simple disk, the
cg radius of the inner circle is zero. The disk is
cg dependent on the point used to specify the center of
cg the circles, which may be changed. An annular disk
cg may be used to create a plane, with command "plane".
cg The maximum number of disks is now 1000.
cg
cg The following commands relate to annular
cg disks:
cg copy, debug, delete, disk, help, last, list, plane,
cg point, rename, repack, search, sort, symbol, synonym,
cg tables.
cc disk An option in command "debug", to display GEOM internal
cc parameters and variables for annular disks:
cc ndiskm, ndisks, adisk, radkin, radkout, acendk,
cc xnormdk, ynormdk, znormdk, adisks, ladisks.
cc Synonyms: [disk, disc, dk].
cc disk Command to display or create circular or annular
cc disks. A disk may be replaced. The display for a
cc disk includes the central point, the normal vector,
cc the inner and outer radii, the inner and outer
cc circumferences, and the areas of the central hole and
cc the annulus.
cc See command "circle" to find the circle through
cc three specified points.
cc See "do loop use".
cc
cc Command "disk" relates to objects: disk, point,
cc variable, vector.
cc
cc Forms include:
cc
ccin help disk
ccin disk [help]
cc
cc Display the command options.
cc
ccin disk [all,list]
cc
cc Display all annular disks.
cc
ccin disk list DKNAME1 DKNAME2 DKNAME3 ...
cc
cc Display annular disks DKNAME1, DKNAME2, DKNAME3,
cc ..., with or without subscripts.
cc
ccin disk DKNAME
cc
cc Display annular disk DKNAME.
cc
ccin disk DKNAME fit PCEN VNORM RADKIN RADKOUT
cc
cc Create annular disk DKNAME, centered at point PCEN,
cc with normal vector VNORM, with inner radius RADKIN,
cc outer radius RADKOUT. Any later change in the
cc coordinates or name of point PCEN will change the
cc definition of annular disk DKNAME. Use "+" or "-"
cc instead of DKNAME to form the name by incrementing
cc or decrementing the base name for annular disks.
cc See command "last", "increment names".
cc
cc Synonyms: [disk, disc, dk], [help, h].
cc disk An option in commands "copy", "delete", "last", "list",
cc "rename", "repack" and "sort", to perform the
cc specified operation on one or more annular disks.
cc Synonyms: [disk, disc, dk].
cg disk arrays Disks may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cg displace See "move".
cg displacement A displacement is the difference between the final and
cg initial position of an object.
cc display A synonym for list in command "list".
cg display The code displays data on the user's terminal
cg screen and in the output file (geom_hsp, or the
cg file(s) specified by the user with command "output"),
cg or specified on the GEOM execution line.
cg See "display objects", "redirect output", command
cg "list".
cg display See "display objects", command "list".
cg display objects The commands for displaying objects have the general
cg forms:
cg
cg OBJTYPE [all,list]
cg
cg Display all objects of type OBJTYPE.
cg Use the longest display.
cg
cg OBJTYPE OBJNAME
cg
cg Display object type OBJTYPE with name OBJNAME.
cg Use the longest display.
cg
cg OBJTYPE list OBJNAME1 OBJNAME2 OBJNAME3 ...
cg
cg Display objects of type OBJTYPE with names OBJNAME,
cg OBJNAME2, OBJNAME3, ..., with or without
cg subscripts. Use the shortest display, unless there
cg is only one such object.
cg
cg list [OBJTYPE,all]
cg
cg Display only the names of all objects of [type
cg OBJTYPE, or all types].
cg Synonyms: [list, display, print].
cg
cg last [OBJTYPE,all]
cg
cg Display only the names of the last object specified
cg of [type OBJTYPE, or all types].
cg
cg sort [OBJTYPE,all] [+,-,?|+]
cg
cg Display only the names of all objects of [type
cg OBJTYPE, or all types], after sorting the objects
cg into [increasing, decreasing, random] ASCII order,
cg with increasing order the default option.
cg
cg search OBJNAME1 OBJNAME2 OBJNAME3 ...
cg
cg Display all objects with object names the same as
cg OBJNAME1, OBJNAME2, OBJNAME3, ... or if any of the
cg latter are a single character, with object names
cg
cg Display all marker texts, symbol and alias
cg replacements the same as OBJNAME1, OBJNAME2,
cg OBJNAME3, ... or if any of the latter are a single
cg character, beginning with that character.
cg
cg Display all variables with numerical values equal
cg to OBJNAME1, OBJNAME2, OBJNAME3, ...
cg
cg search all
cg
cg Display all objects with object names.
cg
cg See "OBJTYPE", "OBJNAME", "create objects".
cg dist A synonym for distance in command "distance".
cg dist See "dist to collision".
cg distal The opposite of proximal. The most distant.
cg See "distal point".
cg distal point For an external point P1, the distal point P2 (farthest
cg from point P1) on a quadric surface F(x,y,z) = 0,
cg with normal vector N = grad F = (NX, NY, NX),
cg satisfies the same equations as a proximal point:
cg
cg (X2 - X1) / NX =
cg (Y2 - Y1) / NY =
cg (Z2 - Z1) / NZ =
cg (P2 - P1) dot N / N^2 = distance / |N|.
cg
cg In general, this leads to a sixth order equation,
cg requiring iterative numerical methods of solution.
cg See commands "distance", "proximal", "side".
cg distance The straight-line distance between two points in 3-D
cg space, or the perpendicular distance from a point to
cg a line, plane or surface, or the perpendicular
cg distance between two parallel lines or planes.
cg See commands "accelerate", "distance", "proximal",
cg "side", "track".
cg
cg To find the distance between two points, use any of
cg the methods:
cg
cg distance point PNAME1 point PNAME2
cg
cg Display the distance between points PNAME1 and
cg PNAME2.
cg
cg line ALNAME = PNAME1 PNAME2
cg
cg Create line ALNAME1 from point PNAME1 to point
cg PNAME2, and display its direction and length.
cg
cg vector VNAME = PNAME1 PNAME2
cg
cg Create vector VNAME, directed from point PNAME1
cg toward point PNAME2, with length equal to the
cg distance from PNAME1 to PNAME2, and bound at
cg PNAME1, and display its direction and length.
cg
cg To find the distance between the two parallel planes
cg of a quadric surface of that form:
cg
cg quadric QNAME
cg
cg Display the coefficients of quadric surface QNAME
cg (before and after a principal axis transformation),
cg the intercepts on the axis, and the distance
cg between the parallel planes.
cg
cg To find the minimum distance between a point and a
cg quadric surface, use command "distance", "proximal"
cg or "side".
cg
cg To find the distances from a point to the six
cg surfaces bounding a brick, and to find if the point
cg is in the brick, use command "distance".
cg Also see command "where".
cg
cg To find the distances from a point to the four planes
cg bounding a tetrahedron, and to find if the point is
cg in the tetrahedron, use command "distance".
cg Also see command "where".
cg
cg To find the distances from a point to the quadric
cg surfaces bounding a zone, and to see if the point is
cg in the zone, use command "distance".
cg Also see command "where".
cg
cg To find the approximate distance or the intersection
cg between a line and a quadric surface, use command
cg "track".
cg
cg To find the distance between two circles in a major
cg plane, use command "intcirc".
cg
cg To find the distance and proximal points and/or
cg intersection of any combination of planes, spheres
cg and circular cylinders, use command "distance".
cg
cg To find the distance from a plane to any quadric
cg surface, use command "distance".
cg
cg To find the distance between a sphere and a quadric
cg surface, first find the distance from the point at
cg the center of the sphere to the quadric surface,
cg with command "distance", "proximal" or "side", then
cg subtract the radius of the sphere. A negative result
cg indicates overlap.
cg
cg To find the distance between any two quadric
cg surfaces, use command "distance".
cg
cg To find the distance between a point and a toroid
cg generated by a quadric curve, see "toroid".
cc distance Command to find the distance between two geometric
cc objects, which may be points, lines, triangles or
cc planes, a point or plane and a quadric surface, or
cc a point and a brick, tetrahedron or zone, any
cc combination of spheres and circular cylinders, or
cc any two quadric surfaces.
cc When possible, find any symmetries, points of
cc intersection or tangency or curves of intersection.
cc In the case of clusters of points, also find the
cc points with the minimum and maximum distances.
cc In the case of two quadric surfaces, specify planes
cc before spheres before other quadric surfaces.
cc Also, see "toroid".
cc
cc Command "distance" relates to objects: axisym,
cc brick, cluster, cone, cylinder, ellipsoid, hyperb,
cc line, plane, point, quadric, sphere, symbol,
cc tetrahedron, triangle, zone.
cc
cc The minimum distance found may be stored in variable
cc VARNAME with command:
cc variable VARNAME distance
cc
cc The proximal point found on the second object may be
cc stored in point PNAME with command
cc "point PNAME proximal".
cc
cc The vector between the proximal points may be stored
cc in vector VNAME with command
cc "vector VNAME proximal".
cc
cc Also see commands "accelerate", "intcirc",
cc "proximal", "side", "track", "variable".
cc
cc Forms include:
cc
ccin help distance
ccin distance [help]
cc
cc Display the command options.
cc
ccin distance point PNAME1 point PNAME2
cc
cc Find the distance from point PNAME1 to point
cc PNAME2. Another way is to create a line from point
cc PNAME1 to point PNAME2.
cc
ccin distance point PNAME cluster CLNAME
cc
cc Find the distances from point PNAME1 to the points
cc in cluster CLNAME.
cc
ccin distance cluster CLNAME1 cluster CLNAME2
cc
cc Find the distances from the points in cluster
cc CLNAME1 to the points in cluster CLNAME2 (which
cc may be CLNAME1).
cc
ccin distance point PNAME line ALNAME
cc
cc Find the distance from point PNAME to line ALNAME,
cc and the nearest point on the line.
cc
ccin distance cluster CLNAME line ALNAME
cc
cc Find the distances from the points in cluster
cc CLNAME to line ALNAME, and the nearest points on
cc the line, for each point.
cc
ccin distance point PNAME triangle TRNAME
cc
cc Find the distance from point PNAME to triangle
cc TRNAME, and the nearest point on the triangle.
cc
ccin distance cluster CLNAME triangle TRNAME
cc
cc Find the distances from the points in cluster PNAME
cc to triangle TRNAME, and the nearest point on the
cc triangle for each point.
cc
ccin distance point PNAME QTYPE QNAME
cc
cc Find the distance from point PNAME to the quadric
cc surface of type QTYPE (plane, sphere, cylinder,
cc cone, hyperb, ellipsoid, axisym, quadric) with name
cc QNAME, and the nearest point on the quadric
cc surface. Check with commands "proximal", "side".
cc See "toroid" for a method of finding the distance
cc from a point to a toroid generated by a quadric
cc curve.
cc
ccin distance cluster CLNAME QTYPE QNAME
cc
cc Find the distances from the points in cluster
cc CLNAME to the quadric surface of type QTYPE (plane,
cc sphere, cylinder, cone, hyperb, ellipsoid, axisym,
cc quadric) with name QNAME, and the nearest point on
cc the quadric surface, if possible.
cc See the preceding command form.
cc
ccin distance point PNAME brick BRNAME
cc
cc Find the distances from point PNAME to each of the
cc six surfaces bounding brick TETNAME, and find if
cc the point is inside the brick. Also see command
cc "where".
cc
ccin distance point PNAME tetrahedron TETNAME
cc
cc Find the distances from point PNAME to each of the
cc four planes bounding tetrahedron TETNAME, and find
cc if the point is inside the tetrahedron. Also see
cc command "where".
cc
ccin distance point PNAME zone ZNAME
cc
cc Find the distances from point PNAME to each of the
cc quadric surfaces bounding zone ZNAME, and find if
cc the point is inside the zone. See the preceding
cc command forms. Also see command "where".
cc
ccin distance line ALNAME1 line ALNAME2
cc
cc Find the distance from line ALNAME1 to line
cc ALNAME2, and the nearest points on each line.
cc
ccin distance line ALNAME triangle TRNAME
cc
cc Find the intersection of line ALNAME and triangle
cc TRNAME or find the distance, if they are parallel.
cc
ccin distance line ALNAME plane PLNAME
cc
cc Find the intersection of line ALNAME and plane
cc PLNAME or find the distance, if they are parallel.
cc
ccin distance triangle TRNAME1 triangle TRNAME2
cc
cc Find the line of intersection of the two triangles
cc TRNAME1 and TRNAME2 or find the distance, if they
cc are parallel.
cc
ccin distance triangle TRNAME plane PLNAME
cc
cc Find the line of intersection of triangle TRNAME
cc and plane PLNAME or find the distance, if they are
cc parallel.
cc
ccin distance plane PLNAME1 plane PLNAME2
cc
cc Find the distance and/or intersection of the two
cc planes PLNAME1 and PLNAME2. For more information,
cc repeat with the second "plane" replaced by
cc "quadric".
cc
ccin distance plane PLNAME sphere SPHNAME
cc
cc Find the distance and/or intersection of plane
cc PLNAME and sphere SPHNAME. See "separation".
cc
ccin distance plane PLNAME cylinder CYLNAME
cc
cc Find the distance and/or intersection of plane
cc PLNAME and circular cylinder CYLNAME. See
cc "separation". For more information, repeat with
cc "cylinder" replaced by "quadric".
cc
ccin distance plane PLNAME QTYPE QNAME
cc
cc Find the distance and/or intersection of plane
cc PLNAME and quadric type QTYPE (axisym, cone,
cc cylinder, ellipsoid, hyperb, plane, quadric or
cc sphere) with name QNAME.
cc See the preceding three commands.
cc Also see "quadric", "separation", "projection".
cc
ccin distance sphere SPHNAME1 sphere SPHNAME2
cc
cc Find the distance and/or intersection of the two
cc spheres SPHNAME1 and SPHNAME2. See "separation".
cc If the spheres are concentric, there are an
cc infinite number of pairs of proximal points.
cc
ccin distance cylinder CYLNAME sphere SPHNAME
cc
cc Find the distance and/or intersection of sphere
cc SPHNAME and circular cylinder CYLNAME. See
cc "separation". If the sphere is on the axis of the
cc cylinder, there are an infinite number of proximal
cc points.
cc
ccin distance cylinder CYLNAME1 cylinder CYLNAME2
cc
cc Find the distance and/or intersection of the two
cc circular cylinders CYLNAME1 and CYLNAME2. See
cc "separation". If the cylinders are concentric,
cc there are an infinite number of pairs of proximal
cc points.
cc
ccin distance quadric QNAME1 quadric QNAME2
cc
cc Find the distance and proximal points, or find a
cc randomly sampled point on the intersection curve of
cc the two quadric surfaces QNAME1 and QNAME2. May
cc fail if the surfaces are almost flat at their
cc proximal points, intersect at very small angles or
cc are tangent.
cc
cc Note: the two surfaces QNAME3 and QNAME4 have the
cc same intersection curve as QNAME1 and QNAME2:
cc quadric QNAME3 sum QNAME1 QNAME2 N2 -N1
cc quadric QNAME4 sum QNAME1 QNAME2 N2 N1
cc and are orthogonal at point P, if N1 and N2 are the
cc magnitudes of the normal vectors of QNAME1 and
cc QNAME2 at point P. See command "arc".
cc
cc Note: either surface QNAME1 or QNAME2 may be
cc replaced by surface QNAME3 above, which will
cc have a zero value of one of the invariants
cc "trace", "dsum" or "det", if N1 and N2 are the
cc values of that invariant for QNAME1 and QNAME2.
cc
cc Synonyms: [brick, br], [cluster, cl],
cc [cylinder, cyl],
cc [distance, dist, int, inter, intersect],
cc [ellipsoid, el, ell, ellipse], [help, h],
cc [hyperb, saddle], [line, l, ln], [plane, pl],
cc [point, p, pnt, pt], [proximal, prox],
cc [quadric, q, quad], [sphere, sph],
cc [tetrahedron, tet, tetra], [triangle, tri],
cc [zone, z, zn].
cc distance An option in command "variable", to use the value of
cc the last distance found with commands "distance",
cc "proximal", "side", "track" or "walk".
cc In the case of command "distance", the distance
cc between any two quadric surfaces, including planes,
cc is the distance to an external tangency, even if the
cc surfaces intersect.
cg distance to collision
cg See "mean free path".
cg distribution See "cosine-power", "exponential", "isotropic",
cg "linear", "Maxwellian", "normal", "Planck spectrum",
cg "power-law", "uniform", "Wien spectrum".
cg See commands "bin", "pdf", "point", "sample",
cg "variable", "vector".
cg divide To divide real or integer numbers, see commands
cg "variable", "icalc", "big".
cg division The division or slash character, "/".
cg divisor See "common divisor", "gcd".
cc dk A synonym for disk.
cc DKNAME The name of an annular disk. May have up to 24
cc characters, and may be ASCII, integer or floating
cc point.
cc No disk name may be "+", "-", "all", "h", "help",
cc "list", "point" or "thru", begin with "!" or contain
cc ";".
cc Also referred to as DKNAME1, DKNAME2, DKNAME3, ...
cc Specified with command "disk".
cc
cc Annular disks may appear in commands:
cc copy, disk, delete, plane, point, rename.
cc Also see commands: last, list, repack, search, sort.
cc DMAX In command "walk", the maximum distance a point is to
cc be randomly walked from its initial position, if it
cc is not walked a total path length of PATHMAX first.
cc May be integer, floating point or a variable.
cc DMEAN In command "walk", the mean free path of a point being
cc displaced by a random walk process.
cc May be integer, floating point or a variable.
cc dms An option in command "angles" to convert angles from or
cc to degrees, minutes and seconds.
cn dms.mac A macro file for converting from degrees in decimal
cn form to degrees, minutes and seconds.
cn In ~/work/geom/test .
cn Type "in dms.mac ?" for info. See "deg.mac".
cc do A command to begin a do loop. Must be followed, after
cc any desired block of commands, by command "enddo".
cc See "do while".
cc
cc Note: do not use the statement separator ";" on the
cc same line as this command.
cc
cc Do loops may be nested, with up to 16 levels.
cc
cc Note: command "goto" may not be used to jump into or
cc out of a do loop. While in a do loop, any commands
cc read from another input file must end with a command
cc to return to the same do loop.
cc
cc Forms include:
cc
ccin help do
ccin do [help]
ccin help enddo
ccin enddo help
cc
cc Display the command options.
cc
ccin do VARNAME [=] N1 N2 [INC|1]
cc
cc Begin a do loop, with loop variable VARNAME ranging
cc from N1 to N2 with increment INC (default 1).
cc Name VARNAME has the same restrictions as any named
cc variable. Arguments N1, N2 and INC must be
cc integers or integer variables. Argument INC may be
cc negative. The value of VARNAME starts at N1, and
cc is incremented by INC each time command "enddo" is
cc executed, until it falls outside the range from N1
cc to N2. Until that happens, all the commands
cc between the initial command "do" of this do loop
cc and its corresonding command "enddo" are executed,
cc for each value of VARNAME.
cc
cc To loop over a range of floating point values,
cc e.g. from X1 to X2, with an increment of DX,
cc use the following commands:
cc
cc s XRANGE = X2 - X1
cc s N2 = XRANGE / DX
cc s N2 = N2 + 1
cc s N2 = 1 int N2
cc s X = X1
cc do N = 1 N2
cc ...
cc s X = X + DX
cc enddo
cc
ccin enddo
cc
cc Repeat the current "do-enddo" block with loop
cc variable VARNAME incremented from its current value
cc N to N + INC, unless N + INC is not in the range
cc from N1 to N2. N1, N2 and INC are arguments in
cc command "do".
cc
cc Synonyms: [help, h].
cg do loop A do loop consists of a block of commands beginning
cg with a "do VARNAME N1 N2 [INC|1]" command and ending
cg with an "enddo" command. The loop variable VARNAME
cg will initially be set at value N1, and when command
cg "enddo" is reached, incremented by INC. If the
cg value of VARNAME is still within the range from
cg N1 to N2, the loop will be repeated, starting at the
cg command after the command "do" that initiated this
cg do loop.
cg
cg Arguments N1, N2 and INC must be integers or integer
cg variables. Argument INC may be negative, and if not
cg specified, defaults to 1. If loop variable VARNAME
cg does not already exist, it will be created, as if
cg command "variable VARNAME = N1" had been used,
cg with the same restrictions on VARNAME.
cg
cg A do loop will be executed 1 + (N2 - N1) / INC
cg times (rounded to an integer). This is the trip
cg count.
cg
cg Do loops may be nested, with up to 16 levels.
cg Each do loop must have a unique loop variable name.
cg Each do loop must be entirely contained within the
cg next outer do loop.
cg
cg Do loops may contain if-endif blocks, which may also
cg be nested. Each such if-endif block must be
cg entirely within its do loop, and may be used to end a
cg do loop based on some other criterion than the values
cg of VARNAME, N1 and N2. See "do while".
cg Jumps outside the do loop block are allowed only if
cg a jump back into the same do loop block follows.
cg Jumps into a do loop block from outside the block
cg should never be used.
cg
cg Do loops may not contain any of the following
cg commands or command synonyms:
cg ".", "call", "goto", "i", "in", "indo", "input",
cg "r", "rd", "read", "return", "rtn", "u", "undo".
cg do loop use Typically, use of do loops involves specifying an
cg initial set of objects with subscripted names, then
cg using a do loop over a range of values of the
cg suscripts to modify the values of the objects and use
cg the modified values to create additional objects with
cg or without subscripted names. When the objects have
cg names with multiple subscripts representing, for
cg example, coordinate directions, two or more do loops
cg may be nested.
cg
cg Do loops may be used in place of certain commands,
cg including those with options for creating a group of
cg objects, including the options "brick", "concentric",
cg "family", "incr", "increment", "nest", "move",
cg "parallel", "rotate", "scale", "series", used in
cg one or more of the commands "cone", "cylinder",
cg "ellipsoid", "line", "plane", "quadric", "sphere",
cg "tetrahedron", "variable", "vector" and "zone".
cg do until See "do while".
cg do while The equivalent of a "do while" or "do until" loop may
cg be done by using an if-endif block within a do loop
cg executed with commands "do" and "enddo", placed
cg just before the "enddo" command, to reset the do loop
cg index outside its initial range.
cg
cg For example, a "do while x .ge. 1.e-12" loop or a
cg "do until x .lt. 1.e-12" loop might look like:
cg
cg do n 1 100
cg ...
cg if x .lt. 1.e-12
cg variable nlast = n
cg variable n = 101
cg endif
cg enddo
cg
cg Note the method of saving the last do loop index
cg used before exiting the loop.
cd doc Directory for documentation of GEOM.
cd Open YANA Cluster: ~edwards/work/geom/doc
cd Archives: /users/u47/edwards/geom/doc
cd See "make", "test".
cg dodecahedron A regular dodecahedron has 20 vertices, 30 edges, and
cg 12 equilateral pentagonal faces.
cg The edge length, face area, volume, radius of
cg inscribed sphere, dihedral angle and central edge
cg angle, for a circumscribed sphere radius of 1.0 are:
cg
cg edge = 4.0 / (sqrt (3.0) + sqrt (15.0))
cg = 0.7136441795462
cg area = 0.25 * sqrt (25.0 + 10.0 * sqrt (5.0)) *
cg edge^2
cg = 0.8762185201985
cg volume = 0.25 * (15.0 + 7.0 * sqrt (5.0)) * edge^3
cg = 2.785163863123
cg rinsc = sqrt ((5.0 + 2.0 * sqrt (5.0)) / 15.0)
cg = 0.7946544722918
cg angdih = acos (-1.0 / sqrt (5.0))
cg = 116.5650511771
cg angcent = acos (sqrt (5.0) / 3.0)
cg = 41.81031489578
cg
cg See "polyhedron".
cg dollar The dollar character, "$".
cg dot The period or dot character, ".". See command "dot".
cg See "dot product".
cc dot An option in command "variable", to find the dot
cc product of two vectors. See "dot product".
cc Synonyms: [dot, inner].
cc dot Command to find the dot product of two vectors, the
cc angle between them, and its cosine.
cc
cc Command "dot" relates to objects: symbol, vector.
cc
cc Forms include:
cc
ccin help dot
ccin dot [help]
cc
cc Display the command options.
cc
ccin dot VNAME1 VNAME2
cc
cc Find the dot (inner) product of vectors VNAME1 and
cc VNAME2, the included angle, in the current angle
cc units, and its cosine.
cc
cc Synonyms: [dot, inner], [help, h].
cg dot product The dot (or inner or scalar) product of two vectors
cg A = (AX, AY, AZ) and B = (BX, BY, BX) is the scalar
cg C = A dot B = AX*BX + AY*BY + AZ*BZ.
cg C = |A| * |B| * cos (THETA), where THETA is the angle
cg between vectors A and B.
cg Note that A dot B = B dot A, and that the dot product
cg of two perpendicular vectors is zero.
cg double In output from commands "root" and "roots", indicates
cg a root of order 2 of a polynomial equation.
cc DPR A uniform relative differential probability of a range
cc of values VRANL to VRANR of a random variable,
cc in command "bin". Must not be negative.
cc See "PRTOT", "DPRL", "DPRR".
cc DPRL A relative differential probability of a value VRANL
cc of a random variable in command "bin".
cc Varies linearly from DPRL at VRANL to DPRR at
cc VRANR. Must not be negative.
cc See "PRTOT", "DPR", "DPRR".
cc DPRR A relative differential probability of a value
cc VRANR of a random variable in command "bin".
cc Varies linearly from DPRL at VRANL to DPRR at
cc VRANR. Must not be negative.
cc See "PRTOT", "DPR", "DPRL".
cg dsum An invariant of a quadric surface, for translations and
cg rotations. See "invariants of quadric".
cc DT In command "accelerate", the increment in time to be
cc used between the initial and final times for which
cc path length, velocity and position are to be
cc displayed. If not specified, defaults to zero.
cc See "TMIN", "TMAX".
cc DU In command "vector" or "plane", a vector component,
cc in the x, rcyl or rsph direction, for a rectangular,
cc cylindrical or spherical coordinate system,
cc respectively.
cc May be integer, floating point or a variable.
cg du An increment or distance or vector component in the
cg u coordinate direction, which may be x, rcyl or rsph,
cg depending on the current coordinate system.
cg du12 The u component of the distance between the centers of
cg the first and second circles, displayed after command
cg "intcirc".
cc dup A synonym for copy.
cc duplicate A synonym for copy.
cg duplicate To duplicate an object, use command "copy".
cc DV In command "vector" or "plane", a vector component,
cc in the y, theta or theta direction, for a
cc rectangular, cylindrical or spherical coordinate
cc system, respectively.
cc May be integer, floating point or a variable.
cc DV In command "slice", the increment between coordinate
cc values, for which points are to be found in a slice
cc of a quadric surface. See "VMIN", "VMAX".
cg dv An increment or distance or vector component in the
cg v coordinate direction, which may be y or theta,
cg depending on the current coordinate system.
cg dv12 The v component of the distance between the centers of
cg the first and second circles, displayed after command
cg "intcirc".
cg dval An increment in the value of a random variable which
cg ranges from VRANL to VRANR. Must be positive.
cc DW In command "vector" or "plane", a vector component,
cc in the z, z or phi direction, for a rectangular,
cc cylindrical or spherical coordinate system,
cc respectively.
cc May be integer, floating point or a variable.
cg dw An increment or distance or vector component in the
cg w coordinate direction, which may be z or phi,
cg depending on the current coordinate system.
cc DX In command "root", the increment between successive
cc trial values of x, to search for roots, extrema
cc and inflection points of a polynomial equation using
cc Newtonian iteration. No more than two roots,
cc extrema or inflection points can be found in each
cc increment DX. Will be changed if either XMIN or
cc XMAX is changed to be within a calculated range of
cc x that contains all roots, extrema and inflection
cc points.
cc See "XMIN", "XMAX".
cg dx An increment or distance or vector component in the
cg x coordinate direction.
cg dy An increment or distance or vector component in the
cg y coordinate direction.
cg dz An increment or distance or vector component in the
cg z coordinate direction.
E-------------------------------------------------------------------------------
cg E See "E, e, E+, e+".
cg e See "E, e, E+, e+".
cg E+ See "E, e, E+, e+".
cg e+ See "E, e, E+, e+".
cg E, e, E+, e+ When preceded and followed by integers, indicates
cg multiplication by the power of ten indicated by the
cg final integer.
cg E- See "E-, e-".
cg e- See "E-, e-".
cg E-, e- When preceded and followed by integers, indicates
cg division by the power of ten indicated by the final
cg integer.
cc ebase An option in command "symbol", argument SYMBNAME,
cc to create symbol ebase with value exp (1) =
cc 2.71828182845904523536028747135266249775724709369995
cc Store as a big integer with command "input big.mac",
cc with file big.mac in the same directory as GEOM.
cg ebase The base of natural logarithms 2.718281828459045...
cg Generated as a symbol at the beginning of a
cg GEOM run. ebase = exp (1).
cg eccentricity The eccentricity e of a hyperbola or a hyperbolic
cg cylinder is sqrt (1 + (B / A)^2), where
cg A is the transverse semiaxis, between the two
cg vertices, and B is the conjugate semiaxis, between
cg the two points where a line tangent to the vertices
cg intersects the asymptotes of the hyperbola.
cg
cg For the hyperbola or hyperbolic cylinder
cg QC + QXX * x^2 + QYY * y^2 = 0
cg (QXX > 0, QYY < 0)
cg the eccentricity is
cg sqrt (1 - QYY / QXX) > 1, if QC > 0 or
cg sqrt (1 - QXX / QYY) > 1, if QC < 0.
cg
cg The eccentricity e of an ellipse or elliptic cylinder
cg is sqrt (1 - (B / A)^2), where A is the major
cg semiaxis, and B is the minor semiaxis.
cg
cg For the ellipse or elliptic cylinder
cg QC + QXX * x^2 + QYY * y^2 = 0
cg (QC < 0, QXX => QYY > 0),
cg the eccentricity is sqrt (1 - QYY / QXX) < 1.
cg
cg For the ellipsoid
cg QC + QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0
cg (QC < 0, QXX => QYY => QZZ),
cg the eccentricities in planes of constant x, y and z
cg are sqrt (1 - QZZ / QYY), sqrt (1 - QZZ / QXX), and
cg sqrt (1 - QYY / QXX), respectively.
cg echo Each non-null input line is echoed in the output file,
cg preceded by the character ">", and if the input
cg medium is not the user's terminal, is echoed on the
cg user's terminal.
cc edge An option in command "trig", indicating that the next
cc argument is the positive length of a edge of a
cc triangle. Synonyms: [edge, side].
cg edge An edge of the mesh or the mesh block occurs wherever
cg two of the three mesh indices k, l and m have either
cg their minimum or maximum value, and the other index
cg ranges from its minimum to its maximum value.
cg The mesh and the mesh block each have 12 edges.
cg
cg To display the 12 edge lengths of a brick, use
cg command "brick".
cg The edges of a brick in the u, v and w directions
cg are labeled "min, min", "min, max", "max, min" and
cg "max, max", indicating the values of the other two
cg coordinates. For example, in spherical coordinates,
cg edge phi (max, min) refers to the edge in the polar
cg angle phi direction, at maximum rsph, minimum theta.
cg
cg To display the edge length of a regular polygon,
cg use command "polygon".
cg
cg To display the average edge length of a general
cg polygon, use command "area".
cg
cg To display the edge length of a regular polyhedron,
cg use command "polyhedron".
cg
cg To find the plane containing the edge of a quadric
cg surface, as viewed from a point, use command "plane",
cg option "outline".
cg edges See "three edges", "triangle solution".
cg edit To display and/or edit a file, use the UNIX text
cg editor VI or GEOM command "vi".
cg For example, the saved input lines in file geom_cmd
cg could be edited to do a different problem, or to
cg correct errors before repeating a problem.
cd edwards Directory for Arthur L. Edwards, L-298, Ph. 422-4123
cd Open YANA Cluster: ~edwards
cd Archives: /users/u47/edwards
cc el A synonym for ellipsoid.
cg element See "point element", "line element", "surface element",
cg "volume element", for elements of a mesh.
cg element See "brick", "tetrahedron", "zone".
cc ell A synonym for ellipsoid.
cc ELL(1) In command "ellipsoid", the name of a base ellipsoid,
cc used to create a family of ellipsoids.
cg ellipse An ellipse is a plane curve, for which the standard
cg equation in the x-y plane is:
cg - 1 + QXX * x^2 + QYY * y^2 = 0
cg (QXX => QYY).
cg The major semiaxis SAY = 1 / sqrt (QYY), and the
cg minor semiaxis SAX = 1 / sqrt (QXX).
cg The area is pi * SAX * SAY.
cg The perimeter requires an elliptic integral.
cc ellipse A synonym for ellipsoid.
cc Also see "cylinder, elliptic".
cg ellipsoid An ellipsoid is a quadric surface in 3-D space,
cg described by an implicit quadric equation.
cg An ellipsoid is a closed surface, with three axes.
cg An ellipsoid is axially symmetric if two of the three
cg axes are equal, and is a prolate spheroid if the
cg unequal axis is longer or an oblate spheroid if the
cg unequal axis is shorter.
cg
cg The standard forms of the implicit equations for
cg ellipsoids (with all coefficients positive) are:
cg
cg Real ellipsoid:
cg - 1 + QXX*x^2 + QYY*y^2 + QZZ*z^2 = 0
cg Real sphere:
cg - 1 + QXX * (x^2 + y^2 + z^2) = 0
cg Imaginary ellipsoid:
cg 1 + QXX*x^2 + QYY*y^2 + QZZ*z^2 = 0
cg Imaginary sphere:
cg 1 + QXX * (x^2 + y^2 + z^2) = 0
cg
cg The semiaxes in the x, y and z directions are
cg SX = 1/sqrt(QXX), SY = 1/sqrt(QYY), SZ = 1/sqrt(QZZ).
cg So, for a real ellipsoid, the standard equation is:
cg (x/SX)^2 + (y/SY)^2 + (z/SZ)^2 = 1
cg
cg For a real ellipsoid aligned with the x, y and z
cg axes, the eccentricities in the major planes are:
cg sqrt (1 - QZZ / QYY) or sqrt (1 - QYY / QZZ),
cg sqrt (1 - QZZ / QXX) or sqrt (1 - QXX / QZZ),
cg sqrt (1 - QYY / QXX) or sqrt (1 - QXX / QYY),
cg (use the positive argument of the square root).
cg
cg The distance D from the center to the surface in the
cg direction of any unit vector U = (UX, UY, UZ) is:
cg D = 1 / sqrt ((UX/SX)^2 + (UY/SY)^2 + (UZ/SZ)^2)
cg and the corresponding surface point P is:
cg P = (X, Y, Z) = (UX * D, UY * D, UZ * D).
cg
cg An ellipsoid centered on the z axis, at Z0, and
cg symmetric around the z axis (QXX = QYY), and passing
cg through the two points (R1, Z1) and (R2, Z2), where
cg R1^2 = X1^2 + Y1^2, and R2^2 = X2^2 + Y2^2,
cg has the equation:
cg QC + QXX * (x^2 + y^2) + QZZ = 0
cg where w = R2^2*(Z1-Z0)^2 - R1^2*(Z2-Z0)^2,
cg A1 = (R2^2 - R1^2) / w
cg A2 = [(Z1 - Z0)^2 - (Z2 - Z0)^2] / w
cg QC = -1 / sqrt(A2)
cg QZZ = A1 / A2
cg This requires that w not be zero, Z1 not be equal to
cg Z2, and that the point further from Z0 have the
cg smaller value of R.
cg
cg In a command, the word "ellipsoid" means a real
cg ellipsoid. Otherwise, use "quadric".
cg
cg To find the distance from a point to an ellipsoid,
cg use command "distance", "proximal" or "side".
cg
cg To find the distance or intersection between a plane
cg and an ellipsoid, use command "distance".
cg
cg The following commands relate to ellipsoids:
cg accelerate, arc, axisym, copy, debug, delete,
cg distance, ellipsoid, extrema, help, invert, last,
cg list, move, operator, point, proximal, quadric,
cg reflect, rename, repack, rotate, scale, search, side,
cg slice, sort, symbol, synonym, tables, track, triple,
cg vector, zone.
cc ellipsoid Command to display or create ellipsoids.
cc Creating an ellipsoid replaces any existing quadric
cc surface having the same name.
cc The normal vectors will be radially outward.
cc See "quadric" for other options.
cc See "do loop use".
cc
cc Command "ellipsoid" relates to objects: axisym,
cc ellipsoid, operator, point, quadric, symbol,
cc variable, vector.
cc
cc Forms include:
cc
ccin help ellipsoid
ccin ellipsoid [help]
cc
cc Display the command options.
cc
ccin ellipsoid [all,list]
cc
cc Display all ellipsoids (short display).
cc
ccin ellipsoid list ELNAME1 ELNAME2 ELNAME3 ...
cc
cc Display ellipsoids ELNAME1, ELNAME2, ELNAME3, ...,
cc with or without subscripts (short display).
cc
ccin ellipsoid ELNAME
cc
cc Display ellipsoid ELNAME (long display).
cc
cc In the following commands, use "+" or "-" instead of
cc ELNAME or ELL(2) to form the name by incrementing or
cc decrementing the base name for ellipsoids.
cc See command "last", "increment names".
cc
ccin ellipsoid ELNAME = PCEN SAX SAY SAZ
cc
cc Create ellipsoid ELNAME, centered at point PCEN,
cc with semiaxes SAX, SAY and SAX in the x, y and z
cc directions, respectively.
cc Note: if any semiaxis is given a very large value,
cc such as 10^99, the resulting quadric surface will
cc be an elliptic cylinder, not an ellipsoid.
cc
ccin ellipsoid ELNAME fit PCEN VAXIS PNAME2 PNAME3
cc
cc Create circular ellipsoid ELNAME, centered at point
cc PCEN, with axis vector VAXIS, and passing through
cc the two points PNAME2 and PNAME3. This is an
cc axially symmetric quadric surface, which may be an
cc oblate or prolate spheroid.
cc
ccin ellipsoid ELL(2) move NUMELL INC ELL(1) VMOVE
cc
cc Create a family of NUMELL ellipsoids ELL(2), ...,
cc with names incremented by INC characters, spaced at
cc intervals of vector VMOVE, starting from ellipsoid
cc ELL(1). See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin ellipsoid ELL(2) rotate NUMELL INC ELL(1) OPNAME PINV
cc
cc Create a family of NUMELL ellipsoids ELL(2), ...,
cc with names incremented by INC characters, by
cc rotating the preceding ellipsoid with operator
cc OPNAME and invariant point PINV, starting from
cc ellipsoid ELL(1). See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
ccin ellipsoid ELL(2) scale NUMELL INC ELL(1) OPNAME PINV
cc
cc Create a family of NUMELL ellipsoids ELL(2), ...,
cc with names incremented by INC characters, by
cc scaling the preceding ellipsoid with operator
cc OPNAME and invariant point PINV, starting from
cc ellipsoid ELL(1). See "increment names".
cc See command "quadric" for an equivalent set of
cc commands using subscripted names and a do loop.
cc
cc Synonyms: [help, h], [ellipsoid, el, ell, ellipse],
cc [move, mv, trans, translate], [rotate, rot].
cc ellipsoid An option in commands "copy", "delete", "last", "list",
cc "rename", "repack" and "sort", to perform the
cc specified operation on one or more ellipsoids.
cc Synonyms: [ellipsoid, el, ell, ellipse].
cg ellipsoid arrays Ellipsoids may be created as arrays with subscripted
cg names. See "subscript", "subscripted names",
cg commands "do" and "enddo".
cg ellipsoids A family of ellipsoids may be created with command
cg "ellipsoid", options "move", "rotate" or "scale"
cg (with restrictions) or as follows:
cg
cg p pinv (options)
cg
cg Create an invariant point, if needed.
cg
cg ell ELL(1) (options)
cg
cg Create a base ellipsoid.
cg
cg op opr (options)
cg
cg Create a tensor operator, to reflect, rotate,
cg invert or scale, if needed.
cg
cg v vmove (options)
cg
cg Create a vector for use as a translation operator,
cg if needed.
cg
cg cp ELL(1) ELL(2)
cg
cg Copy ellipsoid ELL(1) to the first ellipsoid.
cg
cg Repeat the following block of commands as many times
cg as needed to create the rest of the family of
cg ellipsoids. See "shortcuts".
cg
cg mv ell ELL(1) vmove
cg
cg Move the base ellipsoid by amount move, if needed.
cg
cg [invert,reflect,rotate,scale] ell ELL(1) opr [pinv]
cg
cg Invert, reflect, rotate or scale the base ellipsoid
cg with tensor operator opr, if needed.
cg
cg cp ell ELL(1) +
cg
cg Copy the base ellipsoid to the next ellipsoid.
cg elliptic See "elliptic cone", "elliptic cylinder",
cg "elliptic paraboloid".
cg elliptic cone An elliptic cone is a quadric surface for which the
cg standard equation is:
cg x^2 + QYY*y^2 - |QZZ|*z^2 = 0, (QYY>0, QZZ<0).
cg An imaginary elliptic cone is a quadric surface for
cg which the standard equation is:
cg x^2 + QYY*y^2 + QZZ*z^2 = 0, (QYY>0, QZZ>0).
cg This last equation is also satisfied at the real
cg point (0,0,0).
cg
cg To find the distance from a point to an elliptic
cg cone, use command "distance", "proximal" or "side".
cg
cg To find the distance or intersection between a plane
cg and an elliptic cone, use command "distance".
cg elliptic cylinder
cg An elliptic cylinder is a quadric surface for which the
cg standard equation is:
cg - 1 + QXX*x^2 + QYY*y^2 = 0, (QXX>0, QYY>0).
cg An imaginary elliptic cylinder is a quadric surface
cg for which the standard equation is:
cg 1 + QXX*x^2 + QYY*y^2 = 0. (QXX>0, QYY>0).
cg
cg To create an elliptic cylinder aligned with the x,
cg y or z axis, use command:
cg
cg ellipsoid QNAME = PCEN SAX SAY SAZ
cg
cg Create elliptic cylinder QNAME, centered at point
cg PCEN, with semiaxes SAX, SAY and SAX (one of which
cg is very large, say 10^99) in the x, y and z
cg directions, respectively. Any future reference to
cg this quadric surface must use option "quadric", not
cg "ellipsoid".
cg
cg To find the distance from a point to an elliptic
cg cylinder, use command "distance", "proximal" or
cg "side".
cg
cg To find the distance or intersection between a plane
cg and an elliptic cylinder, use command "distance".
cg elliptic paraboloid
cg An elliptic paraboloid is a quadric surface for which
cg the standard equation is:
cg -QZ*z + x^2 + QYY*y^2 = 0.
cg
cg To find the distance from a point to an elliptic
cg paraboloid, use command "distance", "proximal" or
cg "side".
cg
cg To find the distance or intersection between a plane
cg and an elliptic paraboloid, use command "distance".
cc ELNAME The name of an ellipsoid. May have up to 24
cc characters, and may be ASCII, integer or floating
cc point. May not be the same as any other quadric
cc surface name QNAME. Also referred to as ELNAME1,
cc ELNAME2, ... Specified with command "ellipsoid".
cc No ellipsoid name may be "+", "-", "all", "h",
cc "help", "list" or "thru", begin with "!" or contain
cc ";".
cc
cc Ellipsoids may appear in commands:
cc accelerate, arc, axisym, cone, copy, delete,
cc distance, ellipsoid, extrema, help, invert, last,
cc list, move, operator, point, project, proximal,
cc quadric, reflect, rename, repack, rotate, scale,
cc search, side, slice, sort, track, triple, vector.
cg embedded See "embedded lines".
cg embedded lines At any point on some quadric surfaces (all planes,
cg cylinders, cones, hyperbolic paraboloids, and
cg hyperboloids of one sheet) one or more straight lines
cg can be drawn, lying entirely on the surface.
cg These quadric surfaces are ruled surfaces.
cg See "ruled surface".
cg See commands "arc" and "hyperb".
cg encryption Encryption is the process of making data or a text
cg unreadable without special knowledge, intended to
cg be available only to certain recipients.
cg See command "big".
cg end See "end of command", "end of comment".
cc end Command to end the current run.
cc Synonyms: [end, exit, quit, split].
cg end of command The unquoted character ";" ends a command or a comment,
cg when multiple commands and/or comments are on one
cg input line. Ignored if between single or double
cg quotes (as in commands "alias", "define" and
cg "marker"). Does not need to be delimited.
cg If not between single or double quotes, will
cg terminate a comment, allowing a command to follow on
cg the same line. Ignored in command "hex".
cg Can not be used after commands "indo", "input",
cg "read", "redo", "return" or"undo", because chaos
cg might ensue.
cg end of comment The unquoted character ";", if not between single or
cg double quotes, will terminate a comment, allowing a
cg command to follow on the same line. Does not need to
cg be delimited.
cg end-of-file An end-of-file in the input file will have the same
cg effect as command "return" or "input #".
cc enddata An option in command "variable", indicating the end
cc of a table of variable values. See "data".
cc enddo A command to repeat or end a do loop. Must be preceded
cc by command "do". Amy desired block of commands may
cc be used in between command "do" and command "enddo",
cc including other do loops. See "do while".
cc
cc Note: do not use the statement separator ";" on the
cc same line as this command.
cc
cc Note: "do-enddo" blocks of commands may be nested.
cc
cc Forms include:
cc
ccin help enddo
ccin enddo help
cc
cc Display the command options.
cc
ccin enddo
cc
cc Repeat the current "do-enddo" block for loop
cc variable VARNAME incremented from its current value
cc N to N + INC, unless N + INC is not in the range
cc from N1 to N2. N1, N2 and INC are arguments in
cc command "do".
cc
cc Synonyms: [help, h].
cc endif The final command in an "if-endif" block of input
cc lines, which must begin with command "if ...".
cc
cc Command "endif" relates to objects: symbol.
cc
cc Forms include:
cc
ccin help endif
ccin endif help
cc
cc Display the command options commands "if" and
cc "endif". Note that the argument "help" is not
cc optional.
cc
ccin endif
cc
cc End the current "if-endif" block of input lines,
cc which begins with the command "if" defining the
cc current "if-endif" block.
cc
cc Synonyms: [help, h].
cg English Commands and options in GEOM are based on English.
cg See "language".
cc ENTRY In command "define", the name of the entry in geom_base
cc (this file) to be displayed. Must be bracketed by
cc single (') or double (") quotes.
cc If ENTRY is bracketed by single quotes, double any
cc internal single quotes.
cc If ENTRY is bracketed by double quotes, double any
cc internal double quotes.
cc The entry is found by matching columns 7-25 in
cc this file, geom_base, ignoring case, with ENTRY.
cc All lines are displayed until the next non-matching
cc entry. Multiple entries with the same name will be
cc displayed. ENTRY may have up to 19 characters.
cg entry In this file, a section delimited by blank lines, with
cg the name of the entry in columns 7-24 of the first
cg line.
cc env A synonym for environment.
cg environment See "environmental", command "environment".
cc environment An option in command "debug", to display GEOM internal
cc variables for the environment:
cc alodmach, aloddate, alodtime, aversion, amach,
cc adate, atime, atitle, aprompt, aprompts, lprompts.
cc Synonyms: [environment, env, setup].
cc environment An option in command "help", to display a help message
cc for environment commands.
cc environment Command to display a help message for environment
cc commands, which include:
cc alias, angles, binary, commands, coordinate, dec,
cc define, degrees, delimiter, end, endif, help, hex,
cc icalc, if, indo, input, marker, nobin, oct, output,
cc page, plot, prompt, radians, redo, status, symbol,
cc synonym, tables, time, title, tol, tol, trace, undo,
cc variable, vi, when.
cc
cc Forms include:
cc
ccin help environment
ccin environment [help]
cc
cc Display a help message for environment commands.
cc
cc Synonyms: [help, h], [environment, env, setup].
cg environmental To specify, create, display and use environmental
cg objects, see the entries and commands: ".", ";",
cg alias, angles, binary, commands, coordinate, debug,
cg dec, define, degrees, delim, end, endif, help, hex,
cg icalc, if, indo, input, marker, nobin, oct, output,
cg page, plot, prompt, radians, redo, status, symbol,
cg synonym, tables, time, title, tol, tol, trace, undo,
cg variable, vi, when.
cg equal See "equal temperament", "equal zoning",
cg "equally-tempered".
cg equal sign The equal sign, "=".
cg equal temperament
cg See "equally-tempered".
cg equal zoning Planes or other quadric surfaces may be created in a
cg family in which each surface is displaced by a
cg specified constant amount from the preceding surface,
cg in a specified direction.
cg Points may be created in a family in which each point
cg is displaced by a specified constant amount from the
cg preceding point, in a specified direction.
cg See option "move" of commands "point", "sphere",
cg "cylinder", "cone", "axisym", "quadric", and see
cg command "plane", option "parallel".
cg See "ratio zoning".
cg
cg Points may be created in a 3-D array in a brick,
cg in such a way that the volumes of each of the
cg smallest elements with 8 points at their vertices are
cg equal. See command
cg "point PMESH brick BRNAME mesh bloxk [volume]".
cg See "briquette".
cg
cg See "do loops" and commands "do" and "enddo".
cg equally-tempered A musical scale in which adjacent semitones have a
cg fixed frequency ratio, 2^(1/12) = 1.059463094359.
cg For one octave, the results are as follows:
cg
cg Note Equal-temp Value Just Cents Interval
cg ratio cents ratio diff
cg
cg 1 1.000000000000 0 1/1 0 unison
cg 2 1.059463094359 100 16/15 -11.731 semitone
cg 3 1.122462048309 200 9/8 3.910 whole tone
cg 4 1.189207115003 300 6/5 -15.641 minor 3rd
cg 5 1.259921049895 400 5/4 13.686 major 3rd
cg 6 1.334839854170 500 4/3 1.955 perfect 4th
cg 7 1.414213562373 600 45/32 9.776 tritone
cg 8 1.498307076877 700 3/2 -1.955 perfect 5th
cg 9 1.587401051968 800 8/5 -13.687 minor 6th
cg 10 1.681792830507 900 5/3 15.641 major 6th
cg 11 1.781797436281 1000 16/9 3.910 minor 7th
cg 12 1.887748625363 1100 15/8 11.731 major 7th
cg 13 2.000000000000 1200 2/1 0 octave
cg
cg Note Equal-temp Just ratio
cg ratio
cg
cg A 1.000000000000 1.00000
cg Bb 1.059463094359 1.06667
cg B 1.122462048309 1.12500
cg C 1.189207115003 1.20000
cg Db 1.259921049895 1.25000 or 1.26562 = 81/64
cg D 1.334839854170 1.33333
cg Eb 1.414213562373 1.40625 or 1.42383 = 729/512
cg E 1.498307076877 1.50000
cg F 1.587401051968 1.60000
cg Gb 1.681792830507 1.66667 or 1.68750 = 27/16
cg G 1.781797436281 1.77778
cg Ab 1.887748625363 1.82500 or 1.89844 = 243/128
cg A 2.000000000000 2.00000
cg
cg See "piano", "cents".
cg equation The real and/or complex roots of a quadratic
cg (a3 = a4 = 0), cubic (a4 = 0) or quartic polynomial
cg equation of the form:
cg a0 + a1 * z + a2 * z^2 + a3 * z^3 + a4 * z^4 = 0
cg may be found with command "roots".
cg
cg The real coefficients a0, a1, a2, a3 and a4 may be
cg found for any specified set of from two to four real
cg and/or complex roots with command "roots", option
cg "=".
cg
cg To search for real roots, extrema and inflection
cg points of a polynomial equation using Newtonian
cg iteration, use command "root".
cg
cg To find the coefficients of an Nth-order polynomial
cg equation with N specified real roots, use command
cg "root", option "=".
cg equations See "polygon equations", "polynomial", "quadric types",
cg "quadric curves", command "solve".
cg equilateral For every triangle, there are equilateral triangles
cg that have a parallel projection onto the triangle.
cg Whenever the data for a triangle are displayed, the
cg vertex coordinates and edge length of one such
cg triangle, such that one vertex is shared, are
cg displayed.
cc err A synonym for error.
cg err Estimated numerical truncation error in calculating
cg a value, based on TOL. See "error estimate".
cg error Error messages are generated by the code whenever it
cg detects an error in an input line, which may include
cg an unrecognized command, the wrong number, mode or
cg sign of arguments, or the non-existence of an
cg operator, geometric object, file or key word referred
cg to in the command, or the non-existence of a
cg result satisfying the requirements of the command.
cg After an error message, check the command, or type
cg "help COMMAND" to display the options, or type
cg "define 'ENTRY'" to display the entry in geom_base
cg for ENTRY, and retry.
cg Use command "trace" to display the return path from
cg the current input file.
cg See command "error".
cc error Command to display a help message for error control
cc commands, which include: undo, indo, redo, input.
cc
cc Forms include:
cc
ccin help error
ccin error [help]
cc
cc Display a help message for error control commands.
cc
cc Synonyms: [error, err], [help, h].
cc error An option in command "help", to display help messages
cc for error control commands.
cg error See "error estimate", "truncation error".
cg error control See commands "debug", "indo", "input", "parse", "redo",
cg "return", "symbol", "undo".
cg If you have ended the run, see "input file",
cg to find how to make a new input file to repeat
cg the run without the error(s).
cg error correction See "error control".
cg error estimate When calculating a value Z(A, B, C, ...), a function of
cg A, B, C, ..., a first-order estimate of the error
cg in Z, E(Z), is given by:
cg E(Z) = abs (Z'(A)) * E(A) + abs (Z'(B)) * E(B)
cg + abs (Z'(C)) * E(C) + ... ,
cg where Z'(A), Z'(B), Z'(C), ... are the partial
cg derivatives of Z with respect to A, B, C, ..., and
cg E(A), E(B), E(C), ... are the (positive) estimated
cg errors in A, B, C, ...
cg For an input value A, the estimated error E(A) is
cg TOL * abs (A).
cg escape character A character used to force the following character to be
cg interpreted literally, instead of having a special
cg meaning or function. For example, adding an extra
cg quote mark to a quote mark inside of a quoted
cg character string or prefixing a character with a
cg backslash "\" or <control-V> in the text editor VI.
cg estimate To estimate the volume of a zone by a Monte Carlo
cg method, use command "mcvol".
cc Euler A synonym for euler.
cg Euler See "Euler's Totient", "totient function".
cc euler An option in command "symbol", argument VNAME,
cc to create symbol euler with value
cc 0.57721566490153386061...
cc Store as a big integer with command "input big.mac",
cc with file big.mac in the same directory as GEOM.
cg euler Euler's constant. Generated as a symbol at the
cg beginning of a GEOM run.
cg euler = the limit as z approaches infinity of
cg 1 + 1/2 + 1/3 + 1/4 + ... + 1/z - log z =
cg euler = 0.57721566490153386061...
cc Store as a big integer with command "input big.mac",
cc with file big.mac in the same directory as GEOM.
cg Euler's See "Euler's Totient", "totient function".
cg Euler's Totient See "totient function".
cg eV Electron volts (an energy unit).
cg 1 amu = 9.3149432E8 eV (+/- 0.3 ppm).
cg 1 K = 8.617385E-5 eV (+/- 8.5 ppm).
cg 1 Hz = 4.1356692E-15 eV (+/- 0.3 ppm).
cc event An option in command "bin", to create a probability
cc bin for a discrete event, identified by the name of
cc the bin.
cc exch A synonym for exchange.
cc exchange An option in command "mesh", to exchange the layers in
cc the directions of two different indices in a mesh
cc block, and to redefine the mesh indices of any mesh
cc points in the mesh block accordingly. The mesh block
cc must have the same size in the two layer directions.
cc Along with option "invert" in command "mesh", this
cc allows all possible mesh reflections and rotations
cc to be done.
cc Synonyms: [exchange, exch].
cg EXCHANGED In the display for a point, indicates a mesh point in
cg a mesh block for which mesh indices have been
cg exchanged.
cg excluded See "excluded names".
cg excluded names Some names are disallowed for all or some object names,
cg because they make interpretation of a command
cg ambiguous.
cg No name may be "+", "-", "all", "h", "help",
cg "list" or "thru", begin with "!" or contain ";".
cg A point name must not be "cluster".
cg A cluster name must not be "point".
cg A quadric surface name must not be "types".
cg exclusive See "exclusive or", "Boolean".
cg exclusive or See "Boolean".
cg execution See "GEOM execution".
cc execution line See "GEOM execution".
cc exit A synonym for end.
cc exp An option in command "bin", to create an exponential
cc probability distribution function.
cc exp An option in command "variable", argument FUNCTION,
cc to indicate the base e exponential function.
cc A exp B means A * exp (B).
cc exp An option in command "big", to find a base e
cc exponential function of a specified argument,
cc in the form of a big integer.
cf exp The exponential function. Example: y = exp (x)
cf means y = e^x, where e is the base of natural
cf logarithms.
cg expected See "expected value".
cg expected value The expected value of a random variable v(x)^n with
cg a probability distribution p(x) from x1 to x2 is
cg <v^n>, and is equal to the integral from x1 to x2
cg of v(x)^n * p(x) * dx, divided by the integral from
cg x1 to x2 of p(x) dx.
cg The variance of v is <v^2> - <v>^2, and the
cg standard deviation of v is the square root of the
cg variance.
cg See "random walk", commands "bin", "pdf", "sample",
cg "spin", "walk".
cg exponent A floating point number may be represented by a
cg mantissa, e.g. 1.23456789, followed by an exponent
cg indicating a power of ten, e.g, e-3, e22, meaning
cg 10^(-3) or 0.001 and 10^22, respectively.
cg See "E, e, E+, e+", "E-, e-".
cg exponential An exponential probability distribution is a type of
cg probability bin or probability distribution function
cg (pdf) for which the relative differential probability
cg is an exponential function of the value of the random
cg variable, for a specified range of such values.
cg See "discrete event", "discrete object",
cg "discrete value", "uniform", "linear", "power-law".
cg See commands "bin", "pdf", "sample".
cg extend To extend two sides of a triangle, to make a new
cg triangle with twice the area, and a perimeter twice
cg that of the extended sides, see command "cute".
cg exterior An exterior mesh point is one that has exactly one
cg nearest neighbor in one or more of the three mesh
cg index directions k, l and m.
cg An exterior mesh block point is one that has exactly
cg one nearest neighbor in the mesh block, in one or
cg more of the three mesh directions k, l and m.
cc extr A synonym for extrema.
cg extr In display from commands "side" and "distance",
cg indicates an extremum on the quadric surface in a
cg specified vector direction. An estimate of the
cg proximal point on the quadric surface, nearest point
cg PNAME.
cg extract See "extract entries".
cg extract entries To extract entries from geom_base that contain any
cg desired key words, using UNIX command "grep":
cg
cg For a single key word KEYWORD1:
cg
cg grep -p KEYWORD1 geom_base >! OUT_FILE
cg
cg For each occurrence in file geom_base of the key
cg word KEYWORD1, write the entry containing KEYWORD1
cg into file OUT_FILE.
cg
cg For multiple key words KEYWORD1, KEYWORD2, ...:
cg
cg grep -p -f KEYWORD_FILE geom_base >! OUT_FILE
cg
cg For each occurrence in file geom_base of any of the
cg key words in file KEYWORD_FILE, write the entry
cg containing the key word into file OUT_FILE,
cg
cg where KEYWORD_FILE is a file containing all of the
cg key words, each on a single line.
cg extrema The extrema of a curve are any points on the curve,
cg for which the normal vector to the curve is parallel
cg to a specified axis in the plane of the curve
cg An extremum may be a maximum, a minimum or an
cg inversion point.
cg
cg To find the extrema of a quadric curve in a major
cg plane, use command "quadric" or "slice".
cg
cg The extrema of a polynomial equation in z = x + i*y,
cg P(z) = a0 + a1*z + a2*z^2 + a3*z^3 + a4*z^4 + ...
cg are at the roots of the derivative of the equation,
cg P'(z) = a1 + 2*a2*z + 3*a3*z^2 + 4*a4*z^3 + ...,
cg where the slope of the polynomial is zero.
cg See "quadratic", "cubic", "quartic".
cg See commands "root" and "roots".
cg
cg The extrema of a surface are any points or curves on
cg the surface, for which the normal vector to the
cg surface is parallel to a specified axis. An extremum
cg may be a maximum, minimum or saddle point.
cg
cg To find the extrema in any specified direction on a
cg quadric surface, use command "quadric" or "extrema".
cg
cg If a quadric surface is defined by a second order
cg implicit equation F(x,y,z) = 0, then the family of
cg quadric surfaces represented by the function
cg F(x,y,z) = C may have extrema at points on a line
cg or a curve. In general, such points or curves are
cg not proximal or distal to the extrema on the quadric
cg surface for which F = 0.
cg
cg See "proximal".
cc extrema Command to find the extreme points on one or all
cc quadric surfaces in a specified direction, and the
cc nature of the curvature of the surface at any such
cc points. See command "arc".
cc
cc Command "extrema" relates to objects: axisym, cone,
cc cylinder, ellipsoid, hyperb, plane, quadric, sphere,
cc symbol, vector.
cc
cc Forms include:
cc
ccin help extrema
ccin extrema [help]
cc
cc Display the command options.
cc
ccin extrema QNAME VNAME
cc
cc Find the extrema of quadric surface QNAME in the
cc direction of vector VNAME, and the nature of the
cc curvature of the surface and any such extrema.
cc
ccin extrema all VNAME
cc
cc Find the extrema of all quadric surfaces in the
cc direction of vector VNAME, and the nature of the
cc curvature of the surface and any such extrema.
cc
cc Synonyms: [extrema, extr], [help, h].
cg extreme To find the extreme points of a quadric surface in a
cg specified direction, see command "extrema".
F-------------------------------------------------------------------------------
cg F The general equation of a quadric surface is:
cg F(x,y,z) = 0. See "quadric surface".
cc F1-FN Arguments in command "variable", to be added (option
cc "+"), multiplied (option "*"), or their reciprocals
cc added (option "/"), or to be assigned to a set of
cc variables (option "data").
cg face A face of the mesh or the mesh block occurs wherever
cg one of the three mesh indices k, l and m has either
cg its minimum or maximum value, and each of the other
cg two indices ranges from its minimum value to its
cg maximum value. The mesh and the mesh block each have
cg six faces.
cc FACT An argument in command "quadric" option "*" or "/",
cc which will multiply or divide, respectively, the
cc coefficients of the implicit equation for a quadric
cc surface.
cc May be integer, floating point or a variable.
cc fact An option in command "big", to find the factorial
cc function of a specified big integer.
cc fact An option in commands "icalc" and "variable", to find
cc the factorial function (to be done on the following
cc argument, which must be a non-negative integer).
cg factf.mac A macro file for finding the prime factors of factorial
cg functions up to 1012!. In ~/work/geom/test .
cg factor To find all of the prime factors of any integer N from
cg 1 to 10^18 use command "factor".
cg See command "big", option "//".
cg factor See "prime factors", "scale factor", "view factor",
cg command "factor".
cc factor Command to find all of the prime factors and their
cc cofactors, for any specified positive integers M from
cc 1 to 10^18 and for each M, to find the Euler's
cc totient function for modulo M arithmetic, which is
cc the number of integers in the set (1, ..., M - 1)
cc that are relatively prime to M (have no common
cc factors other than 1), and to find the number of
cc integers that do have common factors with M.
cc See "totient function" and "modular arithmetic".
cc
cc Command "factor" relates to objects: symbol,
cc variable.
cc
cc Forms include:
cc
ccin help factor
ccin factor [help]
cc
cc Display the command options.
cc
ccin factor M1 M2 [thru] M3 ...
cc
cc For each integer M = M1, M2 [, through] M3, ...,
cc find all of the prime factors and their cofactors,
cc and find the number of integers in the set
cc (1, ..., M - 1) that are relatively prime to M
cc (have no common factors other than 1), and the
cc number of integers that do have common factors
cc with M. M must be from 1 to 10^18.
cc Negative values are changed to positive.
cc
cc Synonyms: [factor, totient], [help, h].
cg factorial The factorial function, defined only for non-negative
cg integers: n! = 1, n! = 1 * 2 * 3 * ... * n.
cg
cg The average derivative of n! with respect to n is:
cg from n - 1 to n : n! * (1 - 1/n)
cg from n to n + 1: n! * n
cg from n - 1 to n + 1: n! * (n + 1 - 1/n) / 2
cg and at n, approximatly for very large n:
cg n! * (n*log(n) + 1/2) / n
cg
cg The options in commands "icalc" and "variable" are:
cg
cg icalc M fact N
cg
cg Display M * N!. With M = 1, limited to 19!, with
cg 18 digits: 121645100408832000.
cg
cg variable VARNAME = A fact N
cg
cg Create variable VARNAME, equal to A * N!.
cg With A = 1.0, limited to 170!, with 307 digits:
cg 7.25741561530799896739672821112926311471699E+306.
cg
cgin big BIGNAME = BIGNAME2 fact
cg
cg Create big integer BIGNAME, equal to BIGNAME2!.
cg With the current limit of 1001 digits for big
cg integers, limited to 450!, with 1001 digits:
cg 1.733368733112632659344713146104579399677811E+1000.
cg
cg See "prime products".
cg factorial See "factorial factors".
cg factorial factors
cg The factorial function of n, n!, has the factors
cg 1 * 2 * 3 * ... * (n-1) * n. This may also be
cg expressed using only prime numbers as factors.
cg
cg Command "factor" may be used to find the prime
cg factors of a factorial.
cg
cg variable VARNAME = A fact N
cg
cg Create variable VARNAME, equal to A * N!.
cg With A = 1.0, limited to 170!.
cg
cg factor VARNAME
cg
cg Display the prime factors of VARNAME.
cg
cg In the case of factorials that are too big to store
cg as integers in a particular computer, the prime
cg factors of n! may be found as follows:
cg
cg n! = product {p(i)^m(i)}, for i = 1, imax,
cg
cg where the p(i) are all of the prime numbers less than
cg or equal to n, and the m(i) are the exponents
cg
cg m(i) = sum {int (p(imax) / p(i)^k)},
cg for k = 1, kmax > log (p(n)) / log (p(i)).
cg
cg where int (x) is the largest integer <= x, and kmax
cg is just sufficient to make the last term zero.
cg An upper bound on m(p(i)) is p(imax) / (p(i) - 1).
cg Note that in the sum, each term after the first is
cg equal to the preceding term divided by p(i).
cg
cg For example:
cg
cg 13! = 1*2*3*4*5*6*7*8*9*10*11*12*13 = 6227020800
cg
cg m(1) = int(13/1) + int(13/1) + ...
cg = infinity, but 1^infinity = 1, so no matter.
cg m(2) = int(13/2) + int(13/4) + int(13/8) + int(13/16)
cg = 6 + 3 + 1 + 0 = 10
cg m(3) = int(13/3) + int(13/9) + int(13/27)
cg = 4 + 1 + 0 = 5
cg m(5) = int (13/5) + int(13/25) = 2 + 0 = 2
cg m(7) = m(11) = m(13) = 1
cg
cg 13! = 2^10 * 3^5 * 5^2 * 7 * 11 * 13 = 6227020800
cg
cg In another example, 37! ~= 1.376375309122634E43,
cg the powers of 2, 3, 5, 7, 11, 13 and 17 are 34, 17,
cg 8, 5, 3, 2, and 2, respectively, and the remaining
cg powers of 19, 23, 29, 31, and 37 are all 1.
cg
cg This method is implemented for factorials up to
cg 1012! by using macro file factf.mac in directory
cg ~/work/geom/test . See test problem factf.mac.test
cg and output file factf.mac.hsp.
cg factors Selected metric conversion factors volume are in macro
cg file conv.mac in directory ~edwards/work/geom/test .
cg See "prime factors".
cc FADD An additive constant used to create a family of
cc variables with command "variable", option "series".
cc The floating point value var(n) of each variable is
cc generated from the preceding value var(n-1) by the
cc recursion relation:
cc
cc var(n) = FADD + FMULT * var(n-1), n = 2, NUMVAR + 1,
cc
cc where var(1) is the value of variable VAR(1).
cc fam A synonym for family.
cc family An option in command "zone", to create a family of
cc zones bounded by from one to three specified families
cc of quadric surfaces.
cc Synonyms: [family, fam].
cc
cc This command option can be replaced, using a do loop.
cc See "do loop use", commands "do", "enddo".
cg family A family is a group of objects of the same type,
cg sharing some characteristic, such as being parallel,
cg concentric, rotated, nested, coincident, congruent,
cg collinear, coplanar, etc. See "family of objects".
cg
cg One particular type of family of quadric surfaces
cg has an implicit equation F(x,y,z) = C, where C is an
cg arbitrary constant, different for each member of the
cg family. Sometimes the family member for which C = 0
cg is a different type of quadric surface than the other
cg members of the family, e.g., coincident planes
cg instead of parallel planes, intersecting planes
cg instead of hyperbolic cylinders, and cones instead of
cg hyperboloids. Also, changing C may change a
cg hyperboloid of one sheet to a hyperboloid of two
cg sheets or vice versa.
cg family See "family of objects".
cg family of objects
cg Some commands allow a family of objects to be created
cg with a single command. The object names are
cg generated by incrementing the preceding object name
cg by a specified number of characters or digits,
cg starting with an initial object name.
cg The objects are created by transforming the preceding
cg object in a specified way, starting from an initial
cg object, which itself is not part of the family.
cg See "increment names".
cg
cg See the following commands and options:
cg
cg COMMAND OPTIONS
cg
cg variable series
cg vector rotate, scale
cg
cg point rotate, scale, move, polygon,
cg polyhedron, brick
cg triangle increment
cg
cg axisym rotate, scale, move
cg cone rotate, scale, move, nest
cg cylinder rotate, scale, move, concentric
cg ellipsoid rotate, scale, move
cg hyperb rotate, scale, move
cg plane rotate, scale, move, parallel
cg quadric rotate, scale, move
cg sphere rotate, scale, move, concentric
cg
cg brick increment
cg tetrahedron increment
cg zone increment, family
cg fan To create a family of planes at equally spaced angles
cg around a common axis, use command "plane" with
cg option "rotate".
cg farthest See "maximum", "distal".
cg fatal See commands "undo", "redo", "indo".
cg See "error control", "fatal error".
cg fatal error See commands "undo", "redo", "indo".
cg See "error control".
cg Fibonacci See "Fibonacci series".
cg Fibonacci series To find the Fibonacci series for any two initial
cg integers, use input file fib.mac. The series ends
cg when the ratio of the last two terms converges.
cg field See "argument", "delimited", "delimiter",
cg "field delimiter", "field width", "vector field".
cg field delimiter See "delimiter".
cg field width To find the minimum field width for output of floating
cg point numbers, see "format".
cg figures See "significant figures".
cg filament A filament is a single continuous curve in 3-D space,
cg either bounded, as in a brick with zero thickness in
cg two of the three coordinate directions, or unbounded,
cg as in a track.
cg file See "files", "i/o", "input file", "output file".
cg files The command to execute GEOM is as follows:
cg
cg geom [INFILE [OUTFILE]]
cg
cg If an input file INFILE is not specified on the
cg execution line, the initial input medium is the
cg user's terminal.
cg
cg You may change the input to a file, or back to the
cg user's terminal, at any time, with command "input"
cg or "return". Options allow you to specify the line
cg numbers or the initial delimited character strings of
cg the first and last lines to be read, and to specify
cg that the contents of the input file only be
cg displayed, and not executed as commands.
cg
cg If an output file OUTFILE is not specified on the
cg execution line, the initial output file is
cg "geom_hsp".
cg
cg You may change the current output file at any time
cg with command "output".
cg All output sent to the current output file is also
cg sent to the user's terminal (usually too fast to
cg read, if input is from a file).
cg All non-null input lines typed by the user, or read
cg from the current input file, are printed in the
cg current output file, prefixed by the character ">"
cg or "<". This allows the output file(s) to be easily
cg edited into a new input file. See "input".
cg
cg A command summary file, "geom.cmd" is printed fore
cg each run, and contains all input lines, with aliases
cg expanded, except for commands "call", "i", "in",
cg "indo", "input", "r", "rd", "read", "redo", "return",
cg "rtn", "u" or "undo, which are not needed to produce
cg the same output as the original run.
cg
cg The files and directories associated with the GEOM
cg code are summarized in the file "geom_summ", and
cg described in the file "geom_files".
cg files See file geom_files in ~edwards/work/geom/doc .
cg final See "value".
cg final value See "value".
cc find A synonym for search.
cg find Find means search for in a list, or calculate or
cg determine by some other means.
cg See commands "dot", "cross", "root", "roots",
cg "distance", "intersect", "intcirc", "proximal",
cg "track", "side", "where", "area", "volume", "slice",
cg "extrema".
cg Also see command "list", and all commands that have
cg "list" as an option.
cg first See "first character".
cg first character The first character of any variable name must be a
cg lower or upper case letter or "$", "%" or "@".
cg When a variable name is used in place of an integer
cg of floating point argument, the first character may
cg be "-" to indicate use of the negative of the actual
cg variable value, but the "-" is removed to obtain the
cg actual variable name. See "arguments", "VARNAME".
cc fit An option in command "accelerate", to fit a parabolic
cc trajectory to the path of a uniformly accelerated
cc particle, given one, two or three points on the path
cc at one, two or three times.
cc If the initial position, the initial speed (but not
cc its vector components), the constant acceleration,
cc and a second point on the parabolic trajectory are
cc known, use command "accelerate", option "point",
cc with any initial velocity vector with the same
cc magnitude, to find the vector components of any
cc initial velocities that will make the path intersect
cc the second point. None, 1 or 2 may be possible.
cc fit An option in commands "axisym", "cone", "cylinder",
cc "disk", "ellipsoid", "plane", "polygon",
cc "polyhedron", "quadric", "sphere" and "hyperb",
cc between the object name and the specification of the
cc object. Usually means to fit the object to the
cc specified points and/or axis, etc.
cg fit A circle may be fitted to three points. See "circle".
cg A sphere may be fitted to two points, with the
cg center on a specified axis. See "sphere".
cg A sphere may be fitted to four points. See "sphere".
cg A circular ellipsoid (an oblate or prolate spheroid)
cg may be fitted to two points, if the center and axial
cg direction are specified.
cg See "ellipsoid".
cg An axially symmetric quadric surface may be fitted
cg to two points, if the center and axial direction are
cg specified.
cg See "axisym".
cg A linear trajectory may be fitted to two points
cg at two times. See command "accelerate".
cg A parabolic trajectory may be fitted to three points
cg at three times. See command "accelerate".
cg FLAG Indicates type of entry in geom_base:
cg cc Command
cg cd Directory name.
cg cf Function.
cg cg General information.
cg cn File name.
cg cpar Code parameter.
cg cx Executable file.
cg flags See commands "alias", "marker".
cg flip See "flip a coin".
cg flip a coin To randomly choose between two events:
cg
cg To spin the random number sequence first:
cg
cg spin random
cg
cg Set the random number seed to a new value based on
cg the date and clock. This will make any results
cg based on random numbers not reproducible.
cg
cg spin N
cg
cg Use up the next N random numbers.
cg
cg icalc 1 ran 2
cg
cg Randomly sample one of the integers 1 and 2.
cg floating See "floating point".
cg floating point A decimal floating point argument is a delimited
cg character string consisting of a plus (optional) or
cg minus sign, followed by a mantissa consisting only
cg of one or more of the numerals 0-9, and (optionally)
cg a decimal point (in any order), followed (optionally)
cg by an exponent consisting (optionally) by D, d, E or
cg e, followed by a plus (optional) or minus sign,
cg followed by one or more of the numerals 0-9. If
cg neither a decimal point or an exponent is present,
cg the string may also be interpreted as an integer.
cg Any number of meaningless zeroes may precede the
cg leftmost nonzero digit of the mantissa, to the left
cg of any decimal point or sign.
cg Any number of meaningless zeroes may precede the
cg leftmost nonzero digit of the exponent.
cg On the YANA machines, using 64 bit floating point
cg numbers, the mantissa may have a precision of about
cg 1 part in 10^16 (53 bits). Exponents may range from
cg about -308 to 308.
cg
cg Any decimal floating point argument in a command may
cg be replaced by an integer or floating point variable,
cg or by a symbolic word which, after symbol
cg replacement, is an integer or floating point value.
cg
cg Before any command is executed, all floating point
cg variables used for floating point arguments are
cg replaced by their floating point values.
cg
cg See "compress", "integer", "significant figures",
cg command "hex".
cc FMULT In command "variable", option "series", a multiplier
cc used to create a series of variables.
cc Each variable var(n) is generated from the preceding
cc variable var(n-1) by the recursion relation:
cc
cc var(n) = FADD + FMULT * var(n-1), n = 2, NUMVAR + 1,
cc
cc where var(1) is the value of variable VAR(1).
cc May be integer, floating point or an integer or
cc floating point variable.
cc FMULT In command "brick", option "x", "y", "z", "rcyl",
cc "theta", "rsph" or "phi", a multiplier used to create
cc a family of bricks. The ratio of the thickness of
cc each brick in the family to that of the preceding
cc brick is FMULT, which must be positive. May be
cc integer, floating point or a variable.
cc foc A synonym for focus.
cc focal A synonym for focus.
cg focal See "focus".
cg focal point See "focus".
cg foci See "focus".
cg focus A quadric surface may have one or more foci, or focal
cg points, if one of the types:
cg parabolic cylinder, hyperbolic cylinder,
cg elliptic cylinder, hyperbolic paraboloid,
cg elliptic paraboloid, circular paraboloid, or
cg ellipsoid. See a math or geometry handbook for
cg definitions and equations. For a circular cone,
cg the focal point is at the vertex.
cg
cg For the parabola or parabolic cylinder:
cg QY * y + QXX * x^2 = 0, for all z,
cg the focus is at x = 0, y = -0.25 * QY / QXX.
cg
cg For the parabola or parabolic cylinder:
cg QZ * z + QXX * x^2 = 0, for all y,
cg the focus is at x = 0, z = -0.25 * QZ / QXX.
cg
cg For the hyperbola or hyperbolic cylinder:
cg QC + QXX * x^2 + QYY * y^2 = 0, for all z,
cg (QXX > 0, QYY < 0), the two foci are at
cg x = 0, y = (+/-)sqrt (QC / QXX - QC / QYY), (QC > 0),
cg y = 0, x = (+/-)sqrt (QC / QYY - QC / QXX), (QC < 0).
cg
cg For the ellipse or elliptic cylinder:
cg QC + QXX * x^2 + QYY * y^2 = 0, for all z,
cg (QC < 0, QXX => QYY > 0), the two foci are at:
cg x = 0, y = (+/-)sqrt (QC / QXX - QC / QYY).
cg
cg For the circular or elliptic paraboloid:
cg QZ * z + QXX * x^2 + QYY * y^2 = 0,
cg (QXX => QYY => 0), the focus is at x = y = 0,
cg z = -0.25 * QZ / QYY, in plane x = 0, and
cg z = -0.25 * QZ / QXX, in plane y = 0.
cg
cg For the hyperboloid of one sheet:
cg QC + QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QC < 0, QXX => QYY > 0, QZZ < 0),
cg the two foci are at z = 0,
cg y = (+/-)sqrt (QC / QZZ - QC / QYY), in plane x = 0,
cg x = (+/-)sqrt (QC / QZZ - QC / QXX), in plane y = 0.
cg
cg For the hyperboloid of two sheets:
cg QC + QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QC > 0, QXX => QYY > 0, QZZ < 0),
cg the two foci are at x = y = 0,
cg z = (+/-)sqrt (QC / QYY - QC / QZZ), in plane x = 0,
cg z = (+/-)sqrt (QC / QXX - QC / QZZ), in plane y = 0.
cg
cg For the ellipsoid:
cg QC + QXX * x^2 + QYY * y^2 + QZZ * z^2 = 0,
cg (QC < 0, QXX => QYY => QZZ => 0),
cg the two foci are at:
cg z = (+/-)sqrt (QC / QYY - QC / QZZ), in plane x = 0,
cg z = (+/-)sqrt (QC / QXX - QC / QZZ), in plane y = 0,
cg y = (+/-)sqrt (QC / QXX - QC / QYY), in plane z = 0.
cc focus An option in command "axisym", to fit an axially
cc symmetric quadric surface to a specified focal point
cc and axis, given two points in the surface.
cc Synonyms: [focus, foc, focal].
cg form See "command form".
cg format The format to use for output of a floating point
cg number, to minimize the space required for a given
cg number of significant figures, is AB.C, which may be
cg found from:
cg
cg x = the value of the floating point number.
cg E = exponent of x = int (log10 (abs (x))).
cg N = the number of significant figures in output.
cg K = 0 for positive x, 1 for negative x.
cg
cg E A B C
cg --------- --- ------------- ---------
cg < -3 1pe N + 6 + K N - 1
cg -3 to 0 f N + 2 + K - E N - 1 - E
cg 0 to N - 1 f N + 2 + K N - 1 - E
cg N to N + 2 f 3 + K + E 0
cg > N + 2 1pe N + 6 + K N - 1
cg
cg After the output is produced, further reductions may
cg be obtained by editing the output file with UNIX text
cg editor VI as follows:
cg
cg command purpose
cg ------------ --------------------------------------
cg :%s/00*E/E/g eliminate trailing zeros in mantissa
cg :%s/E+00//g eliminate zero exponent
cg :%s/E+0*/+/g minimize characters in positive
cg exponent
cg :%s/E-0*/-/g minimize characters in negative
cg exponent
cg :%s/\.\>//g eliminate final decimal point of
cg integer
cg :%s/ */ /g eliminate multiple blank spaces
cg :%s. *$//g eliminate trailing blanks at end of
cg line
cg fraction See "continued fraction", "fractional dist",
cg "rational fraction".
cg fractional See "fractional dist".
cg fractional dist A useful measure of the local coordinates of a point is
cg often the fractional distance from the beginning to
cg the end of a line, or the fractional distance from
cg one edge of a polygon to an opposite edge, or the
cg fractional distance from one face of a polyhedron to
cg an opposite face.
cg Used in GEOM for bricks, in the sense of dividing
cg the brick into fractional volumes.
cg See "local coordinates", "vertex weights".
cg frequency To randomly sample photon frequencies or energies from
cg a Planck spectrum or a Wien spectrum:
cg
cg bin BINAME [planck,wien] BTEMP
cg
cg Create probability bin BINAME with relative total
cg probability PRTOT, with a probability distribution
cg of a [Planck, Wien] spectrum at temperature BTEMP.
cg The random variable is a frequency XNU (same units
cg as BTEMP) from that spectrum, ranging from 0 to
cg infinity. See "Planck spectrum", "Wien spectrum".
cg 1 K (Kelvin) = 8.617385E-5 eV (+/- 8.5 ppm).
cg
cg pdf PDFNAME = BINAME
cg
cg Create new pdf PDFNAME, consisting only of the
cg probability bin BINAME.
cg
cg sample PDFNAME [NSAMP|1]
cg
cg Randomly sample from probability distribution
cg function (pdf) PDFNAME, to obtain NSAMP values of
cg XNU. If specified, NSAMP must be a positive
cg integer or integer variable. Only the first 26
cg samples will be displayed on the user's
cg terminal. All will be displayed in the current
cg output file. If two or more values are sampled,
cg the total, the minimum and maximum, the mean and
cg the standard deviation are displayed.
cg frequency See "frequency ratios".
cg frequency ratios For the frequency ratios of an equally-tempered musical
cg scale, see "equally-tempered", "scale.mac".
cg FU See "FU, FV, FW".
cc FU, FV, FW Fractional distances (on a volume basis) of a point
cc between the minimum and maximum coordinates of a
cc brick, in the u, v and w coordinate directions,
cc which may be (x, y, z), (rcyl, theta, z) or
cc (rsph, theta, phi), based on the coordinate system
cc used to create the brick. For example, the centroid
cc of a brick is at FU = 0.5, FV = 0.5, FW = 0.5.
cc Used in command "point'.
cc FUNCTION In command "icalc", indicates a type of mathematical
cc operation to be carried out, with two integer
cc arguments, in format "M FUNCTION N":.
cc
cc FUNCTION | value
cc ---------|--------------------------------------
cc + | M + N
cc - | M - N
cc * | M * N
cc / | M / N (N nonzero)
cc ^ | M^N (N > -1)
cc fact | M * N! (-1 < N < 20)
cc abs | M * iabs(N)
cc ---------|--------------------------------------
cc max | max0 (M, N)
cc min | min0 (M, N)
cc mod | mod (M, N) (N nonzero)
cc sign | isign (M, N)
cc ---------|--------------------------------------
cc comp. | Boolean complement
cc .not. | Boolean not
cc .and. | Boolean intersection
cc .nand. | Boolean nonintersection
cc .or. | Boolean union
cc .nor. | Boolean nor
cc .xor. | Boolean exclusive or
cc .xnor. | Boolean equivalence
cc ---------|--------------------------------------
cc perm | M perm N (permutations, P(M,N))
cc comb | M comb N (combinations, C(M,N))
cc ------------------------------------------------
cc
cc Synonyms: [^, **], [.and., .int.], [.or., .un.]
cc [.xnor., .eqv.].
cc FUNCTION In command "variable", indicates a type of mathematical
cc operation to be carried out, with two numerical
cc arguments, which may be integer or floating point
cc values, variables, or symbolic words which, after
cc symbol replacement, are integer or floating point,
cc in format "A FUNCTION B":
cc
cc FUNCTION | value || FUNCTION | value
cc ---------|-----------------||----------|-------------
cc + | A + B || * | A * B
cc - | A - B || / | A / B
cc ^ | A^B || exp | A*exp(B)
cc sqrt | A*sqrt(B) || curt | A*B^(1/3)
cc log | A*log(B) || log10 | A*log10(B)
cc sin | A*sin(B) || asin | A*asin(B)
cc cos | A*cos(B) || acos | A*acos(B)
cc tangent | A*tan(B) || atan | A*atan(B)
cc atan2 | atan2(A,B) ||
cc sinh | A*sinh(B) || asinh | A*atanh(B)
cc cosh | A*cosh(B) || acosh | A*acosh(B)
cc tanh | A*tanh(B) || atanh | A*atanh(B)
cc abs | A*abs(B) || sign | sign(A,B)
cc int | A*aint(B) || nint | A*nint(B)
cc max | amax1(A,B) || min | amin1(A,B)
cc mod | amod(A,B) || |
cc ran | a random number || |
cc | between A and B || |
cc -----------------------------------------------------
cc
cc Synonyms: [^, **], [tangent, tan].
cg function To do simple mathematics, including the use of in-line
cg FORTRAN functions, use command "icalc" or "variable".
cg See command "math".
cg function See "Totient function", "totient function",
cg "zeta function".
cg FV See "FU, FV, FW".
cc FVAR The numerical value of a floating point variable
cc specified with command "variable". If FVAR is within
cc fraction TOL of an integer, the variable will be an
cc integer variable. FVAR itself may be numerical, the
cc name of an integer or floating point variable, or a
cc symbolic word which, after symbol replacement, is
cc integer or floating point. See "AVAR", "IVAR".
cg FW See "FU, FV, FW".
G-------------------------------------------------------------------------------
cg games Command files allowing several games to be played are cg in directory ~/work/geom/test . These files contain cg instructions on how to use them, and include: cg cg card.mac Deals from a deck of cards. cg dice.mac Rolls dice. cg tictactoe.mac Plays tic-tac-toe. cg GAMMA The random variable in a relativistic Maxwellian cg probability distribution function is BETA, the ratio cg of the particle velocity, v, to the velocity of cg light, c = 299,792,458 m / s. cg A related variable is the relativistic function cg GAMMA = 1 / sqrt (1 - BETA^2). cg For RATIO << 1, where RATIO is the dimensionless cg ratio of gas temperature to particle rest mass cg energy, the expected value of BETA is approximately cg 1.60 * sqrt (RATIO), with a standard deviation of cg approximately 0.67 * sqrt (RATIO), and the expected cg value of BETA^2 is 3 * RATIO. cg For RATIO >> 1, the expected value of BETA is cg approximately 1 - 0.23 / RATIO^2, with a standard cg deviation of approximately 1.26 / RATIO^2, cg the expected value of BETA^2 is approximately cg 1 - 0.46 / RATIO^2, the expected value of GAMMA is cg 3 * RATIO, with a standard deviation of approximately cg 1.73 * RATIO, and the expected value of GAMMA^2 is cg 12 * RATIO^2. cc gcd An option in commands "icalc" and "variable", to find cc the greatest common divisor of a pair of numbers. cc For more than two numbers, repeat the command with cc the result and the next number. cc See "common divisor". cg GEOM The code name used in the output file. cd geom Directory for GEOM files. cd Open YANA Cluster: ~edwards/geom cd Subdirectories: doc, make, test cg geom See "GEOM execution". cx GEOM execution Execution line command to run GEOM, the code, cx application or executable program described in this cx database. Although printed as "GEOM" in this cx database, use lower case "geom" to execute. cx cx In Open YANA Cluster: ~edwards/work/bin/geom cx cx Forms include: cx cxin geom cxin geom tty cxin geom IN_FILE cxin geom IN_FILE geom_hsp cxin geom IN_FILE OUT_FILE cxin geom IN_FILE OUT_FILE > STDOUT cx cx Execute the GEOM code. If the input file tty or cx IN_FILE is not specified, it defaults to tty, cx indicating the user's terminal. cx File IN_FILE must not be geom_hsp or geom_cmd, and cx if not tty, it's first line should be command cx "title". cx cx If IN_FILE is specified, and the output file cx geom_hsp or OUT_FILE is not specified, it defaults cx to geom_hsp. cx File OUT_FILE must not be tty or geom_cmd. cx cx If the standard output STDOUT is not specified, it cx defaults to the users terminal. File STDOUT may be cx specified to prevent large amounts of data from cx being displayed on the user's terminal. cx File STDOUT must not be tty, geom_hsp or geom_cmd. cx cx The various possibilities are described below. cx cx geom cx geom tty cx geom tty geom_hsp cx cx Execute the GEOM code, with input from the user's cx terminal, and output to file geom_hsp and to the cx user's terminal, and a command summary to file cx geom_cmd. cx cx If executing GEOM for the first time, after cx (optionally) specifying the problem title, type cx command "help", then any other desired commands. cx cx geom IN_FILE cx geom IN_FILE geom_hsp cx cx Execute the GEOM code, with input from file cx IN_FILE, and output to file geom_hsp and to the cx user's terminal, and a command summary to file cx geom_cmd. cx cx geom IN_FILE OUT_FILE cx cx Execute the GEOM code, with input from file cx IN_FILE, and output to file OUT_FILE and to the cx user's terminal, and a command summary to file cx geom_cmd. cx cx geom IN_FILE OUT_FILE > STDOUT cx cx Execute the GEOM code, with input from file cx IN_FILE, and output to file OUT_FILE and to file cx STDOUT, and a command summary to file geom_cmd. cx cx NOTE: Do NOT use the UNIX execution line symbol cx "<" to redirect the standard input. You may use cx the UNIX execution line symbol ">" to redirect the cx standard output. Use ">!" to write over an existing cx file STDOUT. cx cx NOTE: input will return to the user's terminal after cx the last line of file IN_FILE, unless GEOM first cx executes command "input", "return" or "end". cx See commands "if", "endif". cg geometric To display, create and use geometric objects, see the cg entries and commands: point, cluster, mesh, line, cg triangle, polygon, disk, plane, sphere, cylinder, cg cone, ellipsoid, axisym, quadric, polyhedron, cg tetrahedron, brick, zone. cg geometric See "geometric series". cg geometric optics See "ray tracing". cg geometric series A geometric series is one in which the value of each cg term after the first term differs from the preceding cg term by a constant ratio. See command "ratio". cg To create a family of variables whose values form a cg geometric series: cg cg variable VAR(1) = VALUE cg cg Create variable VAR(1), with the value of the first cg term. cg cg variable VAR(2) series NUMVAR INC VAR(1) 0 FMULT cg cg Create a series of NUMVAR variables VAR(2), ..., cg with names incremented by INC characters, with each cg value equal to the preceding value multiplied by cg FADD, starting from the value of variable VAR(1). cg See "increment names". cg cg To create a family of points, planes or quadric cg surfaces in which the distance of each from an cg invariant point, axis or plane forms a geometric cg series, use option "scale" of command "point", cg "plane", "sphere", "cylinder", "cone", "ellipsoid", cg "axisym" or "quadric". cn geom_APT A list of all APT subroutines, with use by the GEOM cn code indicated. See "calls", "map". cn geom_APT.not A list of APT subroutines not used by GEOM. cn geom_base This file. Database of commands, key words, and all cn related terminology in GEOM. cn Long name: ~edwards/work/geom/doc/geom_base cn cn In Open YANA Cluster: ~edwards/work/geom/doc cn cn To display entries while executing GEOM, see cn command "display". cn geom_cmd A file containing all of the input commands needed to cn reproduce the output produced by the current problem, cn with aliases expanded, and with commands "call", cn "goto", "i", "in", "indo", "input", "r", "rd", cn "read", "redo", "return", "rtn", "u" and "undo cn converted to comments, preceded by "! ". cn The latter commands are preceded by the character cn "<" in the current output file, initially geom_hsp. cn cn May not be specified as an input file on the cn execution line, e.g. "geom geom_cmd" will not work. cn cn May be used as an input file after execution, using cn command "input", but limited to the input commands cn already written into it. cn geom_commands A list of all GEOM commands, with a brief description cn of their function. cn Long name: ~edwards/work/geom/doc/geom_commands cn geom_define A list of all of the entries in this file, without cn definitions. cn geom_diff.all An executable script to compare old and new GEOM test cn problem output files, after running geom_mv.hsp.all cn and geom_exe.all. cn geom_exe.all An executable script to run all GEOM test problems, cn after running geom_mv.hsp.all, and before running cn geom_diff.all. cn geom_files A summary of all subroutines and files associated with cn the GEOM code. cn Long name: ~edwards/work/geom/doc/geom_files cn geom_head A summary of the header sections from all GEOM cn subroutines cn Long name: ~edwards/work/geom/doc/geom_head cn geom_head.make A file used to create file geom_head. cn Long name: ~edwards/work/geom/doc/geom_head.make cn geom_hsp The initial output file of problem results. cn See "output file", "geom_cmd". cn Do not specify as the input file on the GEOM cn execution line, e.g., "geom geom_hsp", or during a cn GEOM run, unless the current output file is not cn geom_hsp, and then only to display lines or execute cn lines that have the form of commands. cn geom_input A list of all GEOM code command lines, including all cn options. cn Long name: ~edwards/work/geom/doc/geom_input cn geom_internal A list of all GEOM internal parameters and variables in cn file store.h, alphabetic and by data groups, with cn definitions. See command "debug". cn geom_log A log of the development, modifications and maintenance cn of the GEOM code. cn Long name: ~edwards/work/geom/doc/geom_log cn geom_make A summary of procedures to maintain and update the cn GEOM code, and add new subroutines. cn Long name: ~edwards/work/geom/make/geom_make cn geom_mv.hsp.all An executable script to rename all GEOM test problem cn output files, by appending the suffix ".old", cn before running geom_exe.all and geom_diff.all. cn geom_summ A summary of the names and locations of the GEOM code cn files. cn Long name: ~edwards/work/geom/doc/geom_summ cn geom_tests A summary of all command lines in GEOM test files. cn Long name: ~edwards/work/geom/doc/geom_tests cg getting started See "starting up". cc go to See command "goto". cg golden See "golden ratio". cg golden ratio The "golden ratio" 0.5 * (1.0 + sqrt (5.0)) or cg 1.618033988749894848204586834365638117720309189 cg Generated as a variable at the beginning of a cg GEOM run. The roots of x^2 - x - 1 = 0 are cg rgold and 1 - rgold. Also rgold = 1 + 1 / rgold. cc Store as a big integer with command "input big.mac", cc with file big.mac in the same directory as GEOM. cc goto Command to jump to a new command in the current input cc file, rather than the next command in sequence. cc See command "input". cc cc Command "goto" relates to objects: symbol, variable. cc cc Note: do not use a "goto" command when input is from cc the user's terminal. cc cc Note: do not use a "goto" command to jump into or cc out of a do loop. cc cc Note: Do not use the statement separator ";" on the cc same line as this command. cc cc Forms include: cc ccin help goto ccin goto [help] cc cc Display the command options. cc ccin goto STRING1 cc cc Read the current input file, from the first line cc starting with STRING1 to the end of the file, cc