Provided by: grap_1.44-1_amd64 bug

NAME

     grap — Kernighan and Bentley's language for typesetting graphs

SYNOPSIS

     grap [-d defines_file] [-D] [-l] [-M include path] [-R] [-r] [-v] [-u] [-C] [-c] [-h]
          [filename ...]

DESCRIPTION

     grap is an implementation of Kernighan and Bentley's language for typesetting graphs, as
     described in ``Grap-A Language for Typesetting Graphs, Tutorial and User Manual,'' by Jon L.
     Bentley and Brian W.  Kernighan, revised May 1991, which is the primary source for
     information on how to use grap.  As of this writing, it is available electronically at
     http://www.kohala.com/start/troff/cstr114.ps.  Additional documentation and examples,
     packaged with grap, may have been installed locally as well.  If available, paths to them
     can be displayed using grap -h or grap -v (or grap --help / grap --version)

     This version is a black box implementation of grap, and some inconsistencies are to be
     expected.  The remainder of this manual page will briefly outline the grap language as
     implemented here.

     grap is a pic(1) pre-processor.  It takes commands embedded in a troff(1) source file which
     are surrounded by .G1 and .G2 macros, and rewrites them into pic commands to display the
     graph.  Other lines are copied.  Output is always to the standard output, which is usually
     redirected.  Input is from the given filenames, which are read in order.  A filename of - is
     the standard input.  If no filenames are given, input is read from the standard input.

     Because grap is a pic preprocessor, and GNU pic will output TeX, it is possible to use grap
     with TeX.

     The -d option specifies a file of macro definitions to be read at startup, and defaults to
     /usr/share/grap/grap.defines .  The -D option inhibits the reading of any initial macros
     file (the -l flag is a synonym for -D, though I do not remember why).  The defines file can
     also be given using the GRAP_DEFINES environment variable. (See below).

     -v prints the version information on the standard output and exits.  --version is a synonym
     for -v.

     -u makes labels unaligned by default.  This version of grap uses new features of GNU pic to
     align the left and right labels with the axes, that is that the left and right labels run at
     right angles to the text of the paper.  This may be useful in porting old grap programs.  -c
     makes plot strings unclipped by default.  Some versions of grap allow users to place a
     string anywhere in the coordinate space, rather than only in the frame.  By default this
     version of grap does not plot any string centered outside the frame.  -c allows strings to
     be placed anywhere.  See also the clipped and unclipped string modifiers described in the
     plot statement.

     -M is followed by a colon-separated list of directories used to search for relative
     pathnames included via copy.  The path is also used to locate the defines file, so if the -d
     changes the defines file name to a relative name, it will be searched for in the path given
     by -M.  The search path always includes the current directory, and by default that directory
     is searched last.

     All numbers used internally by grap are double precision floating point values.  Sometimes
     using floating point numbers has unintended consequences.  To help avoid these problems,
     grap can use two thresholds for comparison of floating point numbers, set by -R or -r.  The
     -R flag sets coarse comparison mode, which is suitable for most applications.  If you are
     plotting small values – less than 1e-6 or so – consider using -r which uses very fine
     comparisons between numbers.  You may also want to rescale your plotted values to be larger
     in magnitude. The coarse comarisons are used by default.

     To be precise, the value by which two numbers must differ for grap to consider them not
     equal is called the comparison limit and the smallest non-zero number is called the minimum
     value.  The values a given version of grap uses for these are included in the output of -v
     or -h.

     All grap commands are included between .G1 and .G2 macros, which are consumed by grap.  The
     output contains pic between .PS and .PE macros.  Any arguments to the .G1 macro in the input
     are arguments to the .PS macro in the output, so graphs can be scaled just like pic
     diagrams.  If -C is given, any macro beginning with .G1 or .G2 is treated as a .G1 or .G2
     macro, for compatibility with old versions of troff.  Using -C also forces pure troff syntax
     on embedded font change commands when strings have the size attribute, and all strings to be
     unclipped.

     The -h flag prints a brief help message and exits.  --help is a synonym for -h.

     It is possible for someone to cause grap to fail by passing a bad format string and data to
     the sprintf command.  If grap is integrated as part of the printing system, this could
     conceivably provided a path to breaching security on the machine.  If you choose to use grap
     as part of a printing system run by the super-user, you should disable sprintf commands.
     This can be done by calling grap with the -S flag, setting the GRAP_SAFER environment
     variable, or compiling with the GRAP_SAFER preprocessor symbol defined.  (The GNU configure
     script included with grap will define that preprocessor symbol if the --with-grap-safe
     option is given.)

     The grap commands are sketched below.  Refer to Kernighan and Bentley's paper for the
     details.

     New versions of groff(1) will invoke grap if -G is given.

   Commands
     Commands are separated from one another by newlines or semicolons (;).

     frame [line_description] [ht height | wid width] [[(top|bottom|left| right)
     line_description] ...]

     frame [ht height | wid width] [line_description] [[(top|bottom|left| right)
     line_description] ...]

           This  describes how the axes for the graph are drawn. A line_description is a pic line
           description, e.g., dashed 0.5, or the literal solid.  It  may  also  include  a  color
           keyword  followed  by  the  color  to  draw  the  string  in double quotes.  Any color
           understood by the underlying groff system can be used.  Color can only be  used  under
           GNU   pic,   and   is  not  available  in  compatibility  mode.   Similarly,  for  pic
           implementations that understand thickness, that attribute may  be  used  with  a  real
           valued parameter.  Thickness is not available in compatibility mode.

           If  the  first  line_description  is  given,  the frame is drawn with that style.  The
           default is solid.  The height and width of the frame can also be specified in  inches.
           The  default  line  style  can  be  over-ridden  for  sides of the frame by specifying
           additional parameters to frame.

           If no plotting commands have been given before the frame command is issued, the  frame
           will  be output at that point in the plotting stream relative to embedded troff or pic
           commands.  Otherwise the frame  is  output  before  the  first  plotted  object  (even
           invisible ones).

           ht  and  wid  are  in  inches  by default, but can be any groff unit.  If omitted, the
           dimensions are 2 inches high by 3 inches wide.

     coord [name] [x expr, expr] [y expr, expr] [log x | log y | log log]

           The coord command specifies a new coordinate system or  sets  limits  on  the  default
           system.  It defines the largest and smallest values that can be plotted, and therefore
           the scale of the data in the frame.  The limits for the x and y coordinate systems can
           be  given  separately.   If a name is given, that coordinate system is defined, if not
           the default system is modified.

           A coordinate system created by one coord command may be modified by  subsequent  coord
           commands.   A  grap program may declare a coordinate space using coord, copy a file of
           data through a macro that plots the data and finds its maxima  and  minima,  and  then
           define the size of the coordinate system with a second coord statement.

           This command also determines if a scale is plotted logarithmically.  log log means the
           same thing as log x log y.

     draw [line_name] [line_description] [plot_string]

           The draw command defines the style with which  a  given  line  will  be  plotted.   If
           line_name  is  given,  the  style  is associated with that name, otherwise the default
           style  is  set.   line_description  is  a  pic  line  description,  and  the  optional
           plot_string is a string to be centered at each point.  The default line description is
           invis, and the default plotting string is a centered bullet, so by default each  point
           is  a  filled  circle,  and they are unconnected.  If points are being connected, each
           draw command ends any current line and begins a new one.

           When defining a line style, that is the first draw command  for  a  given  line  name,
           specifying  no  plot  string means that there are to be no plot strings.  Omitting the
           plot string on subsequent draw commands addressing the same named line  means  not  to
           change the plot string.  If a line has been defined with a plot string, and the format
           is changed by a  subsequent  draw  statement,  the  plot  string  can  be  removed  by
           specifying "" in the draw statement.

           The  plot  string  can  have  its  format  changed  through  several string_modifiers.
           String_modifiers are described in the description of the plot command.

           The standard defines file includes several macros useful as  plot  strings,  including
           bullet, square, and delta.

           new is a synonym for draw.

     next [line_name] at [coordinates_name] expr, expr [line_description]

           The next command plots the given point using the line style given by line_name, or the
           default if none is given.  If line_name is given, it should have been  defined  by  an
           earlier  draw  command, if not a new line style with that name is created, initialized
           the same way as the default style.  The two expressions  give  the  point's  x  and  y
           values,  relative  to  the  optional  coordinate system.  That system should have been
           defined by an earlier coord  command,  if  not,  grap  will  exit.   If  the  optional
           line_description  is  given,  it  overrides the style's default line description.  You
           cannot over-ride the plotting string.  To use a different plotting string use the plot
           command.

           The coordinates may optionally be enclosed in parentheses: (expr, expr)

     quoted_string [string_modifiers] [, quoted_string [string_modifiers]] ...  at
     [coordinates_name] expr, expr

     plot expr [format_string] at [coordinates_name] expr, expr

           These commands both plot a string at the given point.  In the first case  the  literal
           strings   are  stacked  above  each  other.   The  string_modifiers  include  the  pic
           justification modifiers (ljust, rjust, above, and below), and  absolute  and  relative
           size  modifiers.   See  the pic documentation for the description of the justification
           modifiers.  grap also supports the aligned and unaligned modifiers which  are  briefly
           noted in the description of the label command.

           The  standard  defines  file includes several macros useful as plot strings, including
           bullet, square, and delta.

           Strings placed by either format of the plot command are restricted to being within the
           frame.  This can be overridden by using the unclipped attribute, which allows a string
           to be plotted in or out of the frame.  The -c  and  -C  flags  set  unclipped  on  all
           strings, and to prevent a string from being plotted outside the frame when those flags
           are active, the clipped attribute can be used to  retore  clipping  behavior.   Though
           clipped  or  unclipped  can  be  applied  to  any string, it only has meaning for plot
           statements.

           size expr sets the string size to expr points.  If expr is preceded by a + or  -,  the
           size is increased or decreased by that many points.

           If  color  and  a  color name in double quotes appears, the string will be rendered in
           that color under a version of GNU troff that supports color.  Color is  not  available
           in compatibility mode.

           In  the  second  version,  the  expr is converted to a string and placed on the graph.
           format_string is a printf(3) format string.   Only  formatting  escapes  for  printing
           floating point numbers make sense.  The format string is only respected if the sprintf
           command is also active.  See the description  of  sprintf  for  the  various  ways  to
           disable  it.   Plot  and  sprintf  respond  differently  when  grap is running safely.
           Sprintf ignores any arguments, passing the format string through without substitution.
           plot ignores the format string completely, plotting expr using the "%g" format.

           Points are specified the same way as for next commands, with the same consequences for
           undefined coordinate systems.

           The second form of this command is because the first form can  be  used  with  a  grap
           sprintf expression (See Expressions).

     ticks (left|right|top|bottom)[ (in|out) [expr]] [on|auto coord_name]

     ticks (left|right|top|bottom) (in|out) [expr] [up expr | down expr | left expr | right expr]
     at [coord_name] expr [format_string] [[, expr [format_string]] ...]

     ticks (left|right|top|bottom) (in|out) [expr] [up expr | down expr | left expr | right expr]
     from [coord_name] start_expr to end_expr [by [+|-|*|/] by_expr] [format_string]

     ticks [left|right|top|bottom] off

           This  command  controls  the  placement  of ticks on the frame.  By default, ticks are
           automatically generated on the left and bottom sides of the frame.

           The first version of this command turns on the automatic tick generation for  a  given
           side.   The  in or out parameter controls the direction and length of the ticks.  If a
           coord_name is specified, the ticks are automatically generated using  that  coordinate
           system.   If  no  system is specified, the default coordinate system is used.  As with
           next and plot, the coordinate system must be declared before the ticks statement  that
           references  it.   This  syntax  for  requesting  automatically  generated  ticks is an
           extension, and will not port to older grap implementations.

           The second version of the ticks command overrides the automatic placement of the ticks
           by specifying a list of coordinates at which to place the ticks.  If the ticks are not
           defined with respect to the default coordinate system, the coord_name  parameter  must
           be  given.   For  each  tick  a  printf(3)  style  format  string  can  be given.  The
           format_string defaults to "%g".  The format string can also take string  modifiers  as
           described  in  the plot command.  To place ticks with no labels, specify format_string
           as "".

           If sprintf is disabled, ticks behaves as plot with respect to the format string.

           The labels on the ticks may be shifted by specifying a direction and the  distance  in
           inches to offset the label.  That is the optional direction and expression immediately
           preceding the at.

           The third format of the ticks command over-rides the default tick  generation  with  a
           set  of ticks ar regular intervals.  The syntax is reminiscent of programming language
           for loops.  Ticks are placed starting at start_expr ending at end_expr one unit apart.
           If  the by clause is specified, ticks are by_expr units apart.  If an operator appears
           before by_expr each tick is operated on by that operator instead of +.  For example

                       ticks left out from 2 to 32 by *2

           will put ticks at 2, 4, 8, 16, and 32.  If format_string is specified, all  ticks  are
           formatted using it.

           The parameters preceding the from act as described above.

           The  at  and for forms of tick command may both be issued on the same side of a frame.
           For example:

                       ticks left out from 2 to 32 by *2
                       ticks left in 3, 5, 7

           will put ticks on the left side of the frame pointing out at 2, 4, 8, 16, and  32  and
           in at 3, 5, and 7.

           The  final  form  of  ticks  turns off ticks on a given side.  If no side is given the
           ticks for all sides are cancelled.

           tick is a synonym for ticks.

     grid (left|right|top|bottom) [ticks off] [line_description] [up expr | down expr | left expr
     | right expr] [on|auto [coord_name]]

     grid (left|right|top|bottom) [ticks off] [line_description] [up expr | down expr | left expr
     | right expr] at [coord_name] expr [format_string] [[, expr [format_string]] ...]

     grid (left|right|top|bottom) [ticks off] [line_description] [up expr | down expr | left expr
     | right expr] from [coord_name] start_expr to end_expr [by [+|-|*|/] by_expr]
     [format_string]

           The grid command is similar to the  ticks  command  except  that  grid  specifies  the
           placement of lines in the frame.  The syntax is similar to ticks as well.

           By  specifying ticks off in the command, no ticks are drawn on that side of the frame.
           If ticks appear on a side by default, or  have  been  declared  by  an  earlier  ticks
           command, grid does not cancel them unless ticks off is specified.

           Instead  of a direction for ticks, grid allows the user to pick a line description for
           the grid lines.  The usual pic line descriptions are allowed.

           Grids are labelled by default.  To omit labels, specify the format string as "".

           If sprintf is disabled, grid behaves as plot with respect to the format string.

     label (left|right|top|bottom) quoted_string [string_modifiers] [, quoted_string
     [string_modifiers]] ...  [up expr | down expr | left expr | right expr]

           The label command places a label on the given axis.  It is possible to specify several
           labels, which will be stacked over each other as  in  pic.   The  final  argument,  if
           present, specifies how many inches the label is shifted from the axis.

           By default the labels on the left and right labels run parallel to the frame.  You can
           cancel this by specifying unaligned as a string_modifier.

     circle at [coordinate_name] expr, expr [radius expr] [linedesc]

           This draws an circle at the point indicated.  By default, the circle is  small,  0.025
           inches.  This can be over-ridden by specifying a radius.  The coordinates of the point
           are relative to the named  coordinate  system,  or  the  default  system  if  none  is
           specified.

           This  command  has  been  extended  to take a line description, e.g., dotted.  It also
           accepts the filling extensions described below in  the  bar  command.   It  will  also
           accept  a  color  keyword  that gives the color of the outline of the circle in double
           quotes and a fillcolor command that sets the color to fill the circle with  similarly.
           Colors  are  only available when compatibility mode is off, and using a version of GNU
           pic that supports color.

     line [line_description] from [coordinate_name] expr, expr to [coordinate_name] expr, expr
     [line_description]

     arrow [line_description] from [coordinate_name] expr, expr to [coordinate_name] expr, expr
     [line_description]

           This draws a line or arrow from the first point to the second using the  given  style.
           The  default line style is solid.  The line_description can be given either before the
           from or after the to clause.  If both are given the second is used.  It is possible to
           specify  one  point  in  one  coordinate  system and one in another, note that if both
           points are in a named coordinate system (even if they are in the same named coordinate
           system), both points must have coordinate_name given.

     copy ["filename"] [until "string"] [thru macro]

           The copy command imports data from another file into the current graph.  The form with
           only a filename given is a simple file inclusion; the included  file  is  simply  read
           into  the  input stream and can contain arbitrary grap commands.  The more common case
           is that it is a number list; see Number Lists below.

           The second form takes lines from the file, splits them into words delimited by one  or
           more  spaces, and calls the given macro with those words as parameters.  The macro may
           either be defined  here,  or  be  a  macro  defined  earlier.   See  Macros  for  more
           information on macros.

           The filename may be omitted if the until clause is present.  If so the current file is
           treated as the input file until string is encountered at the beginning of the line.

           copy  is   one   of   the   workhorses   of   grap.    Check   out   the   paper   and
           /usr/share/doc/grap/examples  for  more details.  Confirm the location of the examples
           directory using the -v flag.
     print (expr|string)

           Prints its argument to the standard error.

     sh block

           This passes block to sh(1).  Unlike K&B grap no macro or variable expansion  is  done.
           I believe that this is also true for GNU pic version 1.10.  See the Macros section for
           information on defining blocks.

     pic pic_statement

           This issues the given pic statements  in the enclosing .PS and .PE at the point  where
           the command is issued.

           Statements  that  begin  with  a period are considered to be troff(statements) and are
           output in the enclosing .PS and .PE at the point where the command appears.

           For the purposes of relative placement of pic or troff commands, the frame  is  output
           immediately  before  the first plotted object, or the frame statement, if any.  If the
           user specifies pic or troff commands and neither  any  plotable  object  nor  a  frame
           command, the commands will not be output.

     graph Name pic_commands

           This command is used to position graphs with respect to each other.  The current graph
           is given the pic name Name (names used by pic begin with capital  letters).   Any  pic
           commands  following  the  graph are used to position the next graph.  The frame of the
           graph is available for use with pic name Frame. The following places  a  second  graph
           below the first:

                       graph Linear
                       [ graph description ]
                       graph Exponential with .Frame.n at \
                               Linear.Frame.s - (0, .05)
                       [ graph description ]

     name = expr

           This assigns expr to the variable name.  grap has only numeric (double) variables.

           Assignment  creates a variable if it does not exist.  Variables persist across graphs.
           Assignments can cascade; a = b = 35 assigns 35 to a and b.

     bar (up|right) [coordinates_name] offset ht height [wid width] [base base_offset]
     [line_description]

     bar [coordinates_name] expr, expr, [coordinates_name] expr, expr, [line_description]

           The  bar  command  facilitates  drawing  bar  graphs.   The  first form of the command
           describes the bar somewhat generally and has grap place it.  The bar may extend up  or
           to the right, is centered on offset and extends up or right height units (in the given
           coordinate system).  For example

                       bar up 3 ht 2

           draws a 2 unit high bar sitting on the x axis, centered on x=3.  By default bars are 1
           unit  wide,  but this can be changed with the wid keyword.  By default bars sit on the
           base axis, i.e., bars directed up will extend from y=0.  That may be overridden by the
           base keyword.  (The bar described above has corners (2.5, 0) and (3.5, 2).)

           The  line  description has been extended to include a fill expr keyword that specifies
           the shading inside the bar.  Bars may be drawn in any line style.   They  support  the
           color and fillcolor keywords described under circle.

           The  second  form of the command draws a box with the two points as corners.  This can
           be used to draw boxes highlighting certain data as well  as  bar  graphs.   Note  that
           filled bars will cover data drawn under them.

   Control Flow
     if expr then block [else block]

           The  if  statement  provides  simple  conditional execution.  If expr is non-zero, the
           block after the then statement is executed.  If  not  the  block  after  the  else  is
           executed,  if  present.   See  Macros for the definition of blocks.  Early versions of
           this implementation of grap treated  the  blocks  as  macros  that  were  defined  and
           expanded in place.  This led to unnecessary confusion because explicit separators were
           sometimes called for.  Now, grap inserts a separator (;) after the last  character  in
           block, so constructs like

           if (x == 3) { y = y + 1 }
           x = x + 1

           behave as expected.  A separator is also appended to the end of a for block.

     for name from from_expr to to_expr [by [+|-|*|/] by_expr] do block

           This  command  executes  block iteratively.  The variable name is set to from_expr and
           incremented by by_expr until it exceeds to_expr.   The  iteration  has  the  semantics
           defined  in  the  ticks command.  The definition of block is discussed in Marcos.  See
           also the note about implicit separators in the description of the if command.

           An = can be used in place of from.

   Expressions
     grap supports most standard arithmetic operators: + - / * ^.  The carat (^) is
     exponentiation.  In an if statement grap also supports the C logical operators ==, !=, &&,
     || and unary !.  Also in an if, == and != are overloaded for the comparison of quoted
     strings.  Parentheses are used for grouping.

     Assignment is not allowed in an expression in any context, except for simple cascading of
     assignments.  a = b = 35 works as expected; a = 3.5 * (b = 10) does not execute.

     grap supports the following functions that take one argument: log, exp, int, sin, cos, sqrt,
     rand, floor, ceil.  The logarithms are base 10 and the trigonometric functions are in
     radians.  eexp returns Euler's number to the given power and ln returns the natural
     logarithm.  The natural log, exponentiation functions and floor and ceil are extensions and
     are probably not available in other grap implementations.

     rand returns a random number uniformly distributed on [0,1).  The following two-argument
     functions are supported: atan2, min, max.  atan2 works just like atan2(3).  The random
     number generator can be seeded by calling srand with a single parameter (converted
     internally to an integer).  Because its return value is of no use, you must use srand as a
     separate statement, it is not part of a valid expression.  srand is not portable.

     The getpid function takes no arguments and returns the process id.  This may be used to seed
     the random number generator, but do not expect cryptographically random values to result.

     Other than string comparison, no expressions can use strings.  One string valued function
     exists: sprintf (format, [expr [, expr]] ).  It operates like sprintf(3), except returning
     the value.  It can be used anywhere a quoted string is used.  If grap is run with -S, the
     environment variable GRAP_SAFER is defined, or grap has been compiled for safer operation,
     the sprintf command will return the format string.  This mode of operation is only intended
     to be used only if grap is being used as part of a super-user enabled print system.

     grap version 1.44 and beyond support two functions for date and time manipulation, strptime
     and strptime.  strptime parses a time using the strptime(3) function.  It takes two
     parameters, both strings, the format and a string to parse using that format and returns a
     number that can be sorted directly - the number of seconds since the UNIX epoch.  strftime
     does the reverse.  It takes a string and a number and formats the number into a date.  In
     both functions, the format is the first parameter.  The formats are defined in the
     documentation for strftime(3).

   Macros
     grap has a simple but powerful macro facility.  Macros are defined using the define command
     :

     define name block
     undefine name

           Every  occurrence  of  name  in the program text is replaced by the contents of block.
           block is defined by a series of statements in nested { }'s, or a series of  statements
           surrounded by the same letter.  An example of the latter is

                       define foo  X coord x 1,3 X
           Each  time  foo  appears  in the text, it will be replaced by coord x 1,3.  Macros are
           literal, and can contain newlines.  If a macro does not span multiple lines, it should
           end in a semicolon to avoid parsing errors.

           Macros  can  take  parameters,  too.   If a macro call is followed by a parenthesized,
           comma-separated list the values starting with $1 will be replaced in  the  macro  with
           the  elements  of  the  list.   A  $  not followed by a digit is left unchanged.  This
           parsing is very rudimentary; no nesting  or  parentheses  or  escaping  of  commas  is
           allowed.   Also,  there  is  no  way  to  say argument 1 followed by a digit (${1}0 in
           sh(1)).

           The following will draw a line with slope 1.

                       define foo { next at $1, $2 }
                       for i from 1 to 5 { foo(i,i) }
           Macros persist across graphs.  The file /usr/share/grap/grap.defines  contains  simple
           macros for plotting common characters.  The undefine command deletes a macro.

           See  the  directory /usr/share/doc/grap/examples for more examples of macros.  Confirm
           the location of the examples directory using the -v flag.

   Number Lists
     A whitespace-separated list of numbers is treated specially.  The list is taken to be points
     to be plotted using the default line style on the default coordinate system.  If more than
     two numbers are given, the extra numbers are taken to be additional y values to plot at the
     first x value.  Number lists in DWB grap can be comma-separated, and this grap supports that
     as well.  More precisely, numbers in number lists can be separated by either whitespace,
     commas, or both.

           1 2 3
           4 5 6

     Will plot points using the default line style at (1,2), (1,3),(4,5) and (4,6).  A simple way
     to plot a set of numbers in a file named ./data is:

           .G1
           copy "./data"
           .G2

   Pic Macros
     grap defines pic macros that can be used in embedded pic code to place elements in the
     graph.  The macros are x_gg, y_gg, and xy_gg.  These macros define pic distances that
     correspond to the given argument.  They can be used to size boxes or to plot pic constructs
     on the graph.  To place a given construct on the graph, you should add Frame.Origin to it.
     Other coordinate spaces can be used by replacing gg with the name of the coordinate space.
     A coordinate space named gg cannot be reliably accessed by these macros.

     The macros are emitted immediately before the frame is drawn.

     DWB grap may use these as part of its implementation.  This grap provides them only for
     compatibility.  Note that these are very simple macros, and may not do what you expect under
     complex conditions.

ENVIRONMENT VARIABLES

     If the environment variable GRAP_DEFINES is defined, grap will look for its defines file
     there.  If that value is a relative path name the path specified in the -M option will be
     searched for it.  GRAP_DEFINES overrides the compiled in location of the defines file, but
     may be overridden by the -d or -D flags.

     If GRAP_SAFER is set, sprintf is disabled to prevent forcing grap to core dump or smash the
     stack.

FILES

     /usr/share/grap/grap.defines

SEE ALSO

     atan2(3), groff(1), pic(1), printf(3), sh(1), sprintf(3), troff(1)

     If documentation and examples have been installed, grap --version or grap --help will
     display the locations.

BUGS

     There are several small incompatibilities with K&R grap.  They include the sh command not
     expanding variables and macros, and a more strict adherence to parameter order in the
     internal commands.

     Although much improved, the error reporting code can still be confused.  Notably, an error
     in a macro is not detected until the macro is used, and it produces unusual output in the
     error message.

     Iterating many times over a macro with no newlines can run grap out of memory.

AUTHOR

     This implementation was done by Ted Faber <faber@lunabase.org>.  Bruce Lilly
     <blilly@erols.com> contributed many bug fixes, including a considerable revamp of the error
     reporting code.  If you can actually find an error in your grap code, you can probably thank
     him.  grap was designed and specified by Brian Kernighan and Jon Bentley.