*******************************************************************************
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This file documents shortly some parts of the gnuplot internals.

TABLE OF CONTENTS:

  * OVERVIEW OVER CODE STRUCTURE CHANGES AFTER MERGING THE 'AXES' BRANCH
  * TECHNICAL DETAILS FOR MOUSE COMMUNICATION
  * TECHNICAL DETAILS FOR FAST MOUSE ROTATION OF 3D SURFACES
  * TECHNICAL DETAILS ABOUT PM3D

Document version: "$Id: README,v 1.6 2003/01/22 08:47:55 mikulik Exp $"


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OVERVIEW OVER CODE STRUCTURE CHANGES AFTER MERGING THE 'AXES' BRANCH
====================================================================


CODE structure changes --- an overview: 
  - this is important info if you want to work on gnuplot or merge in patches,
  - made against gnuplot versions before 3.8e.

As of November 1st, 2000, a large set of reorganizational changes to
the gnuplot source code, formerly known as 'the axis branch', were
folded into the main source tree. This was tagged as beta version 3.8e
of the program. Due to the massive amount of changes, this will likely
break most patches built against any previous version of gnuplot. To
help others in resolving the conflicts that arise, I've set up this
description.

The change that is most likely to break your patches is that many
variables formerly in setshow.h were renamed and grouped into an array
of structures.  All status that is set/saved for each individual axis
got moved. A little overview:

  autoscale_*		--> axis_array[].autoscale
  *format		--> [].formatstring
  format_is_numeric[*]  --> [].format_is_numeric
  is_log_*		--> [].log
  base_log_*		--> [].base
  log_base_log_*	--> [].log_base
  *label		--> [].label
  *min			--> [].set_min
  *max			--> [].set_max
  min_array[]		--> [].min
  max_array[]		--> [].max
  writeback_min[]	--> [].writeback_min
  writeback_max[]	--> [].writeback_max
  *zeroaxis		--> [].zeroaxis
  *tics			--> [].ticmode
  rotate_*tics		--> [].tic_rotate
  m*tics		--> [].minitics
  m*tfreq		--> [].mtic_freq
  *ticdef		--> [].ticdef
  timefmt		--> [].timefmt    --- one per axis, now!
  datatype[]		--> [].is_timedata

Other, general changes: 

1) All status variables for features that have an axis name
   in 'set' are now contained in axis.c, and declared
   in axis.h. Some internal status variables also were moved there.
2) plot.h is no longer the 'master include file'. The big collection of
   type definitions is now in a new file 'gp_types.h'. Only relatively
   few sources will now want to #include "plot.h", but most will need
   "gp_types.h". It's often indirectly pulled in through other headers.
3) setshow.h now only declares variables that *do* belong to set.c and
   show.c. All the global status variables are now kept in their
   respective implementation modules.
4) Global variables are now all declared in the .h file of their 'home'
   module (i.e. if the definition is in foo.c, the decl is in foo.h). 
5) Frequently repeated code blocks, like log()/pow() conversion of
   values for log axes, are now macros in axis.h or functions in
   the axis module.
6) reset_command() moved from set.c to unset.c
7) Many status variables and implementations for graphical plot elements
   that are not axis-specific (the timestamp, the key, the border, and
   some others) are now in the new source module 'gadgets.h'.
8) there's a header file 'version.h' now for the stuff exported by
   'version.c'. 
9) Variables and functions only used by one particular source file
    have been moved into that and made 'static', to improve mutual
    isolation of the individual source modules.
10) Series of #defines that represent different cases have been turned
    into enums. This makes for easier debugging, and better compiler
    warnings if you forget to handle some case.
11) Default/initial values of variables to be influenced by 'reset'
    usually have a #define in the .h that is used for both, to avoid
    'reset' and the initialization getting out of synch.
12) Types not needed outside a certain module are defined in the source,
    where no other modules sees them, rather than in the header.
13) If an int was used as a yes/no flag, only, I made it a TBOOLEAN.




Details, by file:
=================

now in axis.c/h:(new)
  type axis
  enum AXIS_INDEX
  AXIS_ARRAY_SIZE
  t_ticseries_type
  types ticmark, ticdef, en_minitics_status, tic_callback, AXIS_DEFAULTS
  DEFAULT_AXIS_STRUCT
  axis_array[]    --- what it all started about
  axis_defaults[] 
  INIT_AXIS_ARRAY() --- set a field a given initial value, for all axes
  axisname_tbl[] --- for parsing
  ticscale, miniticscale, tic_in --- tic-related variables
  default_axis_ticdef, default_axis_label --- for unset/reset
  default_axis_zeroaxis, default_grid_lp --- dito
  DEF_FORMAT, TIMEFMT --- dito
  grid_selection, grid_lp, mgrid_lp, polar_grid_angle --- 'set grid'
  tic_start, tic_direction, tic_text, rotate_tics, tic_hjust, ... 
  tic_vjust, tic_mirror --- globals for tic callbacks
  x_axis, y_axis, z_axis --- 'current' x, y and z axis index
  X_AXIS, Y_AXIS, Z_AXIS --- quick-access macros axis_array[x_axis] etc.
  AXIS_MAP, AXIS_MAPBACK --- user <-> term coord mapping
  map_x, map_y --- their old names
  AXIS_WRITEBACK()
  AXIS_DO_LOG(), AXIS_UNDO_LOG() --- log() a value for an axis' logbas
  AXIS_LOG_VALUE(), AXIS_DE_LOG_VALUE() --- same, but test if necessary
  AXIS_INIT3D, AXIS_INIT2D --- prepare axis for use
  ... and lots of others --- go read axis.h yourself :-)

 
removed from command.c: 
  c_dummy_var[][]
now in command.c: 
  replot_disabled, MAX_TOKENS 

removed from contour.c:
  num_approx_points
  bspline_order
now in contour.c:
  contour_format
  contour_kind
  contour_levels_kind
  contour_levels
  contour_order
  contour_pts
  (dyn_)contour_levels_list

removed from datafile.c:
  df_timecol
now in datafile.c:
  missing_val
  plotted_data_from_stdin
  df_axis
renamed: pipe_open -> df_pipe_open

now in eval.c/h:
  udft_entry
  udvt_entry
  argument
  FUNC_PTR
  ft_entry

now in gadgets.c/h:
  types position_type, position, text_label, arrow_def, linestyle_def
  types en_key_horizontal_position, en_key_sample_positioning, key_type
  type label_struct
  EMPTY_LABELSTRUCT --- for initializing/unset/reset
  key, key_user_pos, key_vpos, key_hpos, key_just, key_swidth
  key_vert_factor, key_width_fix, key_reverse, key_title
  default_keybox_lp, key_box  --- status variables of 'set key'
  xleft, xright, ybot, ytop: the graph boundary
  xsize, ysize, ysize, aspect_ratio ---  'set size'
  xoffset, xoffset --- 'set offset'
  lmargin, bmargin,rmargin,tmargin --- set dito
  first_arrow
  first_label
  first_linestyle
  title
  timelabel, timelabel_rotate, timelabel_bottom --- 'set timedate'
  polar, parametric
  zero --- 'set zero'
  draw_border, border_lp
  clip_lines1, clip_lines2, clip_points
  samples_1, samples_2, SAMPLES
  ang2rad --- 'set angle'
  data_style, func_style --- 'set style data/func'
  suppressMove
  draw_clip_line, clip_line, clip_point --- moved from util3d.h
  clip_put_text, clip_put_text_just --- dito (used for 2D, too)
  clip_move, clip_vector --- from graph3d.h (also 2D usage)

now in time.c/gp_time.h:
  ZERO_YEAR
  JAN_FIRST_WDAY 
  SEC_OFFS_SYS
  YEAR_SEC
  MON_SEC
  WEEK_SEC
  DAY_SEC

removed from graph3d.c/h:
  suppress_move
  hidden_active
  hidden_no_update
  map3d_xy() --- moved to util3d
  map3d_z(), dbl_raise() --- unused, anyway
  draw_bottom_grid() --- renamed, now draw3d_graphbox()
  setlinestyle()
  map_x3d & friend macros
  move_pos_x, move_pos_y
  clip_move(), clip_vector()
now in graph3d.c/h:
  types t_contour_placement, gnuplot_contours, iso_curve, surface_points
  xscale3d, yscale3d, zscale3d
  draw_contour
  label_contours
  draw_surface
  hidden3d
  surface_rot_z
  surface_rot_x
  surface_scale
  surface_zscale
  ticslevel
  ISOSAMPLES
  iso_samples_1
  iso_samples_2  
  cntr3d_linespoints() --- new
  cntr3d_dots()	--- new
  setup_3d_box_corners --- new
  find_maxl_cntr() --- static, moved from misc.c
  find_maxl_keys3d() --- static, moved from misc.c
  right_x, right_y, front_x, front_y --- static, new

removed from graphics.c/h:
  statics tic_start, tic_direction, tic_text, rotate_tics, ...
  tic_hjust, tic_vjust, tic_mirror, ...
  ticfmt, timelevel, ticstep --- now function-local
  min_array, max_array, log_array, base_array, scale[] ...
  log_base_array --- now in 'axis' structure.
  x_axis, y_axis --- now in axis.c
  mant_exp() --- now static in axis.c
  time_tic_just(), timetic_format(), fixup_range() --- dito 
  set_tic(), setup_tics(), gen_tics() --- dito
  gprintf() --- now in axis.c (but may not stay there)
  CheckLog()  --- renamed, now in axis.c
  write_multiline() --- now in term.c
  xleft, xright, xtop, xbot --- now in gadgets.c
  dbl_raise() --- unused
now in graphics.c/h:
  type curve_points
  loff, roff, toff, boff
  bar_size
  find_maxl_keys() --- static, moved from misc.c
  default_font
  
removed from hidden3d.h:
  type vertex --- now in util3d.h
  
now in internal.h:
  undefined

removed from misc.c/h:
  static find_maxl_cntr(), find_maxl_keys3d() --- now in graph3d
  static find_maxl_keys() --- now in graphics
  cp_alloc(), cp_extend(), cp_free() --- now in plot2d
  sp_alloc(), sp_extend(), sp_free() --- now in plot3d
  gp_strcspn --- now in stdfn
now in misc.c/h:
  get_style() --- from set.c
  lp_use_properties() --- from set.c
  lp_parse --- from set.c

now in parse.c/h:
  c_dummy_var[]
  set_dummy_var[]
  is_jump()

removed from plot.c/h:
  PROGRAM --- now in show
  PROMPT --- now in command
  SAMPLES --- now in gadgets
  ISO_SAMPLES
  ZERO
  TERM
  TBOOLEAN 
  DTRUE
  DEG2RAD()
  MIN_CRV_POINTS
  MIN_SRF_POINTS
  INT_STR_LEN()
  PATH_CONCAT()
  CONCAT
  CONCAT3
  MAX_LINE_LEN
  MAX_TOKENS 
  MAX_ID_LEN
  MAX_AT_LEN
  NO_CARET --- now in util.h
  MAX_NUM_VAR
  FIRST_AXES --- now in axis
  FIRST_Z_AXIS etc. --- now in axis
  GPHUGE --- now in syscfg
  HUGE_VAL, VERYLARGE --- dito
  coordval --- dito
  GPMAX(), GPMIN(), inrange() --- now in stdfn
  is_comment(), is_system() --- now in syscfg
  is_jump() --- now in parse
  ... lots of types --- now in gp_types.h, or gadgets.h
  type termentry/TERMENTRY --- now in term_api.h
  ... all declarations of variables from other sources --- now there

removed from plot2d.c/h:
  INIT_ARRAYS(), CHECK_REVERSE(), LOAD_RANGE() --- now in axis
  STORE_WITH_LOG_AND_FIXUP_RANGE() --- dito
  FIXUP_RANGE_FOR_LOG() --- dito
  WRITEBACK(), SAVE_WRITEBACK() --- renamed, now in axis
now in plot2d.c/h:
  boxwidth
  cp_alloc()
  cp_extend()
  cp_free()

removed from plot3d.c/h:
  INIT_ARRAYS(), CHECK_REVERSE(), LOAD_RANGE() --- now in axis
  STORE_WITH_LOG_AND_FIXUP_RANGE() --- dito
  FIXUP_RANGE_FOR_LOG() --- dito
  WRITEBACK SAVE_WRITEBACK() --- renamed, now in axis 
  (yes, these were duplicates in plot2d and plot3d...)
now in plot3d.c/h:
  mapping3d
  dgrid3d_row_fineness
  dgrid3d_col_fineness
  dgrid3d_norm_value
  dgrid3d
  calculate_set_of_isolines() --- new, isolated from eval_plots()
  sp_alloc(),  sp_extend(),  sp_free() --- from misc
  sp_replace() --- new

removed from save.c:
  SAVE_NUM_OR_TIME() --- now in setshow.h

removed from set.c/setshow.h:
  GET_NUM_OR_TIME() --- now in axis
  reset_command --- now in unset
  get_writeback_min() and friends --- renamed, now in axis

and many globals that are now structure elements in the axis_array[]:
  autoscale_*		--> axis_array[].autoscale
  *format		--> [].formatstring
  format_is_numeric[*]  --> [].format_is_numeric
  is_log_*		--> [].log
  base_log_*		--> [].base
  log_base_log_*	--> [].log_base
  *label		--> [].label
  *min			--> [].set_min
  *max			--> [].set_max
  min_array[]		--> [].min
  max_array[]		--> [].max
  writeback_min[]	--> [].writeback_min
  writeback_max[]	--> [].writeback_max
  *zeroaxis		--> [].zeroaxis
  *tics			--> [].ticmode
  rotate_*tics		--> [].tic_rotate
  m*tics		--> [].minitics
  m*tfreq		--> [].mtic_freq
  *ticdef		--> [].ticdef
  timefmt		--> [].timefmt    --- one per axis, now!
  datatype[]		--> [].is_timedata

all other globals from set.c went to graph2d if they were 2D-releated,
graph3d if 3D, gadgets if used by both 2D and 3D.

now in stdfn.c/h:
  gp_strcspn()
  INT_STR_LEN
  PATH_CONCAT
  inrange
  GPMAX
  GPMIN

now in syscfg.h:
  GPHUGE, GPFAR
  coordval
  MAX_NUM_VAR
  RETSIGTYPE
  type sortfunc
  GP_INLINE
  TRUE, FALSE, TBOOLEAN

removed from tables.h:
  set_encoding_tbl, set_encoding_id --- now in term_api.h
  
now in term.c/term_api.h:
  *term, term_options
  *outstr
  multiplot
  ignore_enhanced_text
  encoding, encoding_names
  set_encoding_tbl, set_encoding_id
  write_multiline
  types JUSTIFY, VERT_JUSTIFY, lp_style_type, TERMENTRY/termentry
  
in unset.c:
  unset_mtics(), unset_tics(), unset_timedata() and others ---
    replace lots of functions by one, taking an axis_index argument

now in util.c:
  graph_error() --- from graphics

removed from util3d.c:
  clip_point(), draw_clip_line(), clip_put_text(), ...
  clip_put_text_just(), clip_line() --- caused problems with hidden3d
now in util3d.c:
  type vertex --- from hidden3d
  FLAG_VERTEX_AS_UNDEFINED(), VERTEX_IS_UNDEFINED, V_EQUAL --- dito
  TERMCOORD() --- dito
  map3d_xyz 
  map3d_xy --- from graph3d
  draw3d_line() --- new
  draw3d_line_unconditional() --- new
  draw3d_point() --- new --- these replace the old, removed ones


If you've read all through this, you're one determined person ---
congratulations.

Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)
Even if all the snow were burnt, ashes would remain.

---------------------------------------------------------------------------

2001/07/24: I made a lot of changes in the expression parser /
evaluator subsystem. The interface from the expression evaluator to
the rest of gnuplot is now through only *one* header file, eval.h. The
headers interpol.h, specfun.h and standard.h are now used only for
communication to eval.c and its helpers. Other modules should #include
only eval.h, or parse.h if they need to handle user input (parse.h
includes eval.h).

I've also renamed all those incomprehendible functions 'aterms()'
through 'hterms()' in parser.c, according to the type of expression
they actually parse. The expression type names follow those in the C
standard grammar. In order of increasing operator precedence:

express --> parse_expression
xterms --> parse_conditional_expression
aterms --> parse_logical_OR_expression
bterms --> parse_logical_AND_expression
cterms --> parse_inclusive_OR_expression  
dterms --> parse_exclusive_OR_expression  
eterms --> parse_AND_expression           
fterms --> parse_equality_expression      
gterms --> parse_relational_expression    
hterms --> parse_additive_expression      
iterms --> parse_multiplicative_expression
unary --> parse_unary_expression
factor --> parse_primary_expression

Those are the functions that actually parse expressions of a given type
based upon lexical symbols found in the input. A second set of functions
represent the grammar states:

xterm --> accept_logical_OR_expression
aterm --> accept_logical_AND_expression
bterm --> accept_inclusive_OR_expression  
cterm --> accept_exclusive_OR_expression  
dterm --> accept_AND_expression           
eterm --> accept_equality_expression      
fterm --> accept_relational_expression    
gterm --> accept_additive_expression      
hterm --> accept_multiplicative_expression



*******************************************************************************
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TECHNICAL DETAILS FOR HOTKEYS/MOUSE COMMUNICATION
=================================================

The communication between a mouseable terminal and the main gnuplot core goes
via structures defined in mousecmn.h. Further, the following terminal entries
are used (see USE_MOUSE #defined code in .trm files):
	void XX_set_ruler (int, int);
	void XX_set_cursor (int, int, int);
	void XX_put_tmptext (int, const char str[]);
	void XX_set_clipboard (const char[]);

On OS/2, the communication of these structures between the stand-alone
terminals gnupmdrv.exe or gnuplot_x11.exe and the main gnuplot.exe executable
is implemented by shared memory and an event semaphore.

On Unix, a bidirectional pipe is implemented for the ipc (inter-process)
communication between gnuplot_x11 and gnuplot. The readline interfaces were
modified to listen to both stdin and the ipc file descriptor.  (Well, that's
just the usual way). Note that if compiling with gnu readline, you must have a
gnu readline version > 2.2 (3.0).  This will not be a major drawback, as 2.2 is
out for years now and the current gnu readline version is 4.0.

On VGAGL, the communication is done by...?

On Windows, the windows terminal is a part of the gnuplot executable
wgnuplot.exe. Thus it is possible to call the executing routine do_event(&ge);
directly, without any communication at all.


History of mouseable terminals:
(*) March 1998: Implementation of mousing in OS/2 Presentation Manager terminal
(Petr Mikulik). 
(*) April 1999: Proper implementation of the gnupmdrv-gnuplot communication by
shared memory and event semaphores (Franz Bakan, Petr Mikulik).
(*) October 1999: Mouseable X11 terminal on Unix and OS/2 (Johannes Zellner,
Petr Mikulik).

The stand-alone terminals gnupmdrv.exe and gnuplot_x11(.exe) had full control
over mousing over its displayed graph (all relevant gnuplot structures were
passed into the terminal). 

(*) January 2000: Mousing re-implemented by means of new terminal (.trm)
entries, i.e. with a call-back of events passed from the stand-alone terminal
to the main gnuplot (Pieter-Tjerk de Boer, Johannes Zellner, Petr Mikulik).

(*) January 2000: Implemented mousing in vgagl terminal, the fast linux console
terminal (Johannes Zellner).

(*) February 2002: Implemented mousing in windows terminal (Petr Mikulik,
Hans-Bernhard Broeker).


*******************************************************************************
*******************************************************************************


TECHNICAL DETAILS FOR FAST MOUSE ROTATION OF 3D SURFACES
========================================================

For splots (3d) the data of all surfaces of the current graph are cached and
can therefore be redrawn very quickly, without rereading and reparsing the
input files. This enables smooth rotating and zooming of splots. Note that
gnuplot frees the allocated data of the current graph when it starts to plot a
new graph.


*******************************************************************************
*******************************************************************************


TECHNICAL DETAILS ABOUT PM3D
============================

The pm3d splot mode for gray and colour maps and surface (and much later for
much more: splots with color lines, plots with filled curves) has been
implemented by Petr Mikulik in December 1998 and January 1999. It was released
for public on 14. 3. 1999 as a patch for gnuplot 3.7. Below you can find the
original notes about the implementation, slightly modified in February 2002.


The pm3d algorithm: History and description
-------------------------------------------

The gnuplot pm3d splot mode is a successor to my pm3d algorithm coded
previously in my Turbo Vision Pascal plotting program "pmgraf" for DOS (April
1994) and the C++ command line "pm3d" program which is converting the input
data into postscript maps (March 1995). Both programs are available on my
homepage.

The pm3d algorithm (in pmgraf, pm3d and now in gnuplot) draws a gray or colour
map (or surface, in gnuplot only) of a 3D data, which are supposed to be a
sequence of scans. Scan is the same what is called 'iso_curve' in gnuplot.

For the given surface, the algorithm takes one scan after the other scan until
the last but one. For a scan number K it looks at the subsequent scan K+1. For
each (but the last one) point on scan K, it makes a quadrangle with 4 corners:
two subsequent points at scan K and two points at scan K+1. (The quadrangle is
a rectangle if the data are matrix-like.) The quadrangle is filled by the
colour corresponding to the averaged Z coordinate of its 4 corners.

Therefore it can plot matricial as well as non-rectangular non-gridded data
without any preprocessing, and on single pass through the data. It does not
require that the scans have the same number of points (see the details on
flushing below or 'set pm3d flush').


pm3d implementation in gnuplot
------------------------------

Below, you find the basic description of gnuplot implementation of pm3d, colour
palette and filled colour polygons.

The pm3d implementation in gnuplot is is based on the following terminal
entries (see below for more details):
	term->make_palette
	term->previous_palette
	term->set_color
	term->filled_polygon

The topmost implementation of colour filled areas in plot3d.c:

(*) pm3d mode is set on if (pm3d.where[0]). Its setting, or using 'with ...
palette', requests the palette of continuous (smooth) colours for the given
terminal according to 'set palette' setup. The palette is created by a call to
make_palette(). The routine make_palette() is coded in pm3d.c. It will be
commented below.

(*) pm3d plot for a given surface is called from graph3d.c, just before the
stuff for hidden line removal, i.e. before plotting surfaces and contours. For
each surface, it calls
               pm3d_plot( this_plot, pm3d.where[i] );

(*) The colour box showing the sequence of continuous colours is drawn in routine 
draw_color_smooth_box(). Postscript output uses the box implementation directly
in the postscript language, see below.

(*) Routine term->previous_palette() is called after the plot. Currently, it is
needed only for printing the string "grestore" into a postscript file. 


----- Implementation of pm3d_plot( this_plot, at_which_z ) in pm3d.c -----

(*) This plots the map (for at_which_z=PM3D_AT_BASE or PM3D_AT_TOP) or surface
(for at_which_z=PM3D_AT_SURFACE) for the given surface (variable this_plot).

(*) The implementation of the pm3d algorithm is schematically:

for scan J=1 to scans-1 { /* for each scan in the surface */
  for pt=1 to min( points(J), points(J+1) ) { /* go over min nb of points */
    pt' = ...; pt'' = ... /* see below */
    ptJa = point(J,pt')
    ptJb = point(J,pt'+1)
    ptJ+1a = point(J+1,pt'')
    ptJ+1b = point(J+1,pt'')
    averagedZ = ( z(ptJa) + z(ptJb) + z(ptJ+1a) + z(ptJ+1b) ) / 4
    set_color( averagedZ normalized to [0;1] )
    fill_polygon( 4 corners, 
                  those 4 points transformed into coordinates of
                  the map or surface on the terminal )
    }
  }

If the two subsequent scans have the same number of points, then pt''=pt'=pt.
Otherwise, pt''=pt'=pt if 'scans flushed begin', pt'=points(J)-pt and
pt''=points(J+1)-pt if 'scans flushed end', and similarly for 'scans center'.
And nothing is drawn if there is only one point in the scan.


----- Implementation of make_palette() in pm3d.c -----

(*) Look into color.h, structure t_sm_palette: declaration of smooth palette,
i.e. palette for smooth colours. It documents how gray [0,1] is mapped into
(R,G,B) = ([0,1], [0,1], [0,1]).

(*) Ask for the number of colours that are (still) available on the current
terminal:
	i = term->make_palette(NULL);

Postscript terminal returns 0 since it supports all RGB values (no limit on
discrete number of colours). It has its own mapping: transformation of gray
[0,1] is coded as postscript functions, and also in order to make the output
size of the postscript file as small as possible, i.e. the same as the output
from the pm3d program. Further, not 3 values of the RGB triplet but only 1 gray
value is written into the postscript file. This is achieved by the analytical
functions: pm3dGetColorValue() are coded as postscript functions, see post.trm:
PostScriptColorFormulae[] used in PS_make_palette entry. PS->make_palette()
looks itself into sm_palette and writes a header with the appropriate
postscript codes for formulaR, formulaG, formulaB transformations. See also
post.trm: PostScriptColorFormulae[] used in PS_make_palette. Return from
make_palette().

All other terminals have discrete number of colours. Currently an RGB palette
is allocated for the number of available colours returned by make_palette(); if
pm3d is used in gnuplot's multiplot mode, then the result would be incorrect if
the previous palette is not reused or if the number of colours is not limited
by 'set palette maxcolors'.

Creating the RGB palette: make the array of (RGB) triplets according to items in 
sm_palette (not for postscript) 
	sm_palette.color = malloc( sm_palette.colors * sizeof(rgb_color) );

And then
for (i = 0; i < sm_palette.colors; i++) {
  gray = (double)i / (sm_palette.colors - 1); /* rescale to [0;1] */
  if (sm_palette.ColorMode == colorModeGRAY) /* gray scale only */
     sm_palette.color[i].r = sm_palette.color[i].g = sm_palette.color[i].b
     			   = gray;
  else { /* i.e. sm_palette.ColorMode == colorModeRGB */
    sm_palette.color[i].r = pm3dGetColorValue(sm_palette.formulaR, gray);
    sm_palette.color[i].g = pm3dGetColorValue(sm_palette.formulaG, gray);
    sm_palette.color[i].b = pm3dGetColorValue(sm_palette.formulaB, gray);
    }
  }

Finally, tell the terminal to allocate the palette for the (RGB) triplets 
(again, not for postscript)
	term->make_palette(&sm_palette);


----- Transformation of the z-coordinate to gray and RGB in pm3c.c -----

How a colour is transformed from the gray?  AveragedZ is mapped into the 
interval [min_z:max_z] which is transformed into [0:1], see routine
	double z2gray ( double z ) 
which rescales z into the interval [0,1]. This works fine also for the 
logarithmic z axis. Later, this is used by
	gray = z2gray ( avgZ );
This value can be used directly as a gray for gray maps. For colour maps
it further needs to transform 
	gray -> (R,G,B): [0:1] -> ([0:1], [0:1], [0:1])
thus some nice three functions have to be choosen --- see pm3d.c, function
pm3dGetColorValue(), for the available mapping functions.

Note that after the complete separation of the z and cb axes (cb-axis is the
axis of colors) in February 2002, there is a new function z2cb(), and z2gray()
was replaced by cb2gray().


----- Implementation of pm3d terminal entries in *.trm -----

In this section you will find a brief discussion on the following pm3d-related
terminal entries:
	term->make_palette
	term->previous_palette
	term->set_color
	term->filled_polygon
which are required to make pm3d to work. Files considered by these functions
are color.h, color.c, plot.h, and all .trm which are pm3d-capable. If you are
coding pm3d support for a new terminal, then you can have a look at the code
in these files:
	gif.trm (bitmap GIF terminal implementation),
	post.trm (PostScript terminal implementation),
	pm.trm + gclient.c (OS/2 PM terminal implementation),
	x11.trm + gplt_x11.c (X11 terminal implementation).

The pm3d-specific code is surrounded by #ifdef PM3D ... #endif, so it is
possible to compile gnuplot with or without pm3d support just bey (un)defining
the PM3D constant.

In plot.h, the following new terminal entries are added into struct TERMENTRY:

int (*make_palette) __PROTO((t_sm_palette *palette));
    1. If palette==NULL, then return nice/suitable maximal number of colours
    supported by this terminal. Returns 0 if it can make colours without
    palette (like postscript).
    2. If palette!=NULL, then allocate its own palette return value is
    undefined.
    3. Available: some negative values of max_colors for whatever it can be 
    useful.

    Some particular notes:
    (*) Terminals with palette (GIF, PM): there are already some basic colours
    allocated (see gnuplot command 'test'), thus an offset for the `part with
    smooth colours' is needed. 
    (*) GIF: can allocate up to 256 colours, i.e. discrete number of colours.  
    (*) PM: discrete number of colours.  Passes the rgbTable through the pipe
    into standalone gnupmdrv driver.  X11 should be implemented in the same
    way.
    (*) PostScript: continuous colours, as "setrgbcolor" PS command takes the
    triplet of intervals [0,1].

void (*previous_palette) __PROTO((void));	
    Release the palette that the above routine allocated and get back the
    palette that was active before. Some terminals, like displays, may draw
    parts of the figure using their own palette. The terminals possessing only
    one palette for the whole plot don't need this routine.

    Actually, this routine is currently used only for postscript terminal,
    where it writes "grestore" as make_palette() starts its postscript
    definitions by "gsave"... that's because there are the analytical mapping
    functions gray->RGB defined in the local header.

void (*set_color) __PROTO((double gray));
    The value of gray is [0;1]. The terminal uses its color palette or any
    other way to transform in into true gray or to r,g,b. This terminal entry
    remembers (or not) this colour so that it can reuse it for a subsequent
    drawing (for each terminal separately).

void (*filled_polygon) __PROTO((int points, gpiPoint *corners));
    The declaration has been made the same as in GIF's gd.h. It fills the given
    polygon according to color set by the previous call to set_color().


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