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                                                                                                                                          33. Graphics

J gives you several ways to draw pictures.  The Plot Package is a quick but powerful way to display datasets in 2D or 3D form.  If you want to draw your own graphics, you can use the gl2 library for 2D graphics, or OpenGL for 3D.

Plot Package

The easy way to display data in J is with Plot.  First, load the Plot Package:

   load 'plot'

Hand your data to the plot verb:

   plot 3 1 4 1 5 9

and it will give you a graph of your data.

Plot Demo

To see what J Plot can do, go to the menu bar in a J session and click down to Studio|Demos|plot.  A Plot window will pop up, on whose menu bar pulldowns labeled 2D, 3D, Multi, Styles, and Gallery contain lists of demo plots.  Click on one and you will immediately see the plot.  When you find an interesting one, you may click Options|View Definition to see the commands that created it.

Interfaces to Plot

The Plot Package has two interfaces: lightning-fast (the plot verb) and fast (the pd verb).  pd lets you build a custom plot containing multiple datasets and options.  The picture described by plot 3 1 4 1 5 9 could have been built with

   pd 'reset'

   pd 'type line'

   pd 3 1 4 1 5 9

   pd 'show'

plot and pd make up the Plot Package, which I will refer to simply as Plot.

Plot has a great variety of options which you can find listed in the User Guide.  Here I will give enough of an overview to get started.  If you need a feature for your plot, there's a good chance it's described in the User Guide.  If you need to direct your plot to PostScript or to a control on a form, the User Guide explains that too.

Plot accepts a series of commands, options, and data.  Commands are actions taken independent of any data: setting the size of the plot window(s), writing annotation text, and the like.  Options, which include things like axis scaling and color selection, control the interpretation of subsequent data, which is added to the plot using whatever options are in effect when the data is encountered.  A single plot may contain multiple sets of data with different options.

Commands and Options

Plot Type

The most important option is the type of plot: surface or wire to display 3-D data, line to graph 2-D or 3D data, symbol and dot to plot points individually, and a variety of types to produce bar charts, pie charts, error bars, and many others.


The components of a plot have different colors which you can specify.  A color is given either as a 3-item list of red,green,blue intensity in the range 0-255, or as a name taken from J's list in system\packages\color\colortab.ijs.  Names of colors are not case-sensitive.  The standard colors for plot are BLUE, RED, GREEN, PURPLE, FUCHSIA, OLIVE, TEAL, YELLOW, MEDIUMBLUE, AQUA, BROWN, and GRAY.

The background of the plot is made up of two parts, the graph background which is the canvas the plot is drawn on, and the frame background which surrounds the graph background, filling out the window.  These colors can be set simultaneously with

   backcolor color_spec

The default is backcolor 255 255 255 or, equivalently, backcolor WHITE.  The components of the background can be set individually with

   framebackcolor color_spec

   graphbackcolor color_spec

Most plotted data is drawn with the item colors.  The data is broken into sets of points, and the item colors are assigned to the sets sequentially.  By default the item colors are the standard colors; they can be set by

  itemcolor color_spec,color_spec...

The list of item colors can be as long as you want; it recycles as needed.

Certain plot types, such as density, derive the plotted colors from the data.  For these plots you use

   bandcolor color_spec,color_spec...

to specify the colors used for the bands of data.

Other components have their own colors, set by the following commands whose names are mostly self-explanatory: axiscolor, captioncolor, edgecolor (for edges of filled regions), gridcolor, keycolor (a list, used for legend boxes), rulecolor, symbolcolor (for symbol plots), textcolor, and titlecolor.


You can select the font for the different kinds of text drawing.  The commands are captionfont, keyfont, labelfont, symbolfont, textfont, and titlefont.  An example is

   titlefont Arial 18

Postscript Type 1 fonts are also supported.

Titles, Captions, and Labels

The title of the plot is drawn above the plot.  You give the title with

   title title_text

titlecolor and titlefont apply to the title.

A caption is a character string displayed running parallel to an axis, and can be had with

   Ccaption caption_text

(C is replaced by x, y, or z to select the coordinate), where caption_text should be enclosed in double-quotes if it contains spaces.  captioncolor and captionfont apply to captions.

Labeling the axes means marking them to indicate coordinate values and is controlled by

   labels xon yon [zon]

(default 1 1) to turn labeling on or off.  By default the labels are just the numeric values of the coordinates at the tic marks, but you can use

   Clabel label1 label2...

to specify the label at each tic.  If labeln contains spaces, it should be enclosed in double-quotes.  You can specify the coordinates at which labels are to be shown with

   Cticpos positions

or you can apply labels at regular intervals with

   Ctic label_interval tics_between_labels

which will write a label at intervals of label_interval, and add tics_between_labels unlabeled tics between labeled tics.  The plot will be scaled to match the range of your data unless you specify the range of the coordinate with

   Crange min max

labelcolor and labelfont apply to labels.

Annotation (Text in the Drawing Area)

Annotation text is given by the text options:

   textcolor color

where color is red,green,blue or a name such as RED;

   textfont font_name size

to select the font;

   text xpos ypos text

   textc xpos ypos text

   textr xpos ypos text

to draw text at the given position, left-aligned, centered, or right-aligned.

Many other options are on view in the User Guide.

Data; Constructing a Plot with pd

Commands, options, and data are all added to the plot using the monadic pd verb.  Character operands to pd are interpreted as commands or options with the format name value  where name identifies the command/option, which is set to the (optional) value.  Multiple commands/options can be given to pd, either as a list of boxed strings, or as one long string with semicolons used as a separator between command/options.

Numeric operands to pd are data: one or more sets of points, where a point comprises a dependent variable and one or two independent variables  Normally data will be a list of boxes, x;y for 2-D data or x;y;z for 3-D data.  The last item (y for 2-D, z for 3-D) is the dependent variable whose values correspond to the independent variables given by the previous items.  We can distinguish 3 types of plot: 2-D line plots, 3-D line plots, and surface plots.

2-D Line Plots

The dependent variable y may be a list or an array.  Each 1-cell of y gives a set of points, and each set is plotted with a different item color.  x may have the same shape as y, or x may be a list with the shape of a 1-cell of y in which case it is repeated for each 1-cell of .

3-D Line and Point Plots

The dependent variable z may be a list or an array.  Each 1-cell of z gives a set of points, and each set is plotted with a different item color.  x and y must each be a list, with the shape of a 1-cell of z, which is repeated for each 1-cell of z.

surface and wire Plots (3-D)

The dependent variable z is an array.  x may have the same shape as z, or be a list with one atom for each row of z: the atom is repeated across the row.  y may have the same shape as z, or be a list with one atom for each column of z: the atom is repeated down the column.

Unboxed operands to pd

The boxing can be omitted from a data operand to pd, in which case it gives values of the dependent variable (y  for 2-D, z for 3-D) and the independent variables are taken to be integers starting at 0.  Or, the operand can be a complex list in which case the real parts are x and the imaginary parts are .

Control Commands to pd: Starting and Ending a Plot

The first command in a plot should be pd 'reset'.  After you have sent all your data through pd, your last command should be pd 'show' which causes the plot to be displayed.

Quick Plots Using plot

If your plot does not require multiple datasets with different options, you can display the whole thing with one use of the plot verb:

   commands_and_options plot data

plot starts a new plot, sends the commands_and_options through pd, sends the data through pd, and issues pd 'show' to display the result.  The axes will be scaled to fit your data.  If data is made up of a rank-2 array of boxes each of which contains a list of boxes, each box gives the data for a subplot: the plot window is divided into tiles based on the shape of data, and each atom of data is opened revealing a list of x;y[;z] boxes containing data to be plotted in corresponding tile.  An example of subplots is

   plot 2 1 $ (<3 1 4 1 5 9) ,&< (<2 7 1 8 2 8)

Generating Plots of Functions

Idioms for Generating Plot Operands: the steps verb

For a simple 2-D plot of the value of a function f evaluated at the values x, use

   plot x ; f x

If you just want evenly-spaced values of x, you can use the steps verb:

   steps initial_value final_value number_of_intervals

A plot of one period of the sine function is given by

plot (steps 0 2p1 100) ; sin steps 0 2p1 100

(2p1 is 2π).  To plot two functions at the same x values, make each function's values a row of an array:

   x =. steps 0 2p1 100

   plot x ; (sin x) ,: cos x

Using a fork, you can express this plot as

   plot (; sin,:cos) steps 0 2p1 100

For 3-D plot of a function f evaluated on a grid of x and y values, use

   plot x ; y ; x f"0/ y

f"0/ is described in the "Make a Table" section of the chapter "Odds and Ends".  x f"0/ y evaluates f at each combination of x and .  To plot cos(r)/(1+r) we would use

   x =. y =. steps _4 4 100

   f =. 4 : '(cos r) % 1 + r =. x +&:*: y'

   plot x ; y ; x f"0/ y

Using a fork, this plot is given succinctly by

   plot x ([ ; ] ; f"0/) y

The Simplest Function Plotting: Let Plot Evaluate Your Function

The simplest way to plot a function is to give Plot the description of the function and the domain, and let Plot decide where to evaluate the function.  You do this by giving the function instead of the data as the dependent variable in the right argument to plot or pd .  The plot may be 2-D or 3-D.  An example is

   plot 0 10 ; 'sin'

The character string instead of data tells Plot to evaluate the sin function over the interval [0,10].

The independent variable(s) are given either as intervals or as lists of points.  An interval is indicated by 2 or 3 numbers, specifying start value,end value,number of steps.  A list of points is indicated by a boxed argument containing the points, or by an unboxed list of more than 3 points.  Multiple intervals or point-lists are allowed.

If the number of steps is omitted or 0, Plot will pick an appropriate number of points to use.  It does so by repeatedly subdividing the interval until the curve is smooth or it decides that the curve is discontinous, in which case it plots continuous sections separately.

The subdivision is controlled by the plot commands Cfuncres and singtoler.  Cfuncres (C is x or y) gives the subdivision resolution: an interval smaller than 1/Cfuncres of the screen will not be split.  Cfuncres defaults to twice the pixel resolution of the plot.  singtoler is used when the display has singularities, and controls how much of the heading-off-to-infinity tail of the curve will be shown at the singularity.  You can experiment to find a good value for singtoler for your application; the default is 10 and higher numbers cause more of the tail to be displayed.

The function(s) to be displayed can be given as a list of gerunds, one for each verb to be drawn, or as a string where the verb-specifiers are separated by the ` character (use doubled ` as an escape if your verb contains a ` character).  Each verb-specifier can be in either tacit or explicit form: if it contains the word y.or y it is assumed to describe an explicit verb, otherwise a tacit one.

The verbs are invoked with lists as arguments and should be able to return a list of results.  If you use pd, note that the verbs are not executed until pd 'show' is processed, so the values of any public variables that are referred to by an explicit verb will use the values in effect when the pd 'show' is executed.  Public variables referred to in a tacit verb are frozen (using f.) when the pd for the function is issued.

Examples of function plots:

plot _10 10 ; '%'  NB. reciprocal: has a discontinuity

plot _10 10 ; 'sin`cos'  NB. two curves

plot 0.001 0.1 ; 'sin % y'  NB. sin(1/x), a busy function

The 3-D plot shown above can be created with

f =: 4 : '(cos r) % 1 + r =. x +&:*: y'

plot _4 4 100 ; _4 4 100 ; 'f'

Assembling a Multipart Plot with pd

A plot of a function with discontinuities, or multiple functions with different domains, can be assembled using pd.  If we want to plot the function 1/x (the J primitive %) by hand rather than using function plotting as shown above, we need to plot the negative and positive sides individually:

   pd 'reset'

   pd 'type line'

   pd 'color 0 0 255'

   pd (^ steps _2 2 50) ; % (^ steps _2 2 50)

   pd (- ^ steps _2 2 50) ; % (- ^ steps _2 2 50)

   pd 'show'

Here we plotted the positive x values, then the negative ones.  We set color to override Plot's default behavior of giving each dataset a different color.  The exponential applied to the x values keeps the points spaced fairly uniformly along the curve.

Examples of Plots with Multiple Sets of Points

A 2-D plot with multiple sets of points was given above by

plot _10 10 ; 'sin`cos'  NB. two curves

A 3-D line plot with 3 sets of lines:

   x =. i. 5

   y =. *: x

   z =. 0 10 20 + 1 , x ,: *: x

   'line' plot x ; y ; z

Plots of Parametric Functions

Although we often think of one variable as dependent and the others independent, this is our interpretation, not a restriction in Plot.  y does not have to be a function of x: y may just represent data measurements at values of x, or x and y can both be parametric functions of something else.  For example, a lovely Lissajous figure can be plotted with

  plot (sin 3 * steps 0 2p1 100) ; (cos steps 0 2p1 100)

Output Options

pd 'show' creates a 480x360-pixel window and draws your plot into it.  You have several other options for output, using one of the following commands in place of pd 'show':

   pd 'isi [width height]'   NB. items in [] are optional

creates a window of size width and height, and displays the plot in it.  For normal J sessions, pd 'show' and pd 'isi' are equivalent.

   pd 'eps [filename width height]'

creates a plot in EPS format.  filename defaults to ~temp\plot.eps, and the default size is 480x360.

   pd 'pdf [filename width height]'

creates a plot in PDF format.  filename defaults to ~temp\plot.pdf, and the default size is 480x360.  For Jconsole sessions, pd 'show' produces pd 'pdf', since there are no windows in a Jconsole session.

If you have created your plot in a window using plot, pd 'show', or pd 'isi', you can treat the bitmap of the plot as pixel data:

   pd 'print'

sends the bitmap to the printer;

   pd 'clip'

copies the bitmap to the clipboard;

   pd 'save type filename'

saves the bitmap in filename encoded according to type, which may be bmp, wmf, jpg, pgm, png, ppm, or tga.  All but bmp and wmf require the image3 addon to J.

2D Graphics: the gl2 Library

The gl2 Library is a set of functions for drawing 2D graphics into windows.  There are many more functions in this library than can be discussed here: to see the full list, open a J session, press F1 for help, click on 'wd' at the top of the page, then click the link for 'gl2 commands'.  It will be worth your time to read through the commands a few times to get an idea about what's available.

To use the gl2 commands you must include them in your program with

   load 'gl2'

Because there are so many functions, they are defined in a locale of their own, called jgl2 .  To have access to the functions in jgl2, you should include the line

   coinsert 'jgl2'

at the top of each file using the gl2 commands.  Alternatively, you could add jgl2 to the name of each gl2 function you use, but it is easier to use the coinsert.

Example of Drawing

A simple program to draw a line could look like the following:

load 'gl2'

coinsert 'jgl2'

load 'graph'

gopen''                 NB. Create drawing surface

glrgb 255 0 0           NB. set the color

glpen 2, PS_DASH        NB. pen width 2, dashed line

gllines 0 1000  1000 0  NB. draw using current pen

glpaint''               NB. display the drawing

Creating an isigraph Graphics Control

Graphics are drawn into an object called an isigraph control (the isi comes from Iverson Software, Inc., the original name of Jsoftware, Inc.) which resides in a window.

You can choose from several ways to create an isigraph control, depending on what features you need.  The quickest way to get one is with

   load 'graph'

   gopen ''

which will leave you ready for drawing with an isigraph control 150 pixels on a side.  If you want to specify your own options for the parent window or isigraph control, you can bypass the graph package, using instead a line like

   wd 'pc x closeok;xywh 0 0 200 200;cc g isigraph;pas 0 0;pshow'

which will also leave you ready for drawing.  In this example, the parent window was named x and the isigraph control was named g with a size of 200x200 pixels.  The pas 0 0 caused the parent to fit tightly around the isigraph. 

If you simply want a standalone window to display graphics in, either of the preceding methods is adequate.  If you want your graphics to be part of a form which can contain other graphics controls as well as text, sliders, selection boxes, and the like, you will want to learn how to use the Form Editor, either by reading the User Guide or by running the Labs.  Use the Form Editor to create a form, and include a child control of type isigraph   Your gl2 commands will be drawn into this child control.

All isigraph controls have the same capabilities, no matter what method was used to create them.

Selecting an isigraph Control for Output

If you have simply created a single isigraph control for use as a display, it was automatically selected for output when created and you do not need to do anything more than write to it.

If you have a more complex environment, where there are perhaps several isigraph controls in a form and many forms open at once, you need to select the correct isigraph control before you write to it.  gl2 commands operate on the currently-selected isigraph control.

First, you select the parent window, using

   wd 'psel windowname'

and then select the isigraph you want to draw into, using

   glsel 'isigraphname'

Now you are ready to push pixels.

Addressing the Screen

The glxxx verbs take integer arguments that represent pixel coordinates in the isigraph control.  The top-left pixel has coordinates (0,0), and the bottom-right pixel has coordinates (xsize-1,ysize-1). 

Drawing Graphics

You will issue a sequence of glxxx verbs.  (The graph library defines verbs to interface to the glxxx verbs, but I recommend you avoid them in the interests of performance)  The pixel-writing verbs, such as glrect and gllines, make use of the current pen (the linestyle used to draw the outline) and the current brush (the fill style used for the interior).  The pen and brush commands, and some of the other glxxx verbs, use the current color, a list of RGB (red-green-blue) values from 0 to 255.

As an example, to draw a 2-pixel-wide dashed red line from the top-left corner to the bottom-right corner of the selected isigraph, use

   glrgb 255 0 0  NB. set the color

   glpen 2,PS_DASH  NB. use that color for the pen

   gllines 0 0   150 150  NB. lines use current pen

Drawing Text

Text can be mixed with graphics.  First, set the font:

   glfont name size styles

where styles can be any of italic, bold, underline, oem, default, and anglexxx (where xxx is the angle of the font, in tenths of a degree clockwise).  size is in points.  Example:

   glfont "Times New Roman" 12 italic

Next, draw the background rectangle if any.  Text itself is transparent, in other words the background shows though the text.  If you want a solid background for the text, you must draw one.  Find out how big the text will be in pixels:

   extent =. glqextent textstring

then create a brush with the background color, and draw the background rectangle:

   glbrush '' [ glrgb red green blue

   glrect xcoord,ycoord,extent

Next, set the color for the text itself:

   gltextcolor '' [ glrgb red green blue

Finally, set the text position in pixels and draw the text. 

   gltextxy xcoord,ycoord

   gltext text

where text is the character string to draw.

The settings of the text attributes are preserved, so only the changed values need to be set for subsequent gltext calls.

The Drawing Surface

The glxxx verbs write pixels on the drawing surface, which is a memory area that has the size of your isigraph control.  Changes to the drawing surface are not immediately visible, lest the user be distracted by continual painting and an incomplete picture.  When you have executed enough glxxx commands to have a picture worth seeing, you issue

   glpaint ''

which copies the drawing surface to the visible screen..

Screen Resizing: The paint Event

If your isigraph control never changes size, what is displayed on the screen will be whatever you put there with your last glpaint command.  If, on the other hand, your isigraph can be resized by the user, the display will become invalid whenever the isigraph is resized.  When this happens, the system will signal a paint event, and you will have to recreate the display surface.  See below for a discussion of event handling.

Supporting a resizable isigraph window has profound effects on the design of your program.  You must keep a copy of all the graphics commands needed to regenerate the display, and for most applications you need to keep these commands in a virtual screen space so that they don't suffer unsightly errors in quantization when the screen size changes.

Partial List of glxxx Drawing Commands

i j give the (i,j) coordinates of a point in logical units, where i is the horizontal coordinate and j is the vertical coordinate.  x y w h specifies a rectangular region with one corner at (x,y) and the other at (x+w-1,y+h-1).


glclear ''    clear isigraph drawing buffer to white and reset default values for graphics state variables:
glfont system default
glrgb 0 0 0
glpen 1 0
gltextxy 0 0

Display Settings That You Will Probably Never Need To Modify

glnodblbuf bool  default 0 paints with double buffer to avoid flicker. Set to 1 to paint directly to the screen.

glwindoworg x y  default is 0 0.  The x and y values are added to subsequent graphics coordinates.

glcursor n  sets mouse cursor. Values are defined as IDC_... in gl2.

Setting a Clipping Window for Subsequent Drawing Primitives

glclip x y w h  Only pixels inside the given rectangle will be modified by subsequent drawing commands.

glclipreset ''  Turn off clip rectangle, allowing all pixels to be overwritten by drawing commands

Setting Colors

glrgb color ; set current color

Settings That Apply to Lines (including Borders of Filled Areas)

glpen i [style]  select pen. color is taken from last glrgb command, and the lines are drawn i units wide.  style is from the set (ps_solid, ps_dash, ps_dot, ps_dashdot, ps_dashdotdot, ps_null, ps_insideframe)

Drawing Lines

gllines i j i j ...  draw connected lines. i j... is 2 or more points.  gllines is the verb normally used for line-drawing.

Settings That Apply to Area-Filling Commands

glbrush ''  select solid brush in current color, i. e. fill interiors with solid fill in the color of the most recent glrgb.

glbrushnull ''  select null brush, i. e. leave interiors unfilled

Drawing Rectangles, Ellipses, and Arcs

glrect x y w h  draw rectangle with current pen and current brush

glroundr x y w h rw rh  (not java) draw rectangle with rounded corners defined by ellipse with width rw and height rh.  Use current pen and brush.

glellipse x y w h  draw a filled ellipse in the given rectangle with the current pen and brush

glarc x y w h xa ya xz yz  (not wince) draw arc on the ellipse defined by the given rectangle.  Arc starts at (xa,ya) and ends at (xz,yz).  Start and end points need not lie on the ellipse: they define a line from the center that intersects the ellipse.

Drawing Polygons

glpolygon i j i j ...  draw polygon in current pen and brush.  The list of (i,j) values are the polygon vertices..  glpolygon is the verb normally used to draw polygons.

Settings That Apply to Text

glfont name size styles  sets font for text commands

Drawing Text

gltext text  write text using the font specified by the most recent glfont in the color saved by the most recent gltextcolor.  Where and how the text is displayed is affected by the gltextalign and gltextxy commands.

gltextcolor ''   the color set by the most recent glrgb is saved as the color to be used for text

gltextxy i j  position to be used by gltext when gltexalign specifies TA_NOUPDATECP

Bitmap Operations

glpixel i j   draw pixel at (i,j) in current color

glpixels x y w h pixeldata   write pixels to the given rectangle.  pixeldata is an integer per pixel with RGB values

Metafile Operations

glfile filename   (only win32) set filename for subsequent glemfopen and glemfplay.

glemfopen ''  (only win32) Open the file named in the most recent glfile command.  This file will be an enhanced metafile, and subsequent glxxx commands will be written to this file.

glemfclose ''   (only win32) Close the file opened by glemfopen ..

glemfplay x y [w h]    (only win32) Play the enhanced metafile named in the most recent glfile command.   x y gives the top-left corner of the area on which the metafile will be drawn; w h give the size of the rectangle that the metafile will be scaled to fit into, or may be omitted to display the metafile at full size.

isigraph Events

isigraph controls produce events, which like all window events result in execution of the sentence

   formname_isigraphname_eventname_formlocale_ ''

where formlocale is the name of the locale the form was executed in, and the other names identify the form, isigraph, and event type.  Before execution of this sentence, the variable sysdata is set with information about the event.  The events and their associated sysdata are:

paint Event

The paint event is signalled whenever the isigraph control changes size.  The paint event handler must redraw the drawing surface.  It does not need to issue glpaint to move the display surface to the screen--that will be done automatically.

char Event

When a character is pressed while the cursor is within an isigraph control, a char event is produced.  sysdata is a character list giving the key that was pressed: the character itself for printable keys, or the virtual key VK_name for a special key such as HOME or an arrow key (look in system\packages\graphics\vkeys.ijs for the VK_name definitions).  For example, sysdata is 'a' if the letter-a key is pressed, and 21{a. if the up-arrow is pressed.  The character in sysdata is represented in UTF-8 form, which means that it will be encoded as a multi-character sequence if the ASCII code is 128 or higher.

 sysmodifiers is a single character value indicating whether CTRL or SHIFT was pressed: '0'=neither, '1'=SHIFT, '2'=CTRL, '3'=SHIFT+CTRL.  No event is signaled for CTRL+ASCII-character as that is taken to be a keyboard shortcut.

Mouse Events

The mouse events are mmove, mbldown, mblup, mbldbl, mbrdown, mbrup, and mbrdbl, corresponding to mouse-move and mouse-clicks (left or right button; down, up, or double-click).  sysdata contains a character string which should be converted to numeric using 0&"., after which it will be an 8-item vector indicating the values

cursorx cursory isiwidth isiheight mbl mbr ctrl shift

where cursorx and cursory give the cursor position in pixels, isiwidth and isiheight give the size of the isigraph control in pixels, and mbl, mbr, ctrl, and shift give the status of the corresponding mouse-buttons and keys at the time of the event.

High Performance: Blocks of glxxx Commands Using glcmds

Each call to a glxxx verb makes an addition to the display list.  If your calls have small amounts of data, the overhead of updating the display list could take much more time than the drawing to the screen.  In that case, you can see a performance improvement if you build a graphics block holding the data for several glxxx verbs and then pass the block into J with a single call.

The graphics block will be a numeric list which is a concatenation of graphics orders.  Each graphics order replaces one call to a glxxx verb and has the format


length_of_order is 2+$data (i. e., the length of the graphics order including the length field).  glxxx_code identifies the glxxx verb that the graphics order represents: this is the code used in system\main\gl2.ijs to define the glxxx verb.  For example, the glline verb is defined by

glline=: 11!:2013

so the glxxx_code for glline is 2013.  data is the operand needed by the glxxx verb.

Once you have built the graphics block, you draw it by executing glcmds graphicsblock .  To draw the 2-pixel-wide dashed red line used in the example above, you could issue the glrgb, glpen, and gllines in one go with

block =: 5 2032 255 0 0   4 2022 2 1   6 2015 0 1000 1000 0

glcmds block

Displaying Tabular Data: the Grid Control

The Grid Control is a set of J functions that probably does all you need for displaying a table of data.  See the User Guide for a description of its numerous features.

3D Graphics: OpenGL

For 3-D graphics, J supports OpenGL, a graphics interface of great power with a manual the size of a phonebook.  If you want to learn about it, study the manual; if you know OpenGL and want to use it in J, consult the Labs.

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