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1% language=us runpath=texruns:manuals/luametafun
2
3\environment luametafun-style
4
5\startcomponent luametafun-contour
6
7\startchapter[title={Contour}]
8
9This feature started out as experiment triggered by a request on the mailing
10list. In the end it was a nice exploration of what is possible with a bit of
11\LUA. In a sense it is more subsystem than a simple \METAPOST\ macro because
12quite some \LUA\ code is involved and more might be used in the future. It's part
13of the fun.
14
15A contour is a line through equivalent values $z$ that result from applying a
16function to two variables $x$ and $y$. There is quite a bit of analysis needed
17to get these lines. In \METAFUN\ we currently support three methods for generating
18a colorful background and three for putting lines on top:
19
20One solution is to use the the isolines and isobands methods are described on the
21marching squares page of wikipedia:
22
23\starttyping
24https://en.wikipedia.org/wiki/Marching_squares
25\stoptyping
26
27This method is relative efficient as we don't do much optimization, simply
28because it takes time and the gain is not that much relevant. Because we support
29filling of multiple curves in one go, we get efficient paths anyway without side
30effects that normally can occur from many small paths alongside. In these days of
31multi megabyte movies and sound clips a request of making a \PDF\ file small is kind
32of strange anyway. In practice the penalty is not that large.
33
34As background we can use a bitmap. This method is also quite efficient because we
35use indexed colors which results in a very good compression. We use a simple
36mapping on a range of values.
37
38A third method is derived from the one that is distributed as \CCODE\ source
39file at:
40
41\starttyping
42https://physiology.arizona.edu/people/secomb/contours
43https://github.com/secomb/GreensV4
44\stoptyping
45
46We can create a background image, which uses a sequence of closed curves
47\footnote {I have to figure out how to improve it a bit so that multiple path
48don't get connected.}. It can also provide two variants of lines around the
49contours (we tag them shape and shade). It's all a matter of taste. In the
50meantime I managed to optimize the code a bit and I suppose that when I buy a new
51computer (the code was developed on an 8 year old machine) performance is
52probably acceptable.
53
54In order of useability you can think of isoband (band) with isolines (cell),
55bitmap (bitmap) with isolines (cell) and finally shapes (shape) with edges
56(edge). But let's start with a couple of examples.
57
58\startbuffer[1]
59\startMPcode{doublefun}
60    draw lmt_contour [
61        xmin =  0, xmax = 4*pi, xstep = .05,
62        ymin = -6, ymax = 6,    ystep = .05,
63
64        levels     = 7,
65        height     = 5cm,
66        preamble   = "local sin, cos = math.sin, math.cos",
67        function   = "cos(x) + sin(y)",
68        background = "bitmap",
69        foreground = "edge",
70        linewidth  = 1/2,
71        cache      = true,
72    ] ;
73\stopMPcode
74\stopbuffer
75
76\startplacefigure[reference=contour:1]
77    \getbuffer[1]
78\stopplacefigure
79
80\typebuffer[1][option=TEX]
81
82In \in {figure} [contour:1] we see the result. There is a in this case black and
83white image generated and on top of that we see lines. The step determines the
84resolution of the image. In practice using a bitmap is quite okay and also rather
85efficient: we use an indexed colorspace and, as already was mentioned, because
86the number of colors is limited such an image compresses well. A different
87rendering is seen in \in {figure} [contour:2] where we use the shape method for
88the background. That method creates outlines but is much slower, and when you use
89a high resolution (small step) it can take quite a while to identify the shapes.
90This is why we set the cache flag.
91
92\startbuffer[2]
93\startMPcode{doublefun}
94    draw lmt_contour [
95        xmin =  0, xmax = 4*pi, xstep = .10,
96        ymin = -6, ymax = 6,    ystep = .10,
97
98        levels     = 7,
99        preamble   = "local sin, cos = math.sin, math.cos",
100        function   = "cos(x) - sin(y)",
101        background = "shape",
102        foreground = "shape",
103        linewidth  = 1/2,
104        cache      = true,
105    ] ;
106\stopMPcode
107\stopbuffer
108
109\typebuffer[2][option=TEX]
110
111\startplacefigure[reference=contour:2]
112    \getbuffer[2]
113\stopplacefigure
114
115We mentioned colorspace but haven't seen any color yet, so let's set some in \in
116{figure} [contour:3]. Two variants are shown: a background \type {shape} with
117foreground \type {shape} and a background \type {bitmap} with a foreground \type
118{edge}. The bitmap renders quite fast, definitely when we compare with the shape,
119while the quality is as good at this size.
120
121\startbuffer[3a]
122\startMPcode{doublefun}
123    draw lmt_contour [
124        xmin = -10, xmax = 10, xstep =  .1,
125        ymin = -10, ymax = 10, ystep =  .1,
126
127        levels     = 10,
128        height     = 7cm,
129        color      = "shade({1/2,1/2,0},{0,0,1/2})",
130        function   = "x^2 + y^2",
131        background = "shape",
132        foreground = "shape",
133        linewidth  = 1/2,
134        cache      = true,
135    ] xsized .45TextWidth ;
136\stopMPcode
137\stopbuffer
138
139\startbuffer[3b]
140\startMPcode{doublefun}
141    draw lmt_contour [
142        xmin = -10, xmax = 10, xstep =  .1,
143        ymin = -10, ymax = 10, ystep =  .1,
144
145        levels     = 10,
146        height     = 7cm,
147        color      = "shade({1/2,0,0},{0,0,1/2})",
148        function   = "x^2 + y^2",
149        background = "bitmap",
150        foreground = "edge",
151        linewidth  = 1/2,
152        cache      = true,
153    ] xsized .45TextWidth ;
154\stopMPcode
155\stopbuffer
156
157\typebuffer[3a][option=TEX]
158
159\startplacefigure[reference=contour:3]
160    \startcombination
161        {\getbuffer[3a]} {\bf shape}
162        {\getbuffer[3b]} {\bf bitmap}
163    \stopcombination
164\stopplacefigure
165
166We use the \type {doublefun} instance because we need to be sure that we don't
167run into issues with scaled numbers, the default model in \METAPOST. The
168function that gets passed is {\em not} using \METAPOST\ but \LUA, so basically
169you can do very complex things. Here we directly pass code, but you can for
170instance also do this:
171
172\starttyping[option=TEX]
173\startluacode
174    function document.MyContourA(x,y)
175        return x^2 + y^2
176    end
177\stopluacode
178\stoptyping
179
180and then \type {function = "document.MyContourA(x,y)"}. As long as the function
181returns a valid number we're okay. When you pass code directly you can use the
182\type {preamble} key to set local shortcuts. In the previous examples we took
183\type {sin} and \type {cos} from the math library but you can also roll out your
184own functions and|/|or use the more elaborate \type {xmath} library. The color
185parameter is also a function, one that returns one or three arguments. In the
186next example we use \type {lin} to calculate a fraction of the current level and
187total number of levels.
188
189\startbuffer[4a]
190\startMPcode{doublefun}
191    draw lmt_contour [
192        xmin = -3, xmax = 3, xstep =  .01,
193        ymin = -1, ymax = 1, ystep =  .01,
194
195        levels     = 10,
196        default    = .5,
197        height     = 5cm,
198        function   = "x^2 + y^2 + x + y/2",
199        color      = "lin(l), 0, 1/2",
200        background = "bitmap"
201        foreground = "none",
202        cache      = true,
203    ] xsized TextWidth ;
204\stopMPcode
205\stopbuffer
206
207\typebuffer[4a][option=TEX]
208
209\startplacefigure[reference=contour:4a]
210    \getbuffer[4a]
211\stopplacefigure
212
213Instead of a bitmap we can use an isoband, which boils down to a set of tiny
214shapes that make up a bigger one. This is shown in \in {figure} [contour:4b].
215
216\startbuffer[4b]
217\startMPcode{doublefun}
218    draw lmt_contour [
219        xmin = -3, xmax = 3, xstep =  .01,
220        ymin = -1, ymax = 1, ystep =  .01,
221
222        levels     = 10,
223        default    = .5,
224        height     = 5cm,
225        function   = "x^2 + y^2 + x + y/2",
226        color      = "lin(l), 1/2, 0",
227        background = "band",
228        foreground = "none",
229        cache      = true,
230    ] xsized TextWidth ;
231\stopMPcode
232\stopbuffer
233
234\typebuffer[4b][option=TEX]
235
236\startplacefigure[reference=contour:4b]
237    \getbuffer[4b]
238\stopplacefigure
239
240You can draw several functions and see where they overlap:
241
242\startbuffer[5]
243\startMPcode{doublefun}
244    draw lmt_contour [
245        xmin = -pi, xmax = 4*pi, xstep = .1,
246        ymin = -3,  ymax = 3,    ystep = .1,
247
248        range      = { -.1, .1 },
249        preamble   = "local sin, cos = math.sin, math.cos",
250        functions  = {
251            "sin(x) + sin(y)", "sin(x) + cos(y)",
252            "cos(x) + sin(y)", "cos(x) + cos(y)"
253        },
254        background = "bitmap",
255        linecolor  = "black",
256        linewidth  = 1/10,
257        color      = "shade({1,1,0},{0,0,1})"
258        cache      = true,
259    ] xsized TextWidth ;
260\stopMPcode
261\stopbuffer
262
263\typebuffer[5][option=TEX]
264
265\startplacefigure[reference=contour:5]
266    \getbuffer[5]
267\stopplacefigure
268
269The range determines the $z$ value(s) that we take into account. You can also
270pass a list of colors to be used. In \in {figure} [contour:6] this is
271demonstrated. There we also show a variant foreground \type {cell}, which uses a
272bit different method for calculating the edges. \footnote {This a bit of a
273playground: more variants might show up in due time.}
274
275\startbuffer[6]
276\startMPcode{doublefun}
277    draw lmt_contour [
278        xmin = -2*pi, xmax =  2*pi, xstep = .01,
279        ymin = -3,    ymax =  3,    ystep = .01,
280
281        range      = { -.1, .1 },
282        preamble   = "local sin, cos = math.sin, math.cos",
283        functions  = { "sin(x) + sin(y)", "sin(x) + cos(y)" },
284        background = "bitmap",
285        foreground = "cell",
286        linecolor  = "white",
287        linewidth  = 1/10,
288        colors     = { (1/2,1/2,1/2), red, green, blue }
289        level      = 3,
290        linewidth  = 6,
291        cache      = true,
292    ] xsized TextWidth ;
293\stopMPcode
294\stopbuffer
295
296\typebuffer[6][option=TEX]
297
298Here the number of levels depends on the number of functions as each can overlap
299with another; for instance the outcome of two functions can overlap or not which
300means 3 cases, and with a value not being seen that gives 4 different cases.
301
302\startplacefigure[reference=contour:6]
303    \getbuffer[6]
304\stopplacefigure
305
306\startbuffer[7]
307\startMPcode{doublefun}
308    draw lmt_contour [
309        xmin = -2*pi, xmax =  2*pi, xstep = .01,
310        ymin = -3,    ymax =  3,    ystep = .01,
311
312        range      = { -.1, .1 },
313        preamble   = "local sin, cos = math.sin, math.cos",
314        functions  = {
315            "sin(x) + sin(y)",
316            "sin(x) + cos(y)",
317            "cos(x) + sin(y)",
318            "cos(x) + cos(y)"
319        },
320        background = "bitmap",
321        foreground = "none",
322        level      = 3,
323        color      = "shade({2/3,0,0},{2/3,1,2/3})"
324        cache      = true,
325    ] xsized TextWidth ;
326\stopMPcode
327\stopbuffer
328
329\typebuffer[7][option=TEX]
330
331Of course one can wonder how useful showing many functions but it can give nice
332pictures, as shown in \in {figure} [contour:7].
333
334\startplacefigure[reference=contour:7]
335    \getbuffer[7]
336\stopplacefigure
337
338\startbuffer[8]
339\startMPcode{doublefun}
340    draw lmt_contour [
341        xmin = -2*pi, xmax =  2*pi, xstep = .01,
342        ymin = -3,    ymax =  3,    ystep = .01,
343
344        range      = { -.3, .3 },
345        preamble   = "local sin, cos = math.sin, math.cos",
346        functions  = {
347            "sin(x) + sin(y)",
348            "sin(x) + cos(y)",
349            "cos(x) + sin(y)",
350            "cos(x) + cos(y)"
351        },
352        background = "bitmap",
353        foreground = "none",
354        level      = 3,
355        color      = "shade({1,0,0},{0,1,0})"
356        cache      = true,
357    ] xsized TextWidth ;
358\stopMPcode
359\stopbuffer
360
361\typebuffer[8][option=TEX]
362
363We can enlargen the window, which is demonstrated in \in {figure} [contour:8]. I
364suppose that such images only make sense in educational settings.
365
366\startplacefigure[reference=contour:8]
367    \getbuffer[8]
368\stopplacefigure
369
370% \startbuffer[9a]
371% \startMPcode{doublefun}
372%     draw lmt_contour [
373%         xmin = -10, xmax = 10, xstep = 1,
374%         ymin = -10, ymax = 10, ystep = 1,
375%         function  = "math.random(1,3)", levels    = 3,
376%         linecolor = "white",            linewidth = 1/10,
377%         width     = .3TextWidth,        legend    = "none",
378%         color     = "shade({1/2,1/2,0},{0,0,1})"
379%
380%         background = "bitmap", foreground = "edge",
381%     ] ;
382% \stopMPcode
383% \stopbuffer
384%
385% \typebuffer[9a][option=TEX]
386%
387% \startbuffer[9b]
388% \startMPcode{doublefun}
389%     draw lmt_contour [
390%         xmin = -10, xmax = 10, xstep = 1,
391%         ymin = -10, ymax = 10, ystep = 1,
392%         function  = "math.random(1,3)", levels    = 3,
393%         linecolor = "white",            linewidth = 1/10,
394%         width     = .3TextWidth,        legend    = "none",
395%         color     = "shade({1/2,1/2,0},{0,0,1/2})"
396%
397%         background = "bitmap", foreground = "cell",
398%     ] ;
399% \stopMPcode
400% \stopbuffer
401%
402% \startbuffer[9c]
403% \startMPcode{doublefun}
404%     draw lmt_contour [
405%         xmin = -10, xmax = 10, xstep = 1,
406%         ymin = -10, ymax = 10, ystep = 1,
407%         function  = "math.random(1,3)", levels    = 3,
408%         linecolor = "white",            linewidth = 1/10,
409%         width     = .3TextWidth,        legend    = "none",
410%         color     = "shade({1/2,1/2,0},{0,0,1})"
411%
412%         background = "bitmap", foreground = "none",
413%     ] ;
414% \stopMPcode
415% \stopbuffer
416%
417% \startbuffer[9d]
418% \startMPcode{doublefun}
419%     draw lmt_contour [
420%         xmin = -10, xmax = 10, xstep = 1,
421%         ymin = -10, ymax = 10, ystep = 1,
422%         function  = "math.random(1,3)", levels    = 3,
423%         linecolor = "white",            linewidth = 1/10,
424%         width     = .3TextWidth,        legend    = "none",
425%         color     = "shade({1/2,1/2,0},{0,0,1})"
426%
427%         background = "shape", foreground = "shape",
428%     ] ;
429% \stopMPcode
430% \stopbuffer
431%
432% \startbuffer[9e]
433% \startMPcode{doublefun}
434%     draw lmt_contour [
435%         xmin = -10, xmax = 10, xstep = 1,
436%         ymin = -10, ymax = 10, ystep = 1,
437%         function  = "math.random(1,3)", levels    = 3,
438%         linecolor = "white",            linewidth = 1/10,
439%         width     = .3TextWidth,        legend    = "none",
440%         color     = "shade({1/2,1/2,0},{0,0,1})"
441%
442%         background = "shape", foreground = "edge",
443%     ] ;
444% \stopMPcode
445% \stopbuffer
446%
447% \startbuffer[9f]
448% \startMPcode{doublefun}
449%     draw lmt_contour [
450%         xmin = -10, xmax = 10, xstep = 1,
451%         ymin = -10, ymax = 10, ystep = 1,
452%         function  = "math.random(1,3)", levels    = 3,
453%         linecolor = "white",            linewidth = 1/10,
454%         width     = .3TextWidth,        legend    = "none",
455%         color     = "shade({1/2,1/2,0},{0,0,1})"
456%
457%         background = "shape", foreground = "none",
458%     ] ;
459% \stopMPcode
460% \stopbuffer
461%
462% \startbuffer[9g]
463% \startMPcode{doublefun}
464%     draw lmt_contour [
465%         xmin = -10, xmax = 10, xstep = 1,
466%         ymin = -10, ymax = 10, ystep = 1,
467%         function  = "math.random(1,3)", levels    = 3,
468%         linecolor = "white",            linewidth = 1/10,
469%         width     = .3TextWidth,        legend    = "none",
470%         color     = "shade({1/2,1/2,0},{0,0,1})"
471%
472%         background = "band", foreground = "edge",
473%     ] ;
474% \stopMPcode
475% \stopbuffer
476%
477% \startbuffer[9h]
478% \startMPcode{doublefun}
479%     draw lmt_contour [
480%         xmin = -10, xmax = 10, xstep = 1,
481%         ymin = -10, ymax = 10, ystep = 1,
482%         function  = "math.random(1,3)", levels    = 3,
483%         linecolor = "white",            linewidth = 1/10,
484%         width     = .3TextWidth,        legend    = "none",
485%         color     = "shade({1/2,1/2,0},{0,0,1})"
486%
487%         background = "band", foreground = "cell",
488%     ] ;
489% \stopMPcode
490% \stopbuffer
491%
492% \startbuffer[9i]
493% \startMPcode{doublefun}
494%     draw lmt_contour [
495%         xmin = -10, xmax = 10, xstep = 1,
496%         ymin = -10, ymax = 10, ystep = 1,
497%         function  = "math.random(1,3)", levels    = 3,
498%         linecolor = "white",            linewidth = 1/10,
499%         width     = .3TextWidth,        legend    = "none",
500%         color     = "shade({1/2,1/2,0},{0,0,1})"
501%
502%         background = "band", foreground = "none",
503%     ] ;
504% \stopMPcode
505% \stopbuffer
506%
507% In \in {figure} [contour:9] we see that using the shape option doesn't work out
508% too well here, which again demonstrates that using the bitmap method is not that
509% bad. In that example we use random numbers, just to show the erratic behavior. In
510% \in {figure} [contour:10] a more sane image is used. The band and bitmap examples
511% are generated quite fast so no caching is used there. We only show one definition:
512%
513% \typebuffer[9i][option=TEX]
514%
515% \startplacefigure[reference=contour:9]
516%     \startcombination[3*3]
517%         {\pushrandomseed\setrandomseed{1}\getbuffer[9a]\poprandomseed} {\bf bitmap edge}
518%         {\pushrandomseed\setrandomseed{1}\getbuffer[9b]\poprandomseed} {\bf bitmap cell}
519%         {\pushrandomseed\setrandomseed{1}\getbuffer[9c]\poprandomseed} {\bf bitmap none}
520%         {\pushrandomseed\setrandomseed{1}\getbuffer[9d]\poprandomseed} {\bf shape  shape}
521%         {\pushrandomseed\setrandomseed{1}\getbuffer[9e]\poprandomseed} {\bf shape  edge}
522%         {\pushrandomseed\setrandomseed{1}\getbuffer[9f]\poprandomseed} {\bf shape  none}
523%         {\pushrandomseed\setrandomseed{1}\getbuffer[9g]\poprandomseed} {\bf band   edge}
524%         {\pushrandomseed\setrandomseed{1}\getbuffer[9h]\poprandomseed} {\bf band   cell}
525%         {\pushrandomseed\setrandomseed{1}\getbuffer[9i]\poprandomseed} {\bf band   none}
526%     \stopcombination
527% \stopplacefigure
528
529In \in {figure} [contour:10] we see different combinations of backgrounds (in color)
530and foregrounds (edges) in action.
531
532\startbuffer[10a]
533\startMPcode{doublefun}
534    draw lmt_contour [
535        xmin =  0, xmax = 4*pi, xstep = 0,
536        ymin = -6, ymax = 6,    ystep = 0,
537
538        levels = 5, legend = false, linewidth  = 1/2,
539
540        preamble   = "local sin, cos = math.sin, math.cos",
541        function   = "cos(x) - sin(y)",
542        color      = "shade({1/2,0,0},{0,0,1/2})",
543
544        background = "bitmap", foreground = "edge",
545    ] xsized .3TextWidth ;
546\stopMPcode
547\stopbuffer
548
549\startbuffer[10b]
550\startMPcode{doublefun}
551    draw lmt_contour [
552        xmin =  0, xmax = 4*pi, xstep = 0,
553        ymin = -6, ymax = 6,    ystep = 0,
554
555        levels = 5, legend = false, linewidth  = 1/2,
556
557        preamble   = "local sin, cos = math.sin, math.cos",
558        function   = "cos(x) - sin(y)",
559        color      = "shade({1/2,0,0},{0,0,1/2})",
560
561        background = "bitmap", foreground = "cell",
562    ] xsized .3TextWidth ;
563\stopMPcode
564\stopbuffer
565
566\startbuffer[10c]
567\startMPcode{doublefun}
568    draw lmt_contour [
569        xmin =  0, xmax = 4*pi, xstep = 0,
570        ymin = -6, ymax = 6,    ystep = 0,
571
572        levels = 5, legend = false, linewidth  = 1/2,
573
574        preamble   = "local sin, cos = math.sin, math.cos",
575        function   = "cos(x) - sin(y)",
576        color      = "shade({1/2,0,0},{0,0,1/2})",
577
578        background = "bitmap", foreground = "none",
579    ] xsized .3TextWidth ;
580\stopMPcode
581\stopbuffer
582
583\startbuffer[10d]
584\startMPcode{doublefun}
585    draw lmt_contour [
586        xmin =  0, xmax = 4*pi, xstep = 0,
587        ymin = -6, ymax = 6,    ystep = 0,
588
589        levels = 5, legend = false, linewidth  = 1/2,
590
591        preamble   = "local sin, cos = math.sin, math.cos",
592        function   = "cos(x) - sin(y)",
593        color      = "shade({1/2,0,0},{0,0,1/2})",
594
595        background = "shape",  foreground = "shape", cache = true,
596    ] xsized .3TextWidth ;
597\stopMPcode
598\stopbuffer
599
600\startbuffer[10e]
601\startMPcode{doublefun}
602    draw lmt_contour [
603        xmin =  0, xmax = 4*pi, xstep = 0,
604        ymin = -6, ymax = 6,    ystep = 0,
605
606        levels = 5, legend = false, linewidth  = 1/2,
607
608        preamble   = "local sin, cos = math.sin, math.cos",
609        function   = "cos(x) - sin(y)",
610        color      = "shade({1/2,0,0},{0,0,1/2})",
611
612        background = "shape",  foreground = "edge", cache = true,
613    ] xsized .3TextWidth ;
614\stopMPcode
615\stopbuffer
616
617\startbuffer[10f]
618\startMPcode{doublefun}
619    draw lmt_contour [
620        xmin =  0, xmax = 4*pi, xstep = 0,
621        ymin = -6, ymax = 6,    ystep = 0,
622
623        levels = 5, legend = false, linewidth  = 1/2,
624
625        preamble   = "local sin, cos = math.sin, math.cos",
626        function   = "cos(x) - sin(y)",
627        color      = "shade({1/2,0,0},{0,0,1/2})",
628
629        background = "shape",  foreground = "none", cache = true,
630    ] xsized .3TextWidth ;
631\stopMPcode
632\stopbuffer
633
634\startbuffer[10g]
635\startMPcode{doublefun}
636    draw lmt_contour [
637        xmin =  0, xmax = 4*pi, xstep = 0,
638        ymin = -6, ymax = 6,    ystep = 0,
639
640        levels = 5, legend = false, linewidth  = 1/2,
641
642        preamble   = "local sin, cos = math.sin, math.cos",
643        function   = "cos(x) - sin(y)",
644        color      = "shade({1/2,0,0},{0,0,1/2})",
645
646        background = "band",   foreground = "edge",
647    ] xsized .3TextWidth ;
648\stopMPcode
649\stopbuffer
650
651\startbuffer[10h]
652\startMPcode{doublefun}
653    draw lmt_contour [
654        xmin =  0, xmax = 4*pi, xstep = 0,
655        ymin = -6, ymax = 6,    ystep = 0,
656
657        levels = 5, legend = false, linewidth  = 1/2,
658
659        preamble   = "local sin, cos = math.sin, math.cos",
660        function   = "cos(x) - sin(y)",
661        color      = "shade({1/2,0,0},{0,0,1/2})",
662
663        background = "band",   foreground = "cell",
664    ] xsized .3TextWidth ;
665\stopMPcode
666\stopbuffer
667
668\startbuffer[10i]
669\startMPcode{doublefun}
670    draw lmt_contour [
671        xmin =  0, xmax = 4*pi, xstep = 0,
672        ymin = -6, ymax = 6,    ystep = 0,
673
674        levels = 5, legend = false, linewidth  = 1/2,
675
676        preamble   = "local sin, cos = math.sin, math.cos",
677        function   = "cos(x) - sin(y)",
678        color      = "shade({1/2,0,0},{0,0,1/2})",
679
680        background = "band",   foreground = "none",
681    ] xsized .3TextWidth ;
682\stopMPcode
683\stopbuffer
684
685\typebuffer[10b][option=TEX]
686
687% \page
688
689There are quite some settings. Some deal with the background, some with the
690foreground and quite some deal with the legend.
691
692\starttabulate[|T|T|T|p|]
693\FL
694\BC name             \BC type    \BC default    \BC comment \NC \NR
695\ML
696\NC xmin             \NC numeric \NC 0          \NC needs to be set \NC \NR
697\NC xmax             \NC numeric \NC 0          \NC needs to be set \NC \NR
698\NC ymin             \NC numeric \NC 0          \NC needs to be set \NC \NR
699\NC ymax             \NC numeric \NC 0          \NC needs to be set \NC \NR
700\NC xstep            \NC numeric \NC 0          \NC auto 1/200 when zero \NC \NR
701\NC ystep            \NC numeric \NC 0          \NC auto 1/200 when zero \NC \NR
702\NC checkresult      \NC boolean \NC false      \NC checks for overflow and NaN \NC \NR
703\NC defaultnan       \NC numeric \NC 0          \NC the value to be used when NaN \NC \NR
704\NC defaultinf       \NC numeric \NC 0          \NC the value to be used when overflow \NC \NR
705\ML
706\NC levels           \NC numeric \NC 10         \NC number of different levels to show \NC \NR
707\NC level            \NC numeric \NC            \NC only show this level (foreground) \NC \NR
708\ML
709\NC preamble         \NC string  \NC            \NC shortcuts \NC \NR
710\NC function         \NC string  \NC x + y      \NC the result z value \NC \NR
711\NC functions        \NC list    \NC            \NC multiple functions (overlapping levels) \NC \NR
712\NC color            \NC string  \NC lin(l)     \NC the result color value for level l (1 or 3 values) \NC \NR
713\NC colors           \NC numeric \NC            \NC used when set \NC \NR
714\ML
715\NC background       \NC string  \NC bitmap     \NC band, bitmap, shape \NC \NR
716\NC foreground       \NC string  \NC auto       \NC cell, edge, shape auto \NC \NR
717\ML
718\NC linewidth        \NC numeric \NC .25        \NC \NC \NR
719%NC backgroundcolor  \NC string  \NC black      \NC \NC \NR
720\NC linecolor        \NC string  \NC gray       \NC \NC \NR
721\ML
722\NC width            \NC numeric \NC 0          \NC automatic when zero \NC \NR
723\NC height           \NC numeric \NC 0          \NC automatic when zero \NC \NR
724\ML
725\NC trace            \NC boolean \NC false      \NC \NC \NR
726\ML
727\NC legend           \NC string  \NC all        \NC x y z function range all \NC \NR
728\NC legendheight     \NC numeric \NC LineHeight \NC \NC \NR
729\NC legendwidth      \NC numeric \NC LineHeight \NC \NC \NR
730\NC legendgap        \NC numeric \NC 0          \NC \NC \NR
731\NC legenddistance   \NC numeric \NC EmWidth    \NC \NC \NR
732\NC textdistance     \NC numeric \NC 2EmWidth/3 \NC \NC \NR
733\NC functiondistance \NC numeric \NC ExHeight   \NC \NC \NR
734\NC functionstyle    \NC string  \NC            \NC  \CONTEXT\ style name \NC \NR
735\NC xformat          \NC string  \NC @0.2N      \NC number format template \NC \NR
736\NC yformat          \NC string  \NC @0.2N      \NC number format template \NC \NR
737\NC zformat          \NC string  \NC @0.2N      \NC number format template \NC \NR
738\NC xstyle           \NC string  \NC            \NC \CONTEXT\ style name \NC \NR
739\NC ystyle           \NC string  \NC            \NC \CONTEXT\ style name \NC \NR
740\NC zstyle           \NC string  \NC            \NC \CONTEXT\ style name \NC \NR
741\ML
742\NC axisdistance     \NC numeric \NC ExHeight   \NC \NC \NR
743\NC axislinewidth    \NC numeric \NC .25        \NC \NC \NR
744\NC axisoffset       \NC numeric \NC ExHeight/4 \NC \NC \NR
745\NC axiscolor        \NC string  \NC black      \NC \NC \NR
746\NC ticklength       \NC numeric \NC ExHeight   \NC \NC \NR
747\ML
748\NC xtick            \NC numeric \NC 5          \NC \NC \NR
749\NC ytick            \NC numeric \NC 5          \NC \NC \NR
750\NC xlabel           \NC numeric \NC 5          \NC \NC \NR
751\NC ylabel           \NC numeric \NC 5          \NC \NC \NR
752\LL
753\stoptabulate
754
755\startplacefigure[reference=contour:10]
756    \startcombination[3*3]
757        {\getbuffer[10a]} {\bf bitmap edge}
758        {\getbuffer[10b]} {\bf bitmap cell}
759        {\getbuffer[10c]} {\bf bitmap none}
760        {\getbuffer[10d]} {\bf shape  shape}
761        {\getbuffer[10e]} {\bf shape  edge}
762        {\getbuffer[10f]} {\bf shape  none}
763        {\getbuffer[10g]} {\bf band   edge}
764        {\getbuffer[10h]} {\bf band   cell}
765        {\getbuffer[10i]} {\bf band   none}
766    \stopcombination
767\stopplacefigure
768
769\stopchapter
770
771\stopcomponent
772