summaryrefslogtreecommitdiff
path: root/Master/texmf/asymptote/palette.asy
blob: fabbdc2cd5b80836755ebc0865c721584853b561 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
private import graph;

typedef bounds range(picture pic, real min, real max);

range Range(bool automin=false, real min=-infinity,
            bool automax=false, real max=infinity) 
{
  return new bounds(picture pic, real dmin, real dmax) {
    // autoscale routine finds reasonable limits
    bounds mz=autoscale(pic.scale.z.T(dmin),
                        pic.scale.z.T(dmax),
                        pic.scale.z.scale);
    // If automin/max, use autoscale result, else
    //   if min/max is finite, use specified value, else
    //   use minimum/maximum data value
    real pmin=automin ? pic.scale.z.Tinv(mz.min) : (finite(min) ? min : dmin);
    real pmax=automax ? pic.scale.z.Tinv(mz.max) : (finite(max) ? max : dmax);
    return bounds(pmin,pmax);
  };
}

range Automatic=Range(true,true);
range Full=Range();

void image(frame f, real[][] data, pair initial, pair final, pen[] palette,
           bool transpose=(initial.x < final.x && initial.y < final.y),
           transform t=identity(), bool copy=true, bool antialias=false)
{
  _image(f,transpose ? transpose(data) : copy ? copy(data) : data,
         initial,final,palette,t,copy=false,antialias=antialias);
}

void image(frame f, pen[][] data, pair initial, pair final,
           bool transpose=(initial.x < final.x && initial.y < final.y),
           transform t=identity(), bool copy=true, bool antialias=false)
{
  _image(f,transpose ? transpose(data) : copy ? copy(data) : data,
         initial,final,t,copy=false,antialias=antialias);
}

// Reduce color palette to approximate range of data relative to "display"
// range => errors of 1/palette.length in resulting color space.
pen[] adjust(picture pic, real min, real max, real rmin, real rmax,
             pen[] palette) 
{
  real dmin=pic.scale.z.T(min);
  real dmax=pic.scale.z.T(max);
  real delta=rmax-rmin;
  if(delta > 0) {
    real factor=palette.length/delta;
    int minindex=floor(factor*(dmin-rmin));
    if(minindex < 0) minindex=0;
    int maxindex=floor(factor*(dmax-rmin));
    if(maxindex > palette.length) maxindex=palette.length;
    if(minindex > 0 || maxindex < palette.length) {
      pen[] newpalette;
      for(int i=minindex; i < maxindex; ++i)
        newpalette.push(palette[i]);
      return newpalette;
    }
  }
  return palette;
}

private real[] sequencereal;

bounds image(picture pic=currentpicture, real[][] f, range range=Full,
             pair initial, pair final, pen[] palette,
             bool transpose=(initial.x < final.x && initial.y < final.y),
             bool copy=true, bool antialias=false)
{
  if(transpose) f=transpose(f);
  else if(copy) f=copy(f);
  if(copy) palette=copy(palette);

  real m=min(f);
  real M=max(f);
  bounds bounds=range(pic,m,M);
  real rmin=pic.scale.z.T(bounds.min);
  real rmax=pic.scale.z.T(bounds.max);
  palette=adjust(pic,m,M,rmin,rmax,palette);

  // Crop data to allowed range and scale
  if(range != Full || pic.scale.z.scale.T != identity ||
     pic.scale.z.postscale.T != identity) {
    scalefcn T=pic.scale.z.T;
    real m=bounds.min;
    real M=bounds.max;
    for(int i=0; i < f.length; ++i)
      f[i]=map(new real(real x) {return T(min(max(x,m),M));},f[i]);
  }

  initial=Scale(pic,initial);
  final=Scale(pic,final);

  pic.add(new void(frame F, transform t) {
      _image(F,f,initial,final,palette,t,copy=false,antialias=antialias);
    },true);
  pic.addBox(initial,final);
  return bounds; // Return bounds used for color space
}

bounds image(picture pic=currentpicture, real f(real,real),
             range range=Full, pair initial, pair final,
             int nx=ngraph, int ny=nx, pen[] palette, bool antialias=false)
{
  // Generate data, taking scaling into account
  real xmin=pic.scale.x.T(initial.x);
  real xmax=pic.scale.x.T(final.x);
  real ymin=pic.scale.y.T(initial.y);
  real ymax=pic.scale.y.T(final.y);
  real[][] data=new real[ny][nx];
  for(int j=0; j < ny; ++j) {
    real y=pic.scale.y.Tinv(interp(ymin,ymax,(j+0.5)/nx));
    scalefcn Tinv=pic.scale.x.Tinv;
    // Take center point of each bin
    data[j]=sequence(new real(int i) {
        return f(Tinv(interp(xmin,xmax,(i+0.5)/ny)),y);
      },nx);
  }
  return image(pic,data,range,initial,final,palette,transpose=false,
               copy=false,antialias=antialias);
}

void image(picture pic=currentpicture, pen[][] data, pair initial, pair final,
           bool transpose=(initial.x < final.x && initial.y < final.y),
           bool copy=true, bool antialias=false)
{
  if(transpose) data=transpose(data);
  else if(copy) data=copy(data);

  initial=Scale(pic,initial);
  final=Scale(pic,final);

  pic.add(new void(frame F, transform t) {
      _image(F,data,initial,final,t,copy=false,antialias=antialias);
    },true);
  pic.addBox(initial,final);
}

bounds image(picture pic=currentpicture, pair[] z, real[] f,
             range range=Full, pen[] palette)
{
  if(z.length != f.length)
    abort("z and f arrays have different lengths");

  real m=min(f);
  real M=max(f);
  bounds bounds=range(pic,m,M);
  real rmin=pic.scale.z.T(bounds.min);
  real rmax=pic.scale.z.T(bounds.max);

  palette=adjust(pic,m,M,rmin,rmax,palette);

  // Crop data to allowed range and scale
  if(range != Full || pic.scale.z.scale.T != identity ||
     pic.scale.z.postscale.T != identity) {
    scalefcn T=pic.scale.z.T;
    real m=bounds.min;
    real M=bounds.max;
    f=map(new real(real x) {return T(min(max(x,m),M));},f);
  }

  int[] edges={0,0,1};
  int N=palette.length-1;

  int[][] trn=triangulate(z);
  real step=rmax == rmin ? 0.0 : N/(rmax-rmin);
  for(int i=0; i < trn.length; ++i) {
    int[] trni=trn[i];
    int i0=trni[0], i1=trni[1], i2=trni[2];
    pen color(int i) {return palette[round((f[i]-rmin)*step)];}
    gouraudshade(pic,z[i0]--z[i1]--z[i2]--cycle,
                 new pen[] {color(i0),color(i1),color(i2)},edges);
  }
  return bounds; // Return bounds used for color space
}

bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f,
             range range=Full, pen[] palette)
{
  int n=x.length;
  if(n != y.length)
    abort("x and y arrays have different lengths");

  pair[] z=sequence(new pair(int i) {return (x[i],y[i]);},n);
  return image(pic,z,f,range,palette);
}

// Construct a pen[] array from f using the specified palette.
pen[] palette(real[] f, pen[] palette)
{
  real Min=min(f);
  real Max=max(f);
  if(palette.length == 0) return new pen[];
  real step=Max == Min ? 0.0 : (palette.length-1)/(Max-Min);
  return sequence(new pen(int i) {return palette[round((f[i]-Min)*step)];},
                  f.length);
}

// Construct a pen[][] array from f using the specified palette.
pen[][] palette(real[][] f, pen[] palette)
{
  real Min=min(f);
  real Max=max(f);
  int n=f.length;
  int m=n > 0 ? f[0].length : 0;
  pen[][] p=new pen[n][m];
  real step=(Max == Min) ? 0.0 : (palette.length-1)/(Max-Min);
  for(int i=0; i < n; ++i) {
    real[] fi=f[i];
    p[i]=sequence(new pen(int j) {return palette[round((fi[j]-Min)*step)];},m);
  }
  return p;
}

typedef ticks paletteticks(int sign=-1);

paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null,
                          bool beginlabel=true, bool endlabel=true,
                          int N=0, int n=0, real Step=0, real step=0,
                          pen pTick=nullpen, pen ptick=nullpen)
{
  return new ticks(int sign=-1) {
    format.align(sign > 0 ? RightSide : LeftSide);
    return Ticks(sign,format,ticklabel,beginlabel,endlabel,N,n,Step,step,
                 true,true,extend=true,pTick,ptick);
  };
} 

paletteticks PaletteTicks=PaletteTicks();

void palette(picture pic=currentpicture, Label L="", bounds bounds, 
             pair initial, pair final, axis axis=Right, pen[] palette, 
             pen p=currentpen, paletteticks ticks=PaletteTicks,
             bool copy=true, bool antialias=false)
{
  real initialz=pic.scale.z.T(bounds.min);
  real finalz=pic.scale.z.T(bounds.max);
  bounds mz=autoscale(initialz,finalz,pic.scale.z.scale);
  
  axisT axis;
  axis(pic,axis);
  real angle=degrees(axis.align.dir);

  initial=Scale(pic,initial);
  final=Scale(pic,final);

  pair lambda=final-initial;
  bool vertical=(floor((angle+45)/90) % 2 == 0);
  pair perp,par;

  if(vertical) {perp=E; par=N;} else {perp=N; par=E;}

  path g=(final-dot(lambda,par)*par)--final;
  path g2=initial--final-dot(lambda,perp)*perp;

  if(sgn(dot(lambda,perp)*dot(axis.align.dir,perp)) == -1) {
    path tmp=g;
    g=g2;
    g2=tmp;
  }

  if(copy) palette=copy(palette);
  Label L=L.copy();
  if(L.defaultposition) L.position(0.5);
  L.align(axis.align);
  L.p(p);
  if(vertical && L.defaulttransform) {
    frame f;
    add(f,Label(L.s,(0,0),L.p));
    if(length(max(f)-min(f)) > ylabelwidth*fontsize(L.p)) 
      L.transform(rotate(90));
  }
  real[][] pdata={sequence(palette.length)};
  if(vertical) pdata=transpose(pdata);
  
  pic.add(new void(frame f, transform t) {
      _image(f,pdata,initial,final,palette,t,copy=false,antialias=antialias);
    },true);
  
  ticklocate locate=ticklocate(initialz,finalz,pic.scale.z,mz.min,mz.max);
  axis(pic,L,g,g2,p,ticks(sgn(axis.side.x*dot(lambda,par))),locate,mz.divisor,
       true);

  pic.add(new void(frame f, transform t) {
      pair Z0=t*initial;
      pair Z1=t*final;
      draw(f,Z0--(Z0.x,Z1.y)--Z1--(Z1.x,Z0.y)--cycle,p);
    },true);

  pic.addBox(initial,final);
}

// A grayscale palette
pen[] Grayscale(int NColors=256)
{
  real ninv=1.0/(NColors-1.0);
  return sequence(new pen(int i) {return gray(i*ninv);},NColors);
}

// A color wheel palette
pen[] Wheel(int NColors=32766)
{
  if(settings.gray) return Grayscale(NColors);
  
  int nintervals=6;
  int n=quotient(NColors,nintervals);
                
  pen[] Palette;
  if(n == 0) return Palette;
  
  Palette=new pen[n*nintervals];
  real ninv=1.0/n;

  for(int i=0; i < n; ++i) {
    real ininv=i*ninv;
    real ininv1=1.0-ininv;
    Palette[i]=rgb(1.0,0.0,ininv);
    Palette[n+i]=rgb(ininv1,0.0,1.0);
    Palette[2n+i]=rgb(0.0,ininv,1.0);
    Palette[3n+i]=rgb(0.0,1.0,ininv1);
    Palette[4n+i]=rgb(ininv,1.0,0.0);    
    Palette[5n+i]=rgb(1.0,ininv1,0.0);
  }
  return Palette;
}

// A rainbow palette
pen[] Rainbow(int NColors=32766)
{
  if(settings.gray) return Grayscale(NColors);
  
  int offset=1;
  int nintervals=5;
  int n=quotient(NColors-1,nintervals);
                
  pen[] Palette;
  if(n == 0) return Palette;
  
  Palette=new pen[n*nintervals+offset];
  real ninv=1.0/n;

  for(int i=0; i < n; ++i) {
    real ininv=i*ninv;
    real ininv1=1.0-ininv;
    Palette[i]=rgb(ininv1,0.0,1.0);
    Palette[n+i]=rgb(0.0,ininv,1.0);
    Palette[2n+i]=rgb(0.0,1.0,ininv1);
    Palette[3n+i]=rgb(ininv,1.0,0.0);    
    Palette[4n+i]=rgb(1.0,ininv1,0.0);
  }
  Palette[4n+n]=rgb(1.0,0.0,0.0);
  
  return Palette;
}

private pen[] BWRainbow(int NColors, bool two)
{
  if(settings.gray) return Grayscale(NColors);
  
  int offset=1;
  int nintervals=6;
  int divisor=3;
  
  if(two) nintervals += 6;
  
  int num=NColors-offset;
  int n=quotient(num,nintervals*divisor)*divisor;
  NColors=n*nintervals+offset;
                
  pen[] Palette;
  if(n == 0) return Palette;
  
  Palette=new pen[NColors];
  real ninv=1.0/n;

  int k=0;
  
  if(two) {
    for(int i=0; i < n; ++i) {
      real ininv=i*ninv;
      real ininv1=1.0-ininv;
      Palette[i]=rgb(ininv1,0.0,1.0);
      Palette[n+i]=rgb(0.0,ininv,1.0);
      Palette[2n+i]=rgb(0.0,1.0,ininv1);
      Palette[3n+i]=rgb(ininv,1.0,0.0);
      Palette[4n+i]=rgb(1.0,ininv1,0.0);
      Palette[5n+i]=rgb(1.0,0.0,ininv);
    }
    k += 6n;
  }
  
  if(two)
    for(int i=0; i < n; ++i) 
      Palette[k+i]=rgb(1.0-i*ninv,0.0,1.0);
  else {
    int n3=quotient(n,3);
    int n23=2*n3;
    real third=n3*ninv;
    real twothirds=n23*ninv;
    for(int i=0; i < n3; ++i) {
      real ininv=i*ninv;
      Palette[k+i]=rgb(ininv,0.0,ininv);
      Palette[k+n3+i]=rgb(third,0.0,third+ininv);
      Palette[k+n23+i]=rgb(third-ininv,0.0,twothirds+ininv);
    }
  }
  k += n;

  for(int i=0; i < n; ++i) {
    real ininv=i*ninv;
    real ininv1=1.0-ininv;
    Palette[k+i]=rgb(0.0,ininv,1.0);
    Palette[k+n+i]=rgb(0.0,1.0,ininv1);
    Palette[k+2n+i]=rgb(ininv,1.0,0.0);    
    Palette[k+3n+i]=rgb(1.0,ininv1,0.0);
    Palette[k+4n+i]=rgb(1.0,ininv,ininv);
  }
  Palette[k+5n]=rgb(1.0,1.0,1.0);
  
  return Palette;
}

// Quantize palette to exactly n values
pen[] quantize(pen[] Palette, int n)
{
  if(Palette.length == 0) abort("cannot quantize empty palette");
  if(n <= 1) abort("palette must contain at least two pens");
  real step=(Palette.length-1)/(n-1);
  return sequence(new pen(int i) {
      return Palette[round(i*step)];
    },n); 
}

// A rainbow palette tapering off to black/white at the spectrum ends,
pen[] BWRainbow(int NColors=32761)
{
  return BWRainbow(NColors,false);
}

// A double rainbow palette tapering off to black/white at the spectrum ends,
// with a linearly scaled intensity.
pen[] BWRainbow2(int NColors=32761)
{
  pen[] Palette=BWRainbow(NColors,true);
  int n=Palette.length;
  real ninv=1.0/n;
  for(int i=0; i < n; ++i)
    Palette[i]=i*ninv*Palette[i];
  return Palette;
}

//A palette varying linearly over the specified array of pens, using
// NColors in each interpolation interval.
pen[] Gradient(int NColors=256 ... pen[] p) 
{
  pen[] P;
  if(p.length < 2) abort("at least 2 colors must be specified");
  real step=NColors > 1 ? (1/(NColors-1)) : 1;
  for(int i=0; i < p.length-1; ++i) {
    pen begin=p[i];
    pen end=p[i+1];
    P.append(sequence(new pen(int j) {
          return interp(begin,end,j*step);
        },NColors));
  }
  return P;
}

pen[] cmyk(pen[] Palette) 
{
  int n=Palette.length;
  for(int i=0; i < n; ++i)
    Palette[i]=cmyk(Palette[i]);
  return Palette;
}