-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathjsgl_v1.html
1170 lines (1027 loc) · 38.7 KB
/
jsgl_v1.html
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
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<!-- This is based on DillingerLee's great template here:
https://github.com/Team-Code/KA_Offline -->
<html>
<head>
<title>JS.GL 1.0</title>
</head>
<body>
<p align="center">
<!--This draws the Canvas on the webpage -->
<canvas id="mycanvas"></canvas>
</p>
</body>
<!-- Run all the JavaScript stuff -->
<!-- Include the processing.js library -->
<!-- See https://khanacademy.zendesk.com/hc/en-us/articles/202260404-What-parts-of-ProcessingJS-does-Khan-Academy-support- for differences -->
<script src="https://cdn.jsdelivr.net/processing.js/1.4.8/processing.min.js"></script>
<script>
var sketchProc = function(processingInstance) {
with (processingInstance) {
size(400, 400,WEBGL);
frameRate(0);
{
//JS.GL 3D LIBARY VERSION 1.0
var GLBOX=function(x,y,rx,ry,rz,size){
translate(x,y);
rotateX(rx);
rotateY(ry);
rotateZ(rz);
box(size);
}; //BETTER GL BOX FUNCTION (X,Y,RotateX,RotateY,RotateZ,Size) (Less Efficent but easier)
var GLSPHERE=function(x,y,size){
translate(x,y);
sphere(size);
}; //SAME THING AS GLBOX EXCEPT IT IS A SPHERE (X,Y,Size)
//Bob Lyon's 3D Code + Shapes
//Bob Lyon's Code is very quick and dirty but is not good for advanced shapes with just the examples. Please use GLBOX/GLSPHERE for those uses.
var Face = (function() {
/*
* The drawn faces are rendered using "flat shading". See
* https://en.wikipedia.org/wiki/Shading#Flat_shading The
* light source is infinitely far away, but the lightSrc
* vector is used to determine its 3D angles from the faces.
* So a light source perpendicular to the picture canvas is
* the vector(0, 0, <any positive number>). Note that shapes
* do not cast shadows!
*/
var lightSrc = new PVector(-30, -50, 100);
var lightMag = lightSrc.mag();
var dark = color(40); /* the color of no light */
var staticVisibleFaces = [];
var staticOrig = new PVector();
var staticNext = new PVector();
var staticPrev = new PVector();
/*
* Additional cross product method that does not leak memory
* at Khan Academy because the caller specifies where the
* results are placed. Computes and returns (this ⨯ b). results
* can be any PVector (including this and b) or nothing at all.
*/
PVector.prototype.crossRes = function(b, results) {
results = results || new PVector();
results.set(
this.y * b.z - this.z * b.y,
this.z * b.x - this.x * b.z,
this.x * b.y - this.y * b.x);
return results;
};
/* Constructor function. Uses (does NOT dup) nodes. */
var Face = function(nodes, colour) {
this.nodes = nodes;
this.color = colour || color(random(230), 200, random(230));
this.normal = new PVector();
};
/* Draw this face and update mini & maxi coordinates. */
Face.prototype.draw = function(mini, maxi) {
mini = mini || staticPrev;
maxi = maxi || staticNext;
var cosTheta = this.normal.dot(lightSrc) / this.normal.mag() / lightMag;
var interpolation = (cosTheta < 0) ? 0 : cosTheta;
fill(lerpColor(dark, this.color, interpolation));
beginShape();
for (var nodes = this.nodes, i = nodes.length; --i >= 0; ) {
var persp = nodes[i].persp, x, y, z = persp.z;
vertex(x = persp.x, y = persp.y);
void((x < mini.x) && (mini.x = x));
void((x > maxi.x) && (maxi.x = x));
void((y < mini.y) && (mini.y = y));
void((y > maxi.y) && (maxi.y = y));
void((z < mini.z) && (mini.z = z));
void((z > maxi.z) && (maxi.z = z));
}
endShape(CLOSE);
};
/*
* Return true iff point (x, y) is in this *rendered* face.
* See https://www.khanacademy.org/cs/p/5211412870725632
* which implements even/odd ray tracing.
*/
Face.prototype.isOver = function(x, y) {
var isIn = false;
var nodes = this.nodes;
for (var i = 0, j = nodes.length - 1; i < nodes.length; j = i++) {
var pi = nodes[i].persp, xi = pi.x, yi = pi.y;
var pj = nodes[j].persp, xj = pj.x, yj = pj.y;
var intersect = yi > y !== yj > y &&
x < (xj - xi) * (y - yi) / (yj - yi) + xi;
if (intersect) {
isIn = !isIn;
}
}
return isIn;
};
/*
* Returns the right-handed (unless "left") normal of this face.
* The normal is with respect to the rendered face until raw,
* which used actual coordinates.
*/
Face.prototype.getNormal = function(left, raw) {
var next = staticNext, prev = staticPrev;
var origin, nodes = this.nodes;
/* next and prev vectors share common origin nodes[1] */
if (raw) {
origin = nodes[1];
next.set(nodes[2]);
prev.set(nodes[0]);
} else {
origin = nodes[1].persp;
next.set(nodes[2].persp);
prev.set(nodes[0].persp);
}
next.sub(origin);
prev.sub(origin);
if (left) {
/* left handed ... */
var tmp = next;
next = prev;
prev = tmp;
}
return (this.normal = prev.crossRes(next, this.normal));
};
/*
* Is this face currently visible? See
* https://en.wikipedia.org/wiki/Back-face_culling
*/
Face.prototype.isVisible = function() {
return this.getNormal().z > 0;
};
/*
* Assists both back face culling and flat shading. Assumes
* this face is part of a shape centered at the origin.
* Finds the correct ordering this face's nodes such that
* a cross product of two vectors sharing the common nodes[1]
* points away from the origin.
*/
Face.prototype.rightHandRule = function(shape) {
shape.perspective(); /* heavy handed refresh! */
var common = this.nodes[1];
var right = this.getNormal();
right.add(common);
right = right.mag();
var left = this.getNormal(true);
left.add(common);
if (right < left.mag()) {
this.nodes.reverse();
}
};
/* Compare two faces based on their minimum Z (or average Z) coordinates. */
var compareFace = function(a, b) {
return (a.minZ - b.minZ) || (a.aveZ - b.aveZ);
};
/*
* Draw the faces. Optionally set min and max coordinates.
* Populates visible array with actual faces drawn in the
* the correct order.
*/
Face.draw = function(faces, visible, mini, maxi) {
visible = visible || staticVisibleFaces;
visible.length = 0;
for (var l = faces.length, i = 0; i < l; i++) {
var face = faces[i];
if (face.isVisible()) {
visible.push(face);
/*
* (re)Compute the values of the minimum Z coordinate
* and the average Z value in the face. Useful for
* sorting below.
*/
var nodes = face.nodes, m = nodes.length;
face.minZ = face.aveZ = nodes[0].z;
for (var j = 1; j < m; j++) {
var nz = nodes[j].z;
face.aveZ += nz;
void((nz < face.minZ) && (face.minZ = nz));
}
face.aveZ /= m;
}
}
visible.sort(compareFace);
void(mini && mini.set(+Infinity, +Infinity, +Infinity));
void(maxi && maxi.set(-Infinity, -Infinity, -Infinity));
for (l = visible.length, i = 0; i < l; i++) {
visible[i].draw(mini, maxi);
}
};
Face.bg = dark;
return Face;
})(); //FACE Constructor Code
/*
* Shape3D is a constructor function for a generic shape that is
* always constructed at the origin (0, 0, 0). Shapes have methods
* for moving, scaling, XYZ axes rotating, and rotating around an axle.
*
* Shape3D also provides static library functions that are similar
* to the methods but apply to the entire universe of shapes and
* their nodes.
*/
var Shape3D = (function() {
/*
* A simple perspective is drawn wrt a fixed camera at
* a positive Z offset.
*/
var camera = new PVector(0, 0, 2.2 * max(width, height));
var tau = (cos(PI) < 0) ? TWO_PI : 360; /* KA silliness */
var json = (function(what) { return this[what]; })("JSON");
var jsonInclude = [ "x", "y", "z", "ux", "uy", "uz", "faces", "nodes", "color", "" ];
var defaultOrigin = new PVector(0, 0, 0);
var ux = new PVector(1, 0, 0);
var uy = new PVector(0, 1, 0);
var uz = new PVector(0, 0, 1);
var tmpV = new PVector();
var tmpArray = [];
var shapes = []; /* All managed shapes. */
/* Constructor function of a generic shape. */
var Shape3D = function(noRecord) {
PVector.call(this, 0, 0, 0); /* this shape's coordinates */
this.nodes = [];
this.faces = [];
this.drawn = [];
this.min = new PVector();
this.max = new PVector();
if (! noRecord) {
shapes.push(this);
}
/*
* All constructed nodes are bound to this shape.
* A constructor in a constructor? Really?
*/
var thisShape = this;
this.Node = function(x, y, z) {
PVector.call(this, x, y, z);
thisShape.nodes.push(this);
this.persp = new PVector(); /* perspective of this. */
};
this.Node.prototype = PVector.prototype;
};
Shape3D.prototype = Object.create(PVector.prototype);
/* Remove this shape from the managed shapes array. */
Shape3D.prototype.remove = function() {
shapes.splice(shapes.indexOf(this), 1); /* snip */
};
/* Append this nodes to array a. */
Shape3D.prototype.appendNodes = function(a) {
a.push.apply(a, this.nodes);
a.push(this);
};
/*
* Optionally (re)set unit vectors. They will undergo
* all of the transformations that affect all other
* nodes. Handy for personalized rotation axis...
*/
Shape3D.prototype.setUnitAxes = function() {
if (! this.ux) {
this.ux = new this.Node();
this.uy = new this.Node();
this.uz = new this.Node();
}
this.ux.set(ux);
this.uy.set(uy);
this.uz.set(uz);
};
/* (re)Compute this shape's X and Y coordinates wrt perspective. */
Shape3D.prototype.perspective = function() {
for (var nodes = this.nodes, i = nodes.length; --i >= 0; ) {
var node = nodes[i];
var scale = camera.z / camera.dist(node);
node.persp.set(scale * node.x, scale * node.y, node.z);
}
};
/*
* Moves this shape by a relative amount delta,
* which is either a vector or three numbers.
*/
Shape3D.prototype.move = function() {
var delta = arguments[0];
if (arguments.length === 3) {
delta = tmpV;
delta.set.apply(delta, arguments);
}
for (var nodes = this.nodes, n = nodes.length; --n >= 0; ) {
var node = nodes[n];
node.add(delta);
}
this.add(delta);
};
/*
* Moves this shape to new absolute coordinates,
* either described by a vector or by three coordinates.
*/
Shape3D.prototype.translate = function() {
var delta = tmpV;
delta.set.apply(delta, arguments);
delta.sub(this);
this.move(delta);
};
/*
* Scales this shape according to one number,
* one vector, or three numbers.
*/
Shape3D.prototype.scale = function() {
var sf = arguments[0];
if (arguments.length === 3) {
sf = tmpV;
sf.set.apply(sf, arguments);
}
for (var nodes = this.nodes, n = nodes.length; --n >= 0; ) {
var node = nodes[n];
node.sub(this);
node.mult(sf);
node.add(this);
}
};
/*
* Rotate the nodes about a 3D axle described by
* the line between "from" and "to". Info at
* https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
*/
Shape3D.rotateNodesAxle = function(nodes, theta, from, to) {
if (theta && nodes.length) {
var q = tmpV;
q.set(to);
q.sub(from);
q.normalize();
q.mult(sin(theta/2));
var qr = cos(theta/2),
qi = q.x,
qj = q.y,
qk = q.z,
r11 = 1 - 2*(qj*qj + qk*qk),
r12 = 0 + 2*(qi*qj - qk*qr),
r13 = 0 + 2*(qi*qk + qj*qr),
r21 = 0 + 2*(qi*qj + qk*qr),
r22 = 1 - 2*(qi*qi + qk*qk),
r23 = 0 + 2*(qj*qk - qi*qr),
r31 = 0 + 2*(qi*qk - qj*qr),
r32 = 0 + 2*(qj*qk + qi*qr),
r33 = 1 - 2*(qi*qi + qj*qj),
ox = from.x,
oy = from.y,
oz = from.z;
for (var n = nodes.length; --n >= 0; ) {
var node = nodes[n];
var x = node.x - ox;
var y = node.y - oy;
var z = node.z - oz;
node.x = r11*x + r12*y + r13*z + ox;
node.y = r21*x + r22*y + r23*z + oy;
node.z = r31*x + r32*y + r33*z + oz;
}
}
};
/*
* Rotate every node about a 3D axle described by
* the line between "from" and "to".
*/
Shape3D.rotateAxle = function(theta, from, to) {
var allNodes = tmpArray;
allNodes.length = 0;
for (var s = shapes.length; --s >= 0; ) {
shapes[s].appendNodes(allNodes);
}
Shape3D.rotateNodesAxle(allNodes, theta, from, to);
};
/* Rotate this shape's nodes around its Z-axis. */
Shape3D.prototype.rotateZ3D = function(theta) {
if (theta) {
uz.add(this);
Shape3D.rotateNodesAxle(this.nodes, theta, this, uz);
uz.sub(this);
}
};
/* Rotate this shape's nodes around its Y-axis. */
Shape3D.prototype.rotateY3D = function(theta) {
if (theta) {
uy.add(this);
Shape3D.rotateNodesAxle(this.nodes, theta, this, uy);
uy.sub(this);
}
};
/* Rotate this shape's nodes around its X-axis. */
Shape3D.prototype.rotateX3D = function(theta) {
if (theta) {
ux.add(this);
Shape3D.rotateNodesAxle(this.nodes, theta, this, ux);
ux.sub(this);
}
};
/* Rotate every node around the Z axis at origin. */
Shape3D.rotateZ3D = function(theta, origin) {
void(theta && Shape3D.rotateAxle(theta, origin || defaultOrigin, uz));
};
/* Rotate every node around the Y axis at origin. */
Shape3D.rotateY3D = function(theta, origin) {
void(theta && Shape3D.rotateAxle(theta, origin || defaultOrigin, uy));
};
/* Rotate every node around the X axis at origin. */
Shape3D.rotateX3D = function(theta, origin) {
void(theta && Shape3D.rotateAxle(theta, origin || defaultOrigin, ux));
};
/*
* Rotate the nodes of this shape about a 3D axle described by
* the line between this coordinates and axle.
*/
Shape3D.prototype.rotateAxle = function(theta, axle) {
Shape3D.rotateNodesAxle(this.nodes, theta, this, axle || this.uz || defaultOrigin);
};
/* Compare two shapes based on their centers' Z coordinates. */
var compareShape = function(a, b) {
return a.z - b.z;
};
/*
* Draw all shapes from back to front. The
* rendering of collided shapes is undefined
* and often disappointing.
*/
Shape3D.draw = function(dShapes) {
dShapes = dShapes || shapes;
dShapes.sort(compareShape);
for (var l = dShapes.length, i = 0; i < l; i++) {
var shape = dShapes[i];
shape.perspective();
Face.draw(shape.faces, shape.drawn, shape.min, shape.max);
}
};
/* Is point (x, y) in the vicinity of this shape? */
Shape3D.prototype.isAround = function(x, y) {
return (x >= this.min.x) && (y >= this.min.y) &&
(y <= this.max.y) && (x <= this.max.x);
};
/* Is 2D point (x, y) over this shape's 2D projection? */
Shape3D.prototype.isOver = function(x, y) {
if (this.isAround(x, y)) {
for (var faces = this.drawn, i = faces.length; --i >= 0; ) {
var face = faces[i];
if (face.isOver(x, y)) {
this.overFace = face;
return true;
}
}
}
return false;
};
/*
* Return the shape that the point (x, y) is over.
* NB: Assumes shapes are sorted back to front.
*/
Shape3D.over = function(x, y) {
/* Search *must* be front to back! */
for (var i = shapes.length; --i >= 0; ) {
if (shapes[i].isOver(x, y)) {
return shapes[i];
}
}
};
/*
* Return the JSON description of shape be it
* a shape or an array of shapes.
*/
Shape3D.stringify = function(shape) {
shape = shape || shapes;
var myNodes;
var replacer = function(key, value) {
if ((! Array.isArray(this)) && (jsonInclude.indexOf(key) < 0)) {
return; /* ignore unwanted key and value */
}
if (key === "nodes") {
if (this.faces && typeof this.z === "number") {
/* Remember the actual nodes of this shape. */
myNodes = value;
} else {
/* Replace node references with indices into myNodes. */
var replacement = [];
for (var l = value.length, i = 0; i < l; i++) {
replacement.push(myNodes.indexOf(value[i]));
}
return replacement;
}
} else if (key === "ux" || key === "uy" || key === "uz") {
/* Replace value with an index into myNodes. */
return myNodes.indexOf(value);
}
return value;
};
return json.stringify(shape, replacer);
};
/* Return the JSON description of this shape. */
Shape3D.prototype.stringify = function() {
return Shape3D.stringify(this);
};
/* Make a brand new shape based on the properties of conf. */
var newShape = function(conf) {
var shape = new Shape3D();
var myNodes = shape.nodes;
shape.set(conf.x, conf.y, conf.z);
for (var nodes = conf.nodes, l = nodes.length, i = 0; i < l; i++) {
var node = nodes[i];
new shape.Node(node.x, node.y, node.z);
}
for (var faces = conf.faces, l = faces.length, i = 0; i < l; i++) {
var face = faces[i];
for (var nodes = face.nodes, m = nodes.length, j = 0; j < m; j++) {
nodes[j] = myNodes[nodes[j]];
}
shape.faces.push(new Face(nodes, face.color));
}
if (conf.ux >= 0) {
shape.ux = myNodes[conf.ux];
shape.uy = myNodes[conf.uy];
shape.uz = myNodes[conf.uz];
}
return shape;
};
/* Parse string s and build new shapes. */
Shape3D.parse = function(s) {
var shapes = json.parse(s);
if (! Array.isArray(shapes)) {
shapes = [ shapes ];
}
for (var i = shapes.length; --i >= 0; ) {
newShape(shapes[i]);
}
};
/* Clone this shape. */
Shape3D.prototype.clone = function() {
var s = this.stringify();
var conf = json.parse(s);
return newShape(conf);
};
Shape3D.tau = tau;
return Shape3D;
})();
/* Constructor function for a 3D star. */
var Star = (function() {
var tau = Shape3D.tau;
var ratio = sin(1/20 * tau) / sin(7/20 * tau);
var starNode = [];
/* Constructor function for a star at (0, 0, 0). */
var Star = function(extRadius, depth, topColor, bottomColor) {
Shape3D.call(this);
bottomColor = bottomColor || color(random(50, 110), 250, random(160, 220));
topColor = topColor || color(250, random(160, 220), random(50, 110));
var interior = ratio * extRadius;
var n = 10;
var face;
starNode.length = 0;
for (var theta = 0; theta < tau; theta += tau / n) {
var radius = (radius === extRadius) ? interior : extRadius;
var x = radius * cos(theta - tau/4);
var y = radius * sin(theta - tau/4);
starNode.push(new this.Node(x, y, 0));
}
this.faces = [];
var topNode = new this.Node(0, 0, depth/2);
var bottomNode = this.bottomNode = new this.Node(0, 0, -depth/2);
for (var prev = n - 1, i = 0; i < n; prev = i++) {
this.faces.push(face = new Face([ topNode, starNode[prev], starNode[i] ],
topColor));
face.rightHandRule(this);
this.faces.push(face = new Face([ bottomNode, starNode[prev], starNode[i] ],
bottomColor));
face.rightHandRule(this);
}
this.setUnitAxes();
};
Star.prototype = Shape3D.prototype;
return Star;
})();
/* Constructor function for a cuboid. */
var Cuboid = (function() {
/* Constructor function for cuboid centered at origin. */
var Cuboid = function(w, h, d) {
Shape3D.call(this);
var faces = this.faces;
w /= 2;
h /= 2;
d /= 2;
var bottom = [
new this.Node(-w, -h, -d),
new this.Node(-w, +h, -d),
new this.Node(+w, +h, -d),
new this.Node(+w, -h, -d),
];
var top = [
new this.Node(-w, -h, +d),
new this.Node(-w, +h, +d),
new this.Node(+w, +h, +d),
new this.Node(+w, -h, +d),
];
for (var l = top.length, prev = l - 1, i = 0; i < l; prev = i++) {
faces.push(new Face([ bottom[prev], top[prev], top[i], bottom[i] ],
faceColor()));
}
faces.push(new Face(top, faceColor()), new Face(bottom, faceColor()));
for (i = faces.length; --i >= 0; ) {
faces[i].rightHandRule(this);
}
this.setUnitAxes();
};
Cuboid.prototype = Shape3D.prototype;
var faceColor = function() {
return color(70, random(120, 160), random(190, 230));
};
return Cuboid;
})();
/* Constructor function for a regular icosahedron. */
var Icosahedron = (function() {
var tau = Shape3D.tau;
var phi = (1 + sqrt(5)) / 2; /* golden mean */
var coord = []; /* avoids leaks */
var tmpV = new PVector();
var edge; /* cached answer */
var triangles; /* cached answer */
/* Constructor function. */
var Icosahedron = function(radius, colour) {
Shape3D.call(this);
var nodes = this.nodes;
var faces = this.faces;
colour = colour || color(230, 67, 227);
/*
* See https://en.wikipedia.org/wiki/Regular_icosahedron
* for node coordinates, edge length, and face generation.
*/
for (var sa = -1; sa < 2; sa += 2) {
for (var sb = -1; sb < 2; sb += 2) {
coord.length = 0;
coord.push(0, sa, sb*phi);
for (var i = 0; i < coord.length; i++) {
new this.Node(coord[0], coord[1], coord[2]);
coord.push(coord.shift()); /* rotate */
}
}
}
/* The twelve nodes make thirty edges of length 2. Find them. */
var edge = wireFrame(nodes);
/* Generate twenty triangular faces. */
var triangles = getFaces(edge);
for (var i = 0; i < triangles.length; i++) {
var t = triangles[i];
var face = new Face([ nodes[t[0]], nodes[t[1]], nodes[t[2]] ], colour);
faces.push(face);
face.rightHandRule(this);
}
this.scale(radius / 2 / sin(tau/5));
this.rotateY3D(tau/6);
this.setUnitAxes();
};
Icosahedron.prototype = Shape3D.prototype;
/*
* Compute the edges of the Icosahedron given the nodes.
* Only needed once, ever. The twelve nodes make thirty
* edges of length 2.
*/
var wireFrame = function(nodes) {
if (! edge) {
edge = [];
for (var l = nodes.length, i = 0; i < l; i++) {
for (var j = i + 1; j < l; j++) {
if (nodes[i].dist(nodes[j]) === 2) {
edge[i] = edge[i] || [];
edge[i].push(j);
}
}
}
}
return edge;
};
/*
* Find the triangle faces of the icosahedron given the edges.
* Only needed once, ever.
*/
var getFaces = function(edge) {
if (! triangles) {
triangles = [];
for (var A = 0; A < edge.length; A++) {
var neighborsA = edge[A];
for (var a = 0; a < neighborsA.length; a++) {
var B = neighborsA[a];
var neighborsB = edge[B];
for (var b = 0; neighborsB && b < neighborsB.length; b++) {
var C = neighborsB[b];
if (neighborsA.indexOf(C) >= 0) {
triangles.push([ A, B, C ]);
}
}
}
}
}
return triangles;
};
return Icosahedron;
})();
/* Constructor function for a soccer ball. */
var SoccerBall = (function() {
var tau = Shape3D.tau;
var phi = (1 + sqrt(5)) / 2; /* golden mean */
var pentNodes = []; /* nodes numbers of pentagons that generate hexagons */
var visited5 = []; /* node numbers that made pentagons */
var visited6 = []; /* list of constructed hexagons */
var va = new PVector();
var vc = new PVector();
var edge; /* cached answer */
var polygon; /* cached answer */
/* Constructor function. */
var SoccerBall = function(radius, color5, color6) {
Shape3D.call(this);
var nodes = this.nodes;
var faces = this.faces;
color5 = color5 || color(60, 100, 180);
color6 = color6 || color(220, 200, 150);
/*
* See https://en.wikipedia.org/wiki/Truncated_icosahedron
* for node coordinates, edge length, and face generation.
*/
var x, y, z, sa=0, sb, sc;
for (sb = -1; sb < 2; sb += 2) {
for (sc = -1; sc < 2; sc += 2) {
x = 0; y = sb; z = sc*3*phi;
pentNodes.push(nodes.length);
new this.Node(x, y, z);
void((sc !== sb) && pentNodes.push(nodes.length));
new this.Node(y, z, x);
new this.Node(z, x, y);
}
}
for (sa = -1; sa < 2; sa += 2) {
for (sb = -1; sb < 2; sb += 2) {
for (sc = -1; sc < 2; sc += 2) {
x = sa; y = sb*(2 + phi); z = sc*2*phi;
new this.Node(x, y, z);
new this.Node(y, z, x);
new this.Node(z, x, y);
}
}
}
for (sa = -1; sa < 2; sa += 2) {
for (sb = -1; sb < 2; sb += 2) {
for (sc = -1; sc < 2; sc += 2) {
x = sa*2; y = sb*(1 + 2*phi); z = sc*phi;
new this.Node(x, y, z);
new this.Node(y, z, x);
new this.Node(z, x, y);
}
}
}
/* The sixty nodes make ninety edges of length 2. Find them. */
var edge = wireFrame(nodes);
/* Generate 12 pentagon and 20 hexagon faces. */
var polygon = getFaces(edge, nodes);
for (var i = polygon.length; --i >= 0; ) {
var p = polygon[i];
var ns = nodesFromNumber(p, nodes);
var face = new Face(ns, (ns.length === 5) ? color5 : color6);
faces.push(face);
face.rightHandRule(this);
}
this.scale(radius / sqrt(9*phi + 10));
this.setUnitAxes();
};
SoccerBall.prototype = Shape3D.prototype;
/*
* Compute the edges of the truncated icosahedron given
* the nodes. Only needed once, ever. The sixty nodes
* make ninety edges of length 2.
*/
var wireFrame = function(nodes) {
if (! edge) {
edge = [];
for (var cnt = 0, l = nodes.length, i = 0; i < l; i++) {
for (var j = i + 1; j < l; j++) {
if (nodes[i].dist(nodes[j]) === 2) {
edge[i] = edge[i] || [];
var k = edge[i].indexOf(j);
if (k < 0) {
edge[i].push(j);
}
edge[j] = edge[j] || [];
k = edge[j].indexOf(i);
if (k < 0) {
edge[j].push(i);
}
cnt++;
}
}
}
}
return edge;
};
/* Exchange face's node numbers for actual nodes. */
var nodesFromNumber = function(face, nodes) {
var n = [];
for (var l = face.length, i = 0; i < l; i++) {
n.push(nodes[face[i]]);
}
return n;
};
/* Compute the angle abc */
var angle = function(a, b, c) {
va.set(a);
va.sub(b);
vc.set(c);
vc.sub(b);
var ac = va.dot(vc) / va.mag() / vc.mag();
return acos(ac);
};
/*
* Arrange face's node numbers in a consistent order.
* The first node is the smallest number. The second
* number is the smallest possible.
*/
var beautifyFace = function(face) {
var least = Math.min.apply(null, face);
while (face[0] !== least) {
face.push(face.shift());
}
if (face[1] > face[face.length-1]) {
face.shift(); /* snip */
face.reverse();
face.unshift(least); /* unsnip */
}
};
/* Find the edge that connects the two pentagons. */
var connectPentagons = function(edge, a, b) {
for (var i = a.length; --i >= 0; ) {
var neighbor = edge[a[i]];
for (var j = neighbor.length; --j >= 0; ) {
var k = b.indexOf(neighbor[j]);
if (k >= 0) {
return [ a[i], b[k] ]; /* a new hexagon is born */
}
}
}
};
/* Find a face containing node number n. */
var findByNode = function(faces, n) {
for (var i = faces.length; --i >= 0; ) {
var f = faces[i];
if (f.indexOf(n) >= 0) {
return f;
}
}
};
/* Given a pentagon face, identify five new hexagons. */
var sixFromFive = function(edge, nodes, pentagons, face) {
var faces = [];
for (var l = face.length, p = l - 1, pp = p - 1, i = 0;
i < l; pp = p, p = i++) {
var nj, nk, n = face[p];
var neighbor = edge[n];
for (var j = 0; j < neighbor.length; j++) {
nj = neighbor[j];
if (nj !== face[pp] && nj !== face[i]) {
break;
}
}
var neighborFace1 = findByNode(pentagons, nj);
var next = (i + 1) % l;
var m = face[i];
var neighbor = edge[m];
for (var k = 0; k < neighbor.length; k++) {
nk = neighbor[k];
if (nk !== face[p] && nk !== face[next]) {
break;
}
}
var neighborFace2 = findByNode(pentagons, nk);
var hex = connectPentagons(edge, neighborFace1, neighborFace2);
hex.push(nk, m, n, nj);
beautifyFace(hex);