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No commits in common. "main" and "broken-cursed-links" have entirely different histories.
main
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broken-cur
17
CHANGELOG.md
17
CHANGELOG.md
@ -1,17 +0,0 @@
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CHANGELOG
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=========
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## v1.1 - 1/1/2026
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The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
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looks like less of a mess than I expected it to.
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## v1.0 - 16/11/2025
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It's been [two years](https://mikelynch.org/2023/Sep/02/120-cell/)</a> since
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I first made this, and I haven't updated it in a while, but I got tapered links to
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work without too much performance overhead, so that seemed worth a version.
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The results flicker a bit at low opacities but otherwise I'm pretty happy with
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it.
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`
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26
NOTES.md
26
NOTES.md
@ -1,26 +0,0 @@
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# NOTES
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New approach for the 5-cells:
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Pick a tetrahedron of an inscribed 600-cell with vertices A, B, C, D
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This gives pairs of vertices:
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AB
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AC
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AD
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BC
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BD
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CD
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Each of these gives rise to seven pairs of 5-cells which are on neighboring vertices
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of the 5 600-cells.
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Try enumerating these and inspecting them to find one or more coherent sets of four
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5-cells which lie on one tetrahedron from each of the 600-cells.
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(I expect there to be more than one, like how there are two ways to partition the
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120-cell vertices into 600-cells)
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849
cellindex.js
849
cellindex.js
@ -104,855 +104,6 @@ export const LAYERS120 = {
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163,219,271,223,167]
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};
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export const CELL120_CELL5 = {
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"tetras": {
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},
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"cell5s": {
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"1": [
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||||
27,
|
||||
28,
|
||||
264,
|
||||
309,
|
||||
275
|
||||
],
|
||||
"2": [
|
||||
223,
|
||||
76,
|
||||
238,
|
||||
84,
|
||||
225
|
||||
],
|
||||
"3": [
|
||||
253,
|
||||
44,
|
||||
283,
|
||||
304,
|
||||
42
|
||||
],
|
||||
"4": [
|
||||
419,
|
||||
112,
|
||||
197,
|
||||
578,
|
||||
521
|
||||
],
|
||||
"5": [
|
||||
339,
|
||||
14,
|
||||
384,
|
||||
382,
|
||||
337
|
||||
],
|
||||
"6": [
|
||||
331,
|
||||
4,
|
||||
335,
|
||||
390,
|
||||
386
|
||||
],
|
||||
"7": [
|
||||
427,
|
||||
160,
|
||||
551,
|
||||
146,
|
||||
557
|
||||
],
|
||||
"8": [
|
||||
265,
|
||||
60,
|
||||
64,
|
||||
295,
|
||||
246
|
||||
],
|
||||
"9": [
|
||||
473,
|
||||
100,
|
||||
495,
|
||||
213,
|
||||
462
|
||||
],
|
||||
"10": [
|
||||
393,
|
||||
6,
|
||||
328,
|
||||
397,
|
||||
326
|
||||
],
|
||||
"11": [
|
||||
539,
|
||||
164,
|
||||
439,
|
||||
561,
|
||||
142
|
||||
],
|
||||
"12": [
|
||||
511,
|
||||
122,
|
||||
456,
|
||||
595,
|
||||
181
|
||||
],
|
||||
"13": [
|
||||
555,
|
||||
154,
|
||||
152,
|
||||
545,
|
||||
429
|
||||
],
|
||||
"14": [
|
||||
95,
|
||||
202,
|
||||
486,
|
||||
500,
|
||||
465
|
||||
],
|
||||
"15": [
|
||||
471,
|
||||
208,
|
||||
502,
|
||||
484,
|
||||
89
|
||||
],
|
||||
"16": [
|
||||
347,
|
||||
21,
|
||||
348,
|
||||
374,
|
||||
373
|
||||
],
|
||||
"17": [
|
||||
487,
|
||||
203,
|
||||
94,
|
||||
468,
|
||||
497
|
||||
],
|
||||
"18": [
|
||||
165,
|
||||
139,
|
||||
542,
|
||||
568,
|
||||
434
|
||||
],
|
||||
"19": [
|
||||
367,
|
||||
18,
|
||||
355,
|
||||
368,
|
||||
353
|
||||
],
|
||||
"20": [
|
||||
231,
|
||||
78,
|
||||
86,
|
||||
236,
|
||||
217
|
||||
],
|
||||
"21": [
|
||||
356,
|
||||
17,
|
||||
366,
|
||||
354,
|
||||
365
|
||||
],
|
||||
"22": [
|
||||
503,
|
||||
205,
|
||||
470,
|
||||
92,
|
||||
481
|
||||
],
|
||||
"23": [
|
||||
527,
|
||||
106,
|
||||
584,
|
||||
195,
|
||||
421
|
||||
],
|
||||
"24": [
|
||||
239,
|
||||
73,
|
||||
222,
|
||||
228,
|
||||
81
|
||||
],
|
||||
"25": [
|
||||
543,
|
||||
138,
|
||||
168,
|
||||
435,
|
||||
565
|
||||
],
|
||||
"26": [
|
||||
48,
|
||||
46,
|
||||
302,
|
||||
281,
|
||||
255
|
||||
],
|
||||
"27": [
|
||||
248,
|
||||
62,
|
||||
293,
|
||||
58,
|
||||
267
|
||||
],
|
||||
"28": [
|
||||
440,
|
||||
141,
|
||||
562,
|
||||
540,
|
||||
163
|
||||
],
|
||||
"29": [
|
||||
274,
|
||||
30,
|
||||
312,
|
||||
261,
|
||||
29
|
||||
],
|
||||
"30": [
|
||||
179,
|
||||
128,
|
||||
597,
|
||||
450,
|
||||
505
|
||||
],
|
||||
"31": [
|
||||
376,
|
||||
22,
|
||||
375,
|
||||
346,
|
||||
345
|
||||
],
|
||||
"32": [
|
||||
320,
|
||||
11,
|
||||
405,
|
||||
401,
|
||||
319
|
||||
],
|
||||
"33": [
|
||||
448,
|
||||
173,
|
||||
130,
|
||||
587,
|
||||
519
|
||||
],
|
||||
"34": [
|
||||
460,
|
||||
102,
|
||||
211,
|
||||
489,
|
||||
479
|
||||
],
|
||||
"35": [
|
||||
388,
|
||||
2,
|
||||
392,
|
||||
329,
|
||||
333
|
||||
],
|
||||
"36": [
|
||||
512,
|
||||
182,
|
||||
596,
|
||||
121,
|
||||
455
|
||||
],
|
||||
"37": [
|
||||
592,
|
||||
170,
|
||||
516,
|
||||
443,
|
||||
133
|
||||
],
|
||||
"38": [
|
||||
120,
|
||||
189,
|
||||
529,
|
||||
570,
|
||||
411
|
||||
],
|
||||
"39": [
|
||||
420,
|
||||
198,
|
||||
577,
|
||||
522,
|
||||
111
|
||||
],
|
||||
"40": [
|
||||
272,
|
||||
69,
|
||||
65,
|
||||
290,
|
||||
243
|
||||
],
|
||||
"41": [
|
||||
488,
|
||||
93,
|
||||
498,
|
||||
204,
|
||||
467
|
||||
],
|
||||
"42": [
|
||||
156,
|
||||
150,
|
||||
547,
|
||||
553,
|
||||
431
|
||||
],
|
||||
"43": [
|
||||
252,
|
||||
53,
|
||||
286,
|
||||
297,
|
||||
55
|
||||
],
|
||||
"44": [
|
||||
532,
|
||||
192,
|
||||
117,
|
||||
410,
|
||||
571
|
||||
],
|
||||
"45": [
|
||||
400,
|
||||
7,
|
||||
321,
|
||||
396,
|
||||
323
|
||||
],
|
||||
"46": [
|
||||
580,
|
||||
199,
|
||||
417,
|
||||
110,
|
||||
523
|
||||
],
|
||||
"47": [
|
||||
296,
|
||||
63,
|
||||
245,
|
||||
266,
|
||||
59
|
||||
],
|
||||
"48": [
|
||||
600,
|
||||
125,
|
||||
178,
|
||||
508,
|
||||
451
|
||||
],
|
||||
"49": [
|
||||
68,
|
||||
72,
|
||||
269,
|
||||
242,
|
||||
291
|
||||
],
|
||||
"50": [
|
||||
324,
|
||||
8,
|
||||
399,
|
||||
322,
|
||||
395
|
||||
],
|
||||
"51": [
|
||||
499,
|
||||
96,
|
||||
485,
|
||||
466,
|
||||
201
|
||||
],
|
||||
"52": [
|
||||
406,
|
||||
12,
|
||||
317,
|
||||
318,
|
||||
402
|
||||
],
|
||||
"53": [
|
||||
563,
|
||||
144,
|
||||
437,
|
||||
162,
|
||||
537
|
||||
],
|
||||
"54": [
|
||||
234,
|
||||
88,
|
||||
219,
|
||||
229,
|
||||
80
|
||||
],
|
||||
"55": [
|
||||
350,
|
||||
24,
|
||||
349,
|
||||
371,
|
||||
372
|
||||
],
|
||||
"56": [
|
||||
444,
|
||||
134,
|
||||
515,
|
||||
169,
|
||||
591
|
||||
],
|
||||
"57": [
|
||||
258,
|
||||
40,
|
||||
39,
|
||||
277,
|
||||
307
|
||||
],
|
||||
"58": [
|
||||
285,
|
||||
56,
|
||||
251,
|
||||
54,
|
||||
298
|
||||
],
|
||||
"59": [
|
||||
546,
|
||||
151,
|
||||
153,
|
||||
430,
|
||||
556
|
||||
],
|
||||
"60": [
|
||||
98,
|
||||
215,
|
||||
475,
|
||||
493,
|
||||
464
|
||||
],
|
||||
"61": [
|
||||
474,
|
||||
214,
|
||||
99,
|
||||
461,
|
||||
496
|
||||
],
|
||||
"62": [
|
||||
357,
|
||||
20,
|
||||
363,
|
||||
359,
|
||||
364
|
||||
],
|
||||
"63": [
|
||||
490,
|
||||
212,
|
||||
459,
|
||||
101,
|
||||
480
|
||||
],
|
||||
"64": [
|
||||
185,
|
||||
116,
|
||||
415,
|
||||
533,
|
||||
574
|
||||
],
|
||||
"65": [
|
||||
378,
|
||||
16,
|
||||
343,
|
||||
341,
|
||||
380
|
||||
],
|
||||
"66": [
|
||||
218,
|
||||
85,
|
||||
235,
|
||||
77,
|
||||
232
|
||||
],
|
||||
"67": [
|
||||
342,
|
||||
15,
|
||||
377,
|
||||
379,
|
||||
344
|
||||
],
|
||||
"68": [
|
||||
458,
|
||||
209,
|
||||
491,
|
||||
477,
|
||||
104
|
||||
],
|
||||
"69": [
|
||||
514,
|
||||
135,
|
||||
441,
|
||||
590,
|
||||
172
|
||||
],
|
||||
"70": [
|
||||
226,
|
||||
83,
|
||||
75,
|
||||
237,
|
||||
224
|
||||
],
|
||||
"71": [
|
||||
530,
|
||||
119,
|
||||
569,
|
||||
190,
|
||||
412
|
||||
],
|
||||
"72": [
|
||||
38,
|
||||
37,
|
||||
257,
|
||||
308,
|
||||
278
|
||||
],
|
||||
"73": [
|
||||
414,
|
||||
113,
|
||||
188,
|
||||
575,
|
||||
536
|
||||
],
|
||||
"74": [
|
||||
362,
|
||||
19,
|
||||
358,
|
||||
361,
|
||||
360
|
||||
],
|
||||
"75": [
|
||||
334,
|
||||
1,
|
||||
330,
|
||||
387,
|
||||
391
|
||||
],
|
||||
"76": [
|
||||
438,
|
||||
161,
|
||||
538,
|
||||
143,
|
||||
564
|
||||
],
|
||||
"77": [
|
||||
550,
|
||||
157,
|
||||
426,
|
||||
560,
|
||||
147
|
||||
],
|
||||
"78": [
|
||||
566,
|
||||
167,
|
||||
137,
|
||||
544,
|
||||
436
|
||||
],
|
||||
"79": [
|
||||
126,
|
||||
177,
|
||||
452,
|
||||
507,
|
||||
599
|
||||
],
|
||||
"80": [
|
||||
284,
|
||||
41,
|
||||
254,
|
||||
43,
|
||||
303
|
||||
],
|
||||
"81": [
|
||||
494,
|
||||
97,
|
||||
476,
|
||||
463,
|
||||
216
|
||||
],
|
||||
"82": [
|
||||
200,
|
||||
109,
|
||||
418,
|
||||
524,
|
||||
579
|
||||
],
|
||||
"83": [
|
||||
263,
|
||||
25,
|
||||
26,
|
||||
276,
|
||||
310
|
||||
],
|
||||
"84": [
|
||||
300,
|
||||
50,
|
||||
52,
|
||||
249,
|
||||
287
|
||||
],
|
||||
"85": [
|
||||
558,
|
||||
145,
|
||||
428,
|
||||
159,
|
||||
552
|
||||
],
|
||||
"86": [
|
||||
403,
|
||||
9,
|
||||
316,
|
||||
315,
|
||||
407
|
||||
],
|
||||
"87": [
|
||||
74,
|
||||
82,
|
||||
227,
|
||||
221,
|
||||
240
|
||||
],
|
||||
"88": [
|
||||
289,
|
||||
66,
|
||||
244,
|
||||
271,
|
||||
70
|
||||
],
|
||||
"89": [
|
||||
306,
|
||||
34,
|
||||
280,
|
||||
33,
|
||||
259
|
||||
],
|
||||
"90": [
|
||||
572,
|
||||
118,
|
||||
531,
|
||||
409,
|
||||
191
|
||||
],
|
||||
"91": [
|
||||
207,
|
||||
90,
|
||||
472,
|
||||
483,
|
||||
501
|
||||
],
|
||||
"92": [
|
||||
369,
|
||||
23,
|
||||
370,
|
||||
351,
|
||||
352
|
||||
],
|
||||
"93": [
|
||||
585,
|
||||
132,
|
||||
175,
|
||||
517,
|
||||
446
|
||||
],
|
||||
"94": [
|
||||
105,
|
||||
196,
|
||||
528,
|
||||
583,
|
||||
422
|
||||
],
|
||||
"95": [
|
||||
241,
|
||||
67,
|
||||
292,
|
||||
71,
|
||||
270
|
||||
],
|
||||
"96": [
|
||||
425,
|
||||
148,
|
||||
559,
|
||||
549,
|
||||
158
|
||||
],
|
||||
"97": [
|
||||
525,
|
||||
193,
|
||||
108,
|
||||
423,
|
||||
582
|
||||
],
|
||||
"98": [
|
||||
174,
|
||||
129,
|
||||
588,
|
||||
447,
|
||||
520
|
||||
],
|
||||
"99": [
|
||||
313,
|
||||
10,
|
||||
404,
|
||||
408,
|
||||
314
|
||||
],
|
||||
"100": [
|
||||
413,
|
||||
187,
|
||||
576,
|
||||
535,
|
||||
114
|
||||
],
|
||||
"101": [
|
||||
573,
|
||||
186,
|
||||
416,
|
||||
115,
|
||||
534
|
||||
],
|
||||
"102": [
|
||||
49,
|
||||
51,
|
||||
299,
|
||||
288,
|
||||
250
|
||||
],
|
||||
"103": [
|
||||
449,
|
||||
180,
|
||||
127,
|
||||
598,
|
||||
506
|
||||
],
|
||||
"104": [
|
||||
469,
|
||||
91,
|
||||
206,
|
||||
504,
|
||||
482
|
||||
],
|
||||
"105": [
|
||||
513,
|
||||
171,
|
||||
589,
|
||||
136,
|
||||
442
|
||||
],
|
||||
"106": [
|
||||
279,
|
||||
35,
|
||||
305,
|
||||
260,
|
||||
36
|
||||
],
|
||||
"107": [
|
||||
389,
|
||||
3,
|
||||
385,
|
||||
336,
|
||||
332
|
||||
],
|
||||
"108": [
|
||||
593,
|
||||
183,
|
||||
509,
|
||||
454,
|
||||
124
|
||||
],
|
||||
"109": [
|
||||
149,
|
||||
155,
|
||||
554,
|
||||
432,
|
||||
548
|
||||
],
|
||||
"110": [
|
||||
325,
|
||||
5,
|
||||
394,
|
||||
327,
|
||||
398
|
||||
],
|
||||
"111": [
|
||||
453,
|
||||
123,
|
||||
510,
|
||||
184,
|
||||
594
|
||||
],
|
||||
"112": [
|
||||
383,
|
||||
13,
|
||||
338,
|
||||
340,
|
||||
381
|
||||
],
|
||||
"113": [
|
||||
311,
|
||||
31,
|
||||
273,
|
||||
32,
|
||||
262
|
||||
],
|
||||
"114": [
|
||||
581,
|
||||
107,
|
||||
526,
|
||||
424,
|
||||
194
|
||||
],
|
||||
"115": [
|
||||
61,
|
||||
57,
|
||||
268,
|
||||
247,
|
||||
294
|
||||
],
|
||||
"116": [
|
||||
87,
|
||||
79,
|
||||
230,
|
||||
220,
|
||||
233
|
||||
],
|
||||
"117": [
|
||||
301,
|
||||
47,
|
||||
45,
|
||||
256,
|
||||
282
|
||||
],
|
||||
"118": [
|
||||
131,
|
||||
176,
|
||||
445,
|
||||
518,
|
||||
586
|
||||
],
|
||||
"119": [
|
||||
210,
|
||||
103,
|
||||
457,
|
||||
478,
|
||||
492
|
||||
],
|
||||
"120": [
|
||||
140,
|
||||
166,
|
||||
567,
|
||||
433,
|
||||
541
|
||||
]
|
||||
},
|
||||
|
||||
};
|
||||
|
||||
|
||||
// Schoute's partition via https://arxiv.org/abs/1010.4353
|
||||
|
||||
export const PARTITION600 = {
|
||||
|
||||
@ -14,7 +14,6 @@ export const get_colours = (basis) => {
|
||||
const hsl = colours.map((c) => Color("#" + c).hsl());
|
||||
const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber());
|
||||
resaturated.unshift(basis);
|
||||
console.log(resaturated);
|
||||
return resaturated;
|
||||
}
|
||||
|
||||
|
||||
@ -1 +0,0 @@
|
||||
|
||||
@ -1,492 +0,0 @@
|
||||
|
||||
import * as POLYTOPES from './polytopes.js';
|
||||
|
||||
// exploring more inscriptions of the 120-cell
|
||||
|
||||
|
||||
function choice(a) {
|
||||
const r = Math.floor(Math.random() * a.length);
|
||||
return a[r];
|
||||
}
|
||||
|
||||
export function nodes_links(links, nodeid) {
|
||||
return links.filter((l) => l.source === nodeid || l.target === nodeid);
|
||||
}
|
||||
|
||||
|
||||
export function linked(links, n1, n2) {
|
||||
const ls = nodes_links(nodes_links(links, n1), n2);
|
||||
if( ls.length ) {
|
||||
return ls[0]
|
||||
} else {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
function fingerprint(ids) {
|
||||
const sids = [...ids];
|
||||
sids.sort();
|
||||
return sids.join(',');
|
||||
}
|
||||
|
||||
export function dist(n1, n2) {
|
||||
return Math.sqrt((n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2);
|
||||
}
|
||||
|
||||
|
||||
export function make_120cell() {
|
||||
const nodes = POLYTOPES.make_120cell_vertices();
|
||||
const links = POLYTOPES.auto_detect_edges(nodes, 4);
|
||||
return {
|
||||
nodes: nodes,
|
||||
links: links
|
||||
}
|
||||
}
|
||||
|
||||
function round_dist(raw) {
|
||||
return Math.floor(raw * 100000) / 100000;
|
||||
}
|
||||
|
||||
export function distance_groups(cell120) {
|
||||
// get list of other nodes by distance
|
||||
// sort them and dump them out
|
||||
const dists = {};
|
||||
|
||||
cell120.nodes.map((n) => {
|
||||
const draw = dist(cell120.nodes[0], n);
|
||||
const dtrunc = round_dist(draw);
|
||||
if( !(dtrunc in dists) ) {
|
||||
dists[dtrunc] = [];
|
||||
}
|
||||
dists[dtrunc].push(n);
|
||||
});
|
||||
return dists;
|
||||
}
|
||||
|
||||
function distance_group(cell120, n0, chord) {
|
||||
const nodes = []
|
||||
cell120.nodes.map((n) => {
|
||||
const d = round_dist(dist(n0, n));
|
||||
if( d == chord ) {
|
||||
nodes.push(n);
|
||||
}
|
||||
});
|
||||
// filter and return those whose chord is also the same
|
||||
const equidistant = [];
|
||||
for( const n1 of nodes ) {
|
||||
for( const n2 of nodes ) {
|
||||
if( n2.id > n1.id ) {
|
||||
if( round_dist(dist(n1, n2)) == chord ) {
|
||||
equidistant.push([n1, n2]);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return equidistant;
|
||||
}
|
||||
|
||||
|
||||
export function chord_survey() {
|
||||
const cell120 = POLYTOPES.cell120_inscribed();
|
||||
|
||||
const dgroups = distance_groups(cell120);
|
||||
|
||||
const dists = Object.keys(dgroups);
|
||||
|
||||
dists.sort();
|
||||
|
||||
for( const d of dists ) {
|
||||
const g0 = dgroups[d][0];
|
||||
dgroups[d].map((g) => {
|
||||
console.log(`${g0.id}-${g.id}: ${round_dist(dist(g0, g))}`);
|
||||
});
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
function overlap(c1, c2) {
|
||||
for( const l in c1 ) {
|
||||
if( c1[l] === c2[l] ) {
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
function c5match(c1, c2) {
|
||||
for( const l in c1 ) {
|
||||
if( c1[l] != c2[l] ) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
export function gather_5cells(cell120) {
|
||||
const CHORD5 = round_dist(Math.sqrt(2.5));
|
||||
const bins = [];
|
||||
const all = [];
|
||||
cell120.nodes.filter((n) => n.label === 1).map((n) => {
|
||||
const cells = [ ];
|
||||
const g = distance_group(cell120, n, CHORD5);
|
||||
for( const pair of g ) {
|
||||
let seen = false;
|
||||
for( const cell of cells ) {
|
||||
const c = Object.values(cell);
|
||||
if( c.includes(pair[0].id) || c.includes(pair[1].id) ) {
|
||||
if( !c.includes(pair[0].id) ) {
|
||||
cell[pair[0].label] = pair[0].id;
|
||||
}
|
||||
if( !c.includes(pair[1].id) ) {
|
||||
cell[pair[1].label] = pair[1].id;
|
||||
}
|
||||
seen = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
if( !seen ) {
|
||||
const cell = {};
|
||||
cell[1]= n.id;
|
||||
cell[pair[0].label] = pair[0].id;
|
||||
cell[pair[1].label] = pair[1].id;
|
||||
cells.push(cell);
|
||||
}
|
||||
}
|
||||
all.push(...cells);
|
||||
});
|
||||
return all;
|
||||
}
|
||||
|
||||
function audit_5cells(cells) {
|
||||
// this verifies that for each label (a 600-cell set), each of its
|
||||
// vertices is in exactly 7 5-cells. It checks out.
|
||||
|
||||
['1','2','3','4','5'].map((l) => {
|
||||
const sets = {};
|
||||
for( const cell of cells ) {
|
||||
const lv = cell[l];
|
||||
if( !(lv in sets) ) {
|
||||
sets[lv] = [];
|
||||
}
|
||||
sets[lv].push(cell);
|
||||
}
|
||||
for( const lv in sets ) {
|
||||
const ok = ( sets[lv].length === 7 ) ? 'ok' : 'miss';
|
||||
console.log(`${l},${lv},${sets[lv].length},${ok}`);
|
||||
}
|
||||
});
|
||||
}
|
||||
|
||||
function try_120_5_cells_fails(cell120, cells, l) {
|
||||
// iterate over every vertex in the 600-cell defined by label l,
|
||||
// get all 7 5-cells including that vertex, and add them if they are
|
||||
// disjoint with what we already have
|
||||
|
||||
// this always runs out of disjoint nodes early
|
||||
|
||||
const vertices = cell120.nodes.filter((n) => n.label === l);
|
||||
|
||||
const cellset = [];
|
||||
for( const v of vertices ) {
|
||||
console.log(`Vertex ${v.id}`);
|
||||
const vcells = cells.filter((c) => c[l] === v.id);
|
||||
const overlap_any = (cs, c) => {
|
||||
for( const seen of cs ) {
|
||||
if( overlap(seen, c) ) {
|
||||
console.log("overlap");
|
||||
console.log(c);
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
const disjoint = vcells.filter((c) => ! overlap_any(cellset, c));
|
||||
console.log(`Found ${disjoint.length} disjoint cells`);
|
||||
if( disjoint.length > 0 ) {
|
||||
cellset.push(choice(disjoint));
|
||||
}
|
||||
}
|
||||
console.log(`Found total of ${cellset.length} disjoint cells`);
|
||||
//console.log(cellset);
|
||||
}
|
||||
|
||||
function overlap_any(cs, c) {
|
||||
for( const seen of cs ) {
|
||||
if( overlap(seen, c) ) {
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
function explore_disjoint(cell120, all5, l) {
|
||||
const a = all5[0];
|
||||
|
||||
const overlaps = all5.filter((c) => overlap(c, a));
|
||||
|
||||
console.log(a);
|
||||
|
||||
console.log(overlaps.length);
|
||||
console.log(overlaps);
|
||||
}
|
||||
|
||||
// select a five-cell from a starting vertex v
|
||||
// find a neighbor of v vn on its 600 cell, find all of the 5-cells which include
|
||||
// vn. Then see if we can find any from that set which are similiar neighbours to
|
||||
// the other four vertices in the first 5-cell
|
||||
|
||||
// the idea is that the 600-cells are a guide to finding the right subset of
|
||||
// 5-cells
|
||||
|
||||
function neighbours600(cell120, vid) {
|
||||
const v = cell120.nodes.filter((node) => node.id === vid)[0];
|
||||
const label = v.label;
|
||||
const links = cell120.links.filter((l) => {
|
||||
return l.label === v.label && (l.source === v.id || l.target == v.id );
|
||||
});
|
||||
const nodes = links.map((l) => {
|
||||
if( l.source === v.id ) {
|
||||
return l.target;
|
||||
} else {
|
||||
return l.source;
|
||||
}
|
||||
});
|
||||
return nodes;
|
||||
}
|
||||
|
||||
function cell120node(cell120, nid) {
|
||||
return cell120.nodes.filter((n) => n.id === nid)[0];
|
||||
}
|
||||
|
||||
function node_dist(cell120, aid, bid) {
|
||||
const a = cell120node(cell120, aid);
|
||||
const b = cell120node(cell120, bid);
|
||||
return dist(a, b);
|
||||
}
|
||||
|
||||
function print_row(v1, v2, p, v5) {
|
||||
console.log(`${v1.id},${v2.id},${p},${v5[1]},${v5[2]},${v5[3]},${v5[4]},${v5[5]}`);
|
||||
}
|
||||
|
||||
// for a pair of vertices which are on the same inscribed 600 cell,
|
||||
// this returns all 7 pairs of 5-cells which contain v1 and v2 and
|
||||
// which are also evenly spaced (ie every pair of vertices on the
|
||||
// same 600-cell is one edge apart)
|
||||
|
||||
|
||||
function find_adjoining_5cells(cell120, all5, v1, v2) {
|
||||
const DIST600 = round_dist(node_dist(cell120, v1.id, v2.id));
|
||||
const v15s = all5.filter((c5) => c5[v1.label] === v1.id);
|
||||
const v25s = all5.filter((c5) => c5[v2.label] === v2.id);
|
||||
let p = 0;
|
||||
const c5pairs = [];
|
||||
for( const v5a of v15s ) {
|
||||
for( const v5b of v25s ) {
|
||||
let match = true;
|
||||
const d = {};
|
||||
for( const label in v5a ) {
|
||||
d[label] = round_dist(node_dist(cell120, v5a[label], v5b[label]));
|
||||
if( d[label] != DIST600 ) {
|
||||
match = false;
|
||||
}
|
||||
}
|
||||
if( match ) {
|
||||
c5pairs.push([ v5a, v5b ]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return c5pairs;
|
||||
}
|
||||
|
||||
function tetras(cell120, v) {
|
||||
// given a vertex v, find all of the 600-cell tetras it's on
|
||||
|
||||
const n600s = neighbours600(cell120, v.id);
|
||||
// need to find all sets of three neighbours which are neighbours: there
|
||||
// should be 20 of these because they're faces of an icosahedron
|
||||
const tetras = new Set;
|
||||
for( const v2id of n600s ) {
|
||||
// find mutual neighbours of the first two
|
||||
const n2600s = neighbours600(cell120, v2id);
|
||||
const mutuals = n2600s.filter((nid) => {
|
||||
return nid != v2id && nid != v.id && n600s.includes(nid)
|
||||
});
|
||||
for( const nm of mutuals ) {
|
||||
const nnms = neighbours600(cell120, nm);
|
||||
const mutuals2 = nnms.filter((nid) => {
|
||||
return nid != nm && nid != v2id && nid != v.id && mutuals.includes(nid)
|
||||
});
|
||||
for( const m2 of mutuals2 ) {
|
||||
const t = [ v.id, v2id, nm, m2 ];
|
||||
t.sort((a, b) => a - b);
|
||||
const tstr = t.join(',');
|
||||
tetras.add(tstr);
|
||||
}
|
||||
}
|
||||
}
|
||||
const tarray = [];
|
||||
for( const t of tetras ) {
|
||||
const ta = t.split(',').map((v) => Number(v));
|
||||
tarray.push(ta);
|
||||
}
|
||||
return tarray;
|
||||
}
|
||||
|
||||
function vertices(hedra) {
|
||||
const v = new Set;
|
||||
for ( const h of hedra) {
|
||||
for( const p of h ) {
|
||||
v.add(p);
|
||||
}
|
||||
}
|
||||
return Array.from(v);
|
||||
}
|
||||
|
||||
function str5cell(c5) {
|
||||
return ["1","2","3","4","5"].map((l) => String(c5[l]).padStart(3, '0')).join('-');
|
||||
}
|
||||
|
||||
function tetra_sets(cell120, all5, tetra) {
|
||||
// given a tetrahedron on a 600-cell, find the sets of adjacent 5-cells on
|
||||
// all of the pairs
|
||||
// this is ass-backwards. Need to find tetras on the other 4 vertices of a 5-cell
|
||||
|
||||
const vs = tetra.map((tid) => cell120node(cell120, tid));
|
||||
const pairs = [[0,1], [0,2], [0, 3], [1, 2], [1, 3], [2, 3]];
|
||||
for( const p of pairs ) {
|
||||
const v1 = vs[p[0]];
|
||||
const v2 = vs[p[1]];
|
||||
const c5pairs = find_adjoining_5cells(cell120, all5, v1, v2);
|
||||
console.log(v1.id, v2.id);
|
||||
console.log(c5pairs.map((p) => str5cell(p[0]) + " " + str5cell(p[1])));
|
||||
}
|
||||
}
|
||||
|
||||
function cell5_neighbourhoods(cell120, all5, c5) {
|
||||
const neighbours = {}
|
||||
|
||||
for( const l in c5 ) {
|
||||
const v = cell120node(cell120, c5[l]);
|
||||
neighbours[l] = vertices(tetras(cell120, v));
|
||||
}
|
||||
|
||||
// now take the set of all 5-cells and filter it to only those whose vertices
|
||||
// are in the neighour sets. On first inspection there are 13?
|
||||
|
||||
const n5cells = all5.filter((c5) => {
|
||||
for( const l in c5 ) {
|
||||
if( ! neighbours[l].includes(c5[l]) ) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
});
|
||||
return n5cells;
|
||||
}
|
||||
|
||||
|
||||
function cell5_tetras(cell120, all5, c5) {
|
||||
const nb = cell5_neighbourhoods(cell120, all5, c5);
|
||||
const v1 = cell120node(cell120, c5["1"]);
|
||||
const ts = tetras(cell120, v1);
|
||||
|
||||
const c5s = [];
|
||||
for( const t of ts ) {
|
||||
const nt = nb.filter((n) => {
|
||||
for( const l in n ) {
|
||||
if( t.includes(n[l]) ) {
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false
|
||||
});
|
||||
for( const nc5 of nt ) {
|
||||
const exact = c5s.filter((c) => c5match(c, nc5));
|
||||
if( exact.length === 0 ) {
|
||||
const o = c5s.filter((c) => overlap(c, nc5));
|
||||
if( o.length > 0 ) {
|
||||
console.log("Overlap", c5, o);
|
||||
} else {
|
||||
c5s.push(nc5);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return c5s;
|
||||
}
|
||||
|
||||
|
||||
function coherent_5cells_r(cell120, all5, c5s, c50) {
|
||||
// Find next set of c5s, see if there are any we haven't seen,
|
||||
// recurse into those ones
|
||||
const c5ns = cell5_tetras(cell120, all5, c50);
|
||||
const c5unseen = c5ns.filter((c5) => {
|
||||
const matched = c5s.filter((c5b) => c5match(c5b, c5));
|
||||
return matched.length === 0;
|
||||
});
|
||||
for( const c5u of c5unseen ) {
|
||||
c5s.push(c5u);
|
||||
}
|
||||
for( const c5u of c5unseen ) {
|
||||
coherent_5cells_r(cell120, all5, c5s, c5u);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
function coherent_5cells(cell120, all5) {
|
||||
// pick a starting point, collect coherent 5_cells, continue till
|
||||
// there aren't any new ones
|
||||
|
||||
const c5set = [];
|
||||
let c5 = all5[0];
|
||||
|
||||
const c5s = [];
|
||||
coherent_5cells_r(cell120, all5, c5s, c5);
|
||||
return c5s;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
const cell120 = POLYTOPES.cell120_inscribed();
|
||||
const all5 = gather_5cells(cell120);
|
||||
|
||||
const c5s = coherent_5cells(cell120, all5);
|
||||
|
||||
const celli = c5s.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
|
||||
|
||||
|
||||
// check it because I don't believe it yet
|
||||
|
||||
const vertex_check = {};
|
||||
|
||||
for( const c5 of celli ) {
|
||||
for( const l in c5 ) {
|
||||
const v = c5[l];
|
||||
if( v in vertex_check ) {
|
||||
console.log(`Double count vertex ${v}`);
|
||||
}
|
||||
vertex_check[v] = 1;
|
||||
}
|
||||
}
|
||||
|
||||
for( let i = 1; i < 601; i++ ) {
|
||||
if( !vertex_check[i] ) {
|
||||
console.log(`v ${i} missing`);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
const idict = {};
|
||||
for( let i = 1; i < 121; i++ ) {
|
||||
idict[i] = celli[i - 1];
|
||||
}
|
||||
|
||||
console.log(JSON.stringify(idict, null, 2));
|
||||
@ -1,11 +1,8 @@
|
||||
import * as THREE from 'three';
|
||||
|
||||
import { TaperedLink } from './taperedLink.js';
|
||||
|
||||
|
||||
const HYPERPLANE = 2.0;
|
||||
const W_FORESHORTENING = 0.04;
|
||||
|
||||
const W_FORESHORTENING = 0.4;
|
||||
|
||||
class FourDShape extends THREE.Group {
|
||||
|
||||
@ -29,12 +26,12 @@ class FourDShape extends THREE.Group {
|
||||
|
||||
// if a node/link has no label, use the 0th material
|
||||
|
||||
getMaterialLabel(entity) {
|
||||
if( "label" in entity ) {
|
||||
return entity.label
|
||||
} else {
|
||||
return 0;
|
||||
}
|
||||
getMaterial(entity, materials) {
|
||||
if( "label" in entity ) {
|
||||
return materials[entity.label];
|
||||
} else {
|
||||
return materials[0];
|
||||
}
|
||||
}
|
||||
|
||||
makeNode(material, v3, scale) {
|
||||
@ -45,24 +42,62 @@ class FourDShape extends THREE.Group {
|
||||
return sphere;
|
||||
}
|
||||
|
||||
makeLink(materialLabel, link) {
|
||||
makeLink(material, link) {
|
||||
const n1 = this.nodes3[link.source];
|
||||
const n2 = this.nodes3[link.target];
|
||||
const s1 = this.link_scale * n1.scale;
|
||||
const s2 = this.link_scale * n2.scale;
|
||||
const basematerial = this.link_ms[materialLabel];
|
||||
const edge = new TaperedLink(basematerial, materialLabel, n1, n2, s1, s2);
|
||||
this.add( edge );
|
||||
const s1 = n1.scale;
|
||||
const s2 = n2.scale;
|
||||
const length = n1.v3.distanceTo(n2.v3);
|
||||
const centre = new THREE.Vector3();
|
||||
centre.lerpVectors(n1.v3, n2.v3, 0.5);
|
||||
const geometry = new THREE.CylinderGeometry(this.link_scale * s2, this.link_scale * s1, 1);
|
||||
const cyl = new THREE.Mesh(geometry, material);
|
||||
const edge = new THREE.Group();
|
||||
edge.add(cyl);
|
||||
edge.position.copy(centre);
|
||||
edge.scale.copy(new THREE.Vector3(1, 1, length));
|
||||
edge.lookAt(n2.v3);
|
||||
cyl.rotation.x = Math.PI / 2.0;
|
||||
this.add(edge);
|
||||
return edge;
|
||||
}
|
||||
|
||||
updateLink(link, links_show) {
|
||||
const n1 = this.nodes3[link.source];
|
||||
const n2 = this.nodes3[link.target];
|
||||
const s1 = this.link_scale * n1.scale;
|
||||
const s2 = this.link_scale * n2.scale;
|
||||
link.object.update(n1, n2, s1, s2);
|
||||
link.object.visible = (!links_show || links_show.includes(link.label));
|
||||
const s1 = n1.scale;
|
||||
const s2 = n2.scale;
|
||||
const length = n1.v3.distanceTo(n2.v3);
|
||||
const centre = new THREE.Vector3();
|
||||
centre.lerpVectors(n1.v3, n2.v3, 0.5);
|
||||
// is this really the only way to do this?
|
||||
//const geometry = new THREE.CylinderGeometry(this.link_scale * s2, this.link_scale * s1, 1);
|
||||
//link.object.children[0].geometry.dispose();
|
||||
this.forshortenLink(link.object.children[0].geometry, this.link_scale * s2, this.link_scale * s1);
|
||||
//const link_hack = this.link_scale * (s1 + s2) * 0.5;
|
||||
link.object.scale.copy(new THREE.Vector3(1, 1, length));
|
||||
link.object.position.copy(centre);
|
||||
link.object.lookAt(n2.v3);
|
||||
link.object.children[0].rotation.x = Math.PI / 2.0;
|
||||
// link.object.children[0].geometry.needsUpdate = true;
|
||||
// link.object.children[0].geometry.computeVertexNormals();
|
||||
link.object.visible = (!links_show || link.label in links_show);
|
||||
}
|
||||
|
||||
forshortenLink(geometry, top, bottom) {
|
||||
const count = geometry.attributes.position.count;
|
||||
for( let i = 0; i < count; i++ ) {
|
||||
const x = geometry.attributes.position.getX(i);
|
||||
const y = geometry.attributes.position.getY(i);
|
||||
const z = geometry.attributes.position.getZ(i);
|
||||
if( z == 0 ) {
|
||||
geometry.attributes.position.setX(i, x * top);
|
||||
geometry.attributes.position.setY(i, y * top);
|
||||
} else {
|
||||
geometry.attributes.position.setX(i, x * bottom);
|
||||
geometry.attributes.position.setY(i, y * bottom);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -91,6 +126,15 @@ class FourDShape extends THREE.Group {
|
||||
}
|
||||
|
||||
|
||||
fourDtoV3_old(x, y, z, w, rotations) {
|
||||
const v4 = new THREE.Vector4(x, y, z, w);
|
||||
for ( const m4 of rotations ) {
|
||||
v4.applyMatrix4(m4);
|
||||
}
|
||||
const k = this.fourDscale(v4.w);
|
||||
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
|
||||
}
|
||||
|
||||
fourDscale(w) {
|
||||
return this.hyperplane / ( this.hyperplane + w );
|
||||
}
|
||||
@ -112,7 +156,7 @@ class FourDShape extends THREE.Group {
|
||||
for( const n of this.nodes4 ) {
|
||||
const k = this.fourDscale(n.w);
|
||||
const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k);
|
||||
const material = this.node_ms[this.getMaterialLabel(n)];
|
||||
const material = this.getMaterial(n, this.node_ms);
|
||||
this.nodes3[n.id] = {
|
||||
v3: v3,
|
||||
scale: k,
|
||||
@ -121,11 +165,11 @@ class FourDShape extends THREE.Group {
|
||||
};
|
||||
}
|
||||
for( const l of this.links ) {
|
||||
const mLabel = this.getMaterialLabel(l);
|
||||
l.object = this.makeLink(mLabel, l);
|
||||
const material = this.getMaterial(l, this.link_ms);
|
||||
l.object = this.makeLink(material, l);
|
||||
}
|
||||
for( const f of this.faces ) {
|
||||
const material = this.face_ms(this.getMaterialLabel(f));
|
||||
const material = this.getMaterial(f, this.face_ms);
|
||||
f.object = this.makeFace(material, f);
|
||||
}
|
||||
}
|
||||
@ -143,7 +187,7 @@ class FourDShape extends THREE.Group {
|
||||
this.nodes3[n.id].scale = k * this.foreshortening;
|
||||
this.nodes3[n.id].object.position.copy(v3);
|
||||
this.nodes3[n.id].object.scale.copy(s3);
|
||||
this.nodes3[n.id].object.visible = ( !nodes_show || nodes_show.includes(n.label) );
|
||||
this.nodes3[n.id].object.visible = ( !nodes_show || n.label in nodes_show );
|
||||
}
|
||||
for( const l of this.links ) {
|
||||
this.updateLink(l, links_show);
|
||||
|
||||
83
gui.js
83
gui.js
@ -2,12 +2,11 @@ import { GUI } from 'lil-gui';
|
||||
|
||||
|
||||
const DEFAULTS = {
|
||||
nodesize: 0.6,
|
||||
nodeopacity: 1,
|
||||
linksize: 1.0,
|
||||
linkopacity: 0.75,
|
||||
thickness: 0.02,
|
||||
nodesize: 0.02,
|
||||
linkopacity: 0.5,
|
||||
link2opacity: 0.5,
|
||||
shape: '120-cell',
|
||||
link2opacity: 0.75,
|
||||
option: 'none',
|
||||
visibility: 5,
|
||||
inscribed: false,
|
||||
@ -16,11 +15,9 @@ const DEFAULTS = {
|
||||
background: 0xd4d4d4,
|
||||
hyperplane: 0.93,
|
||||
zoom: 1,
|
||||
xRotate: 'YZ',
|
||||
yRotate: 'XZ',
|
||||
xRotate: 'YW',
|
||||
yRotate: 'XW',
|
||||
dtheta: 0,
|
||||
damping: false,
|
||||
captions: true,
|
||||
dpsi: 0,
|
||||
}
|
||||
|
||||
@ -28,10 +25,9 @@ const DEFAULTS = {
|
||||
|
||||
class FourDGUI {
|
||||
|
||||
constructor(funcs) {
|
||||
this.shapes = funcs.shapes;
|
||||
constructor(shapes, changeShape, setColor, setBackground, setLinkOpacity, setVisibility) {
|
||||
this.gui = new GUI();
|
||||
const SHAPE_NAMES = this.shapes.map((s) => s.name);
|
||||
const SHAPE_NAMES = shapes.map((s) => s.name);
|
||||
|
||||
this.parseLinkParams();
|
||||
const guiObj = this;
|
||||
@ -40,11 +36,10 @@ class FourDGUI {
|
||||
option: this.link['option'],
|
||||
inscribed: this.link['inscribed'],
|
||||
inscribe_all: this.link['inscribe_all'],
|
||||
linksize: this.link['linksize'],
|
||||
thickness: this.link['thickness'],
|
||||
linkopacity: this.link['linkopacity'],
|
||||
link2opacity: this.link['link2opacity'],
|
||||
link2opacity: this.link['linkopacity'],
|
||||
nodesize: this.link['nodesize'],
|
||||
nodeopacity: this.link['nodeopacity'],
|
||||
depth: this.link['depth'],
|
||||
color: this.link['color'],
|
||||
background: this.link['background'],
|
||||
@ -53,55 +48,44 @@ class FourDGUI {
|
||||
xRotate: this.link['xRotate'],
|
||||
yRotate: this.link['yRotate'],
|
||||
damping: false,
|
||||
captions: true,
|
||||
dtheta: this.link['dtheta'],
|
||||
dpsi: this.link['dpsi'],
|
||||
"copy link": function () { guiObj.copyUrl() },
|
||||
"copy link": function () { guiObj.copyUrl() }
|
||||
};
|
||||
if( funcs.extras ) {
|
||||
for( const label in funcs.extras ) {
|
||||
console.log(label);
|
||||
console.log(funcs.extras[label]);
|
||||
this.params[label] = funcs.extras[label];
|
||||
}
|
||||
}
|
||||
let options_ctrl;
|
||||
this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
|
||||
const options = this.getShapeOptions(shape);
|
||||
const options = this.getShapeOptions(shapes, shape);
|
||||
options_ctrl = options_ctrl.options(options).onChange((option) => {
|
||||
funcs.setVisibility(option)
|
||||
setVisibility(option)
|
||||
});
|
||||
options_ctrl.setValue(options[0])
|
||||
funcs.changeShape(shape)
|
||||
changeShape(shape)
|
||||
});
|
||||
const options = this.getShapeOptions(this.params['shape']);
|
||||
const options = this.getShapeOptions(shapes, this.params['shape']);
|
||||
options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
|
||||
funcs.setVisibility(option)
|
||||
setVisibility(option)
|
||||
});
|
||||
this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
|
||||
this.gui.add(this.params, 'zoom', 0.1, 2.0);
|
||||
this.gui.add(this.params, 'nodesize', 0, 1.5);
|
||||
this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(funcs.setNodeOpacity);
|
||||
this.gui.add(this.params, 'linksize', 0, 2);
|
||||
console.log(funcs.setLinkOpacity);
|
||||
this.gui.add(this.params, 'linkopacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, true));
|
||||
this.gui.add(this.params, 'link2opacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, false));
|
||||
this.gui.addColor(this.params, 'color').onChange(funcs.setColor);
|
||||
this.gui.addColor(this.params, 'background').onChange(funcs.setBackground);
|
||||
this.gui.add(this.params, 'thickness', 0, 0.1);
|
||||
this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
|
||||
(v) => setLinkOpacity(v, true)
|
||||
);
|
||||
this.gui.add(this.params, 'link2opacity', 0, 1).onChange(
|
||||
(v) => setLinkOpacity(v, false)
|
||||
);
|
||||
this.gui.add(this.params, 'nodesize', 0, 0.1);
|
||||
this.gui.addColor(this.params, 'color').onChange(setColor);
|
||||
this.gui.addColor(this.params, 'background').onChange(setBackground);
|
||||
this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
|
||||
this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
|
||||
this.gui.add(this.params, 'captions').onChange(this.showDocs);
|
||||
this.gui.add(this.params, 'damping');
|
||||
this.gui.add(this.params, 'copy link');
|
||||
if( funcs.extras ) {
|
||||
for( const label in funcs.extras ) {
|
||||
this.gui.add(this.params, label);
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
getShapeOptions(shape) {
|
||||
const spec = this.shapes.filter((s) => s.name === shape);
|
||||
getShapeOptions(shapes, shape) {
|
||||
const spec = shapes.filter((s) => s.name === shape);
|
||||
if( spec && spec[0].options ) {
|
||||
return spec[0].options.map((o) => o.name);
|
||||
} else {
|
||||
@ -150,11 +134,10 @@ class FourDGUI {
|
||||
}
|
||||
this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
|
||||
this.link['zoom'] = this.numParam('zoom', parseFloat);
|
||||
this.link['linksize'] = this.numParam('linksize', parseFloat);
|
||||
this.link['thickness'] = this.numParam('thickness', parseFloat);
|
||||
this.link['linkopacity'] = this.numParam('linkopacity', parseFloat);
|
||||
this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
|
||||
this.link['nodesize'] = this.numParam('nodesize', parseFloat);
|
||||
this.link['nodeopacity'] = this.numParam('nodeopacity', parseFloat);
|
||||
this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
|
||||
this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
|
||||
this.link['dpsi'] = this.numParam('dpsi', parseFloat);
|
||||
@ -168,10 +151,10 @@ class FourDGUI {
|
||||
url.searchParams.append("option", this.params.option);
|
||||
url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
|
||||
url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
|
||||
url.searchParams.append("linksize", this.params.linksize.toString());
|
||||
url.searchParams.append("thickness", this.params.thickness.toString());
|
||||
url.searchParams.append("nodesize", this.params.nodesize.toString());
|
||||
url.searchParams.append("nodeopacity", this.params.nodesize.toString());
|
||||
url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
|
||||
url.searchParams.append("linkopacity", this.params.thickness.toString());
|
||||
url.searchParams.append("link2opacity", this.params.nodesize.toString());
|
||||
url.searchParams.append("color", this.hexToString(this.params.color));
|
||||
url.searchParams.append("background", this.hexToString(this.params.background));
|
||||
url.searchParams.append("hyperplane", this.params.hyperplane.toString());
|
||||
|
||||
14
index.html
14
index.html
@ -14,15 +14,6 @@
|
||||
font-family: sans-serif;
|
||||
padding: 1em;
|
||||
}
|
||||
div#release_notes {
|
||||
position: fixed;
|
||||
top: 0;
|
||||
left: 0;
|
||||
width: 20%;
|
||||
z-index: 2;
|
||||
padding: 1em;
|
||||
font-family: sans-serif;
|
||||
}
|
||||
div#info {
|
||||
position: fixed;
|
||||
bottom:0;
|
||||
@ -35,10 +26,7 @@
|
||||
<body>
|
||||
<script type="module" src="/main.js"></script>
|
||||
<div id="description"></div>
|
||||
<div id="release_notes"></div>
|
||||
<div id="info"><a href="#" id="show_notes">release 1.1</a> |
|
||||
|
||||
by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> |
|
||||
<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
|
||||
<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
|
||||
</body>
|
||||
</html>
|
||||
119
linktest.js
119
linktest.js
@ -1,119 +0,0 @@
|
||||
import * as THREE from 'three';
|
||||
|
||||
import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
|
||||
import { GUI } from 'lil-gui';
|
||||
|
||||
import { TaperedLink } from './taperedLink.js';
|
||||
|
||||
const FACE_OPACITY = 0.3;
|
||||
const CAMERA_K = 5;
|
||||
|
||||
// scene, lights and camera
|
||||
|
||||
|
||||
|
||||
|
||||
const scene = new THREE.Scene();
|
||||
const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
|
||||
const light = new THREE.PointLight(0xffffff, 2);
|
||||
light.position.set(10, 10, 10);
|
||||
scene.add(light);
|
||||
const light2 = new THREE.PointLight(0xffffff, 2);
|
||||
light2.position.set(-10, 5, 10);
|
||||
scene.add(light);
|
||||
const amblight = new THREE.AmbientLight(0xffffff, 0.5);
|
||||
scene.add(amblight);
|
||||
|
||||
camera.position.set(0, 0, CAMERA_K / 2);
|
||||
|
||||
camera.lookAt(0, 0, 0);
|
||||
camera.position.z = 8;
|
||||
|
||||
const renderer = new THREE.WebGLRenderer({antialias: true});
|
||||
renderer.setSize( window.innerWidth, window.innerHeight );
|
||||
|
||||
renderer.localClippingEnabled = true;
|
||||
|
||||
const controls = new OrbitControls( camera, renderer.domElement );
|
||||
|
||||
|
||||
controls.autoRotate = true;
|
||||
|
||||
document.body.appendChild( renderer.domElement );
|
||||
|
||||
const NODEC = 0x3293a9;
|
||||
const LINKC = 0x00ff88;
|
||||
const BACKGROUNDC = 0xd4d4d4;
|
||||
|
||||
scene.background = new THREE.Color(BACKGROUNDC);
|
||||
const material = new THREE.MeshStandardMaterial({ color: LINKC });
|
||||
|
||||
material.transparent = true;
|
||||
material.opacity = 0.7;
|
||||
|
||||
const node_mat = new THREE.MeshStandardMaterial({ color: NODEC });
|
||||
|
||||
node_mat.transparent = true;
|
||||
node_mat.opacity = 0.5;
|
||||
|
||||
const params = {
|
||||
r1: 0.5,
|
||||
r2: 0.6,
|
||||
sync: false,
|
||||
l: 9,
|
||||
rotx: 1,
|
||||
roty: 0,
|
||||
rotz: 0,
|
||||
};
|
||||
|
||||
const gui = new GUI();
|
||||
|
||||
gui.add(params, "r1", 0.01, 1.5);
|
||||
gui.add(params, "r2", 0.01, 1.5);
|
||||
gui.add(params, "sync");
|
||||
gui.add(params, "l", 0, 10);
|
||||
gui.add(params, "rotx", 0, 4);
|
||||
gui.add(params, "roty", 0, 4);
|
||||
gui.add(params, "rotz", 0, 4);
|
||||
|
||||
function makeNode(material, pos, r) {
|
||||
const geometry = new THREE.SphereGeometry(1);
|
||||
const sphere = new THREE.Mesh(geometry, material);
|
||||
const node = {
|
||||
v3: pos,
|
||||
object: sphere
|
||||
};
|
||||
updateNode(node, pos, r);
|
||||
return node;
|
||||
}
|
||||
|
||||
function updateNode(node, pos, r) {
|
||||
node.v3 = pos;
|
||||
node.object.scale.copy(new THREE.Vector3(r, r, r));
|
||||
node.object.position.copy(pos);
|
||||
}
|
||||
|
||||
|
||||
const n1 = makeNode(node_mat, new THREE.Vector3(-params["l"], -1, -1), params["r1"]);
|
||||
const n2 = makeNode(node_mat, new THREE.Vector3(params["l"], 1, 1), params["r2"]);
|
||||
|
||||
const tl = new TaperedLink(material, n1, n2, params["r1"], params["r2"]);
|
||||
|
||||
scene.add(n1.object);
|
||||
scene.add(n2.object);
|
||||
|
||||
scene.add(tl);
|
||||
|
||||
function animate() {
|
||||
requestAnimationFrame(animate);
|
||||
|
||||
const r1 = params["r1"];
|
||||
const r2 = params["sync"] ? r1 : params["r2"]
|
||||
|
||||
updateNode(n1, new THREE.Vector3(- params["l"], -1, -1), r1);
|
||||
updateNode(n2, new THREE.Vector3(params["l"], 1, 1), r2);
|
||||
tl.update(n1, n2, r1, r2, params["rotx"], params["roty"], params["rotz"]);
|
||||
controls.update();
|
||||
renderer.render(scene, camera);
|
||||
}
|
||||
animate();
|
||||
128
main.js
128
main.js
@ -1,21 +1,5 @@
|
||||
import * as THREE from 'three';
|
||||
|
||||
const RELEASE_NOTES = `
|
||||
<p><b>v1.1 - 1/1/2026</b></p>
|
||||
|
||||
<p>The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
|
||||
looks like less of a mess than I expected it to.</p>
|
||||
|
||||
<p><b>v1.0 - 16/11/2025</b></p>
|
||||
|
||||
<p>It's been <a target="_blank" href="https://mikelynch.org/2023/Sep/02/120-cell/">two years</a> since
|
||||
I first made this, and I haven't updated it in a while, but I got tapered links to
|
||||
work without too much performance overhead, so that seemed worth a version.</p>
|
||||
|
||||
<p>The results flicker a bit at low opacities but otherwise I'm pretty happy with
|
||||
it.</p>
|
||||
`;
|
||||
|
||||
|
||||
|
||||
import * as POLYTOPES from './polytopes.js';
|
||||
@ -47,37 +31,30 @@ camera.lookAt(0, 0, 0);
|
||||
|
||||
const renderer = new THREE.WebGLRenderer({antialias: true});
|
||||
renderer.setSize( window.innerWidth, window.innerHeight );
|
||||
|
||||
renderer.localClippingEnabled = true;
|
||||
|
||||
|
||||
document.body.appendChild( renderer.domElement );
|
||||
|
||||
// set up colours and materials for gui callbacks
|
||||
|
||||
scene.background = new THREE.Color(DEFAULTS.background);
|
||||
const material = new THREE.MeshStandardMaterial({ color: DEFAULTS.color });
|
||||
const node_colours = get_colours(DEFAULTS.color);
|
||||
|
||||
|
||||
material.transparent = true;
|
||||
material.opacity = 0.5;
|
||||
|
||||
|
||||
const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
|
||||
const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
|
||||
|
||||
node_ms.map((m) => {
|
||||
m.transparent = true;
|
||||
m.opacity = 1.0;
|
||||
}
|
||||
);
|
||||
|
||||
link_ms.map((m) => {
|
||||
m.transparent = true;
|
||||
m.opacity = 0.5;
|
||||
}
|
||||
);
|
||||
|
||||
console.log("link_ms", link_ms);
|
||||
|
||||
)
|
||||
|
||||
const face_ms = [
|
||||
new THREE.MeshStandardMaterial( { color: 0x44ff44 } )
|
||||
new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
|
||||
];
|
||||
|
||||
for( const face_m of face_ms ) {
|
||||
@ -118,75 +95,36 @@ function displayDocs(name) {
|
||||
}
|
||||
}
|
||||
|
||||
function showDocs(visible) {
|
||||
const docdiv = document.getElementById("description");
|
||||
if( visible ) {
|
||||
docdiv.style.display = '';
|
||||
} else {
|
||||
docdiv.style.display = 'none';
|
||||
}
|
||||
}
|
||||
|
||||
function releaseNotes() {
|
||||
showDocs(false);
|
||||
const reldiv = document.getElementById("release_notes");
|
||||
reldiv.style.display = '';
|
||||
reldiv.innerHTML = RELEASE_NOTES + '<p><a id="no_notes" href="#">[hide]</a>';
|
||||
const goaway = document.getElementById("no_notes");
|
||||
goaway.addEventListener('click', noNotes);
|
||||
}
|
||||
|
||||
function noNotes() {
|
||||
const reldiv = document.getElementById("release_notes");
|
||||
reldiv.style.display = 'none';
|
||||
}
|
||||
|
||||
const relnotes = document.getElementById('show_notes');
|
||||
|
||||
relnotes.addEventListener('click', releaseNotes);
|
||||
|
||||
|
||||
// initialise gui and read params from URL
|
||||
|
||||
// callbacks to do things which are triggered by controls: reset the shape,
|
||||
// change the colors. Otherwise we just read stuff from gui.params.
|
||||
|
||||
function setColors(c) {
|
||||
const nc = get_colours(c);
|
||||
for( let i = 0; i < node_ms.length; i++ ) {
|
||||
node_ms[i].color = new THREE.Color(nc[i]);
|
||||
link_ms[i].color = new THREE.Color(nc[i]);
|
||||
}
|
||||
if( shape ) {
|
||||
// taperedLink.set_color updates according to the link index
|
||||
shape.links.map((l) => l.object.set_color(nc));
|
||||
}
|
||||
const nc = get_colours(c);
|
||||
for( let i = 0; i < node_ms.length; i++ ) {
|
||||
node_ms[i].color = new THREE.Color(nc[i]);
|
||||
link_ms[i].color = new THREE.Color(nc[i]);
|
||||
}
|
||||
material.color = new THREE.Color(c);
|
||||
}
|
||||
|
||||
function setBackground(c) {
|
||||
scene.background = new THREE.Color(c)
|
||||
}
|
||||
|
||||
// taperedLinks have their own materials so we have to set opacity
|
||||
// on them individually. And also set the base materials as they
|
||||
// will get updated from it when the shape changes
|
||||
|
||||
function setLinkOpacity(o, primary) {
|
||||
link_ms.map((lm) => lm.opacity = o);
|
||||
if( shape ) {
|
||||
shape.links.map((l) => {
|
||||
if( (primary && l.label == 0) || (!primary && l.label !== 0) ) {
|
||||
l.object.material.opacity = o
|
||||
}
|
||||
});
|
||||
}
|
||||
if( structure.nolink2opacity ) {
|
||||
link_ms.map((lm) => lm.opacity = o);
|
||||
} else {
|
||||
if( primary ) {
|
||||
link_ms[0].opacity = o;
|
||||
} else {
|
||||
link_ms.slice(1).map((lm) => lm.opacity = o);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
function setNodeOpacity(o) {
|
||||
node_ms.map((nm) => nm.opacity = o);
|
||||
}
|
||||
|
||||
|
||||
let gui;
|
||||
|
||||
|
||||
@ -196,8 +134,6 @@ function changeShape() {
|
||||
}
|
||||
|
||||
function setVisibility(option_name) {
|
||||
console.log("setVisibility", option_name);
|
||||
console.log(structure.options);
|
||||
const option = structure.options.filter((o) => o.name === option_name);
|
||||
if( option.length ) {
|
||||
node_show = option[0].nodes;
|
||||
@ -209,16 +145,12 @@ function setVisibility(option_name) {
|
||||
|
||||
|
||||
gui = new FourDGUI(
|
||||
{
|
||||
shapes: STRUCTURES,
|
||||
changeShape: changeShape,
|
||||
setColors: setColors,
|
||||
setBackground: setBackground,
|
||||
setNodeOpacity: setNodeOpacity,
|
||||
setLinkOpacity: setLinkOpacity,
|
||||
setVisibility: setVisibility,
|
||||
showDocs: showDocs,
|
||||
}
|
||||
STRUCTURES,
|
||||
changeShape,
|
||||
setColors,
|
||||
setBackground,
|
||||
setLinkOpacity,
|
||||
setVisibility
|
||||
);
|
||||
|
||||
// these are here to pick up colour settings from the URL params
|
||||
@ -284,8 +216,8 @@ function animate() {
|
||||
shape.hyperplane = 1 / gui.params.hyperplane;
|
||||
camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
|
||||
|
||||
shape.link_scale = gui.params.thickness;
|
||||
shape.node_scale = gui.params.nodesize;
|
||||
shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
|
||||
shape.render3(rotations, node_show, link_show);
|
||||
|
||||
|
||||
|
||||
60
polytopes.js
60
polytopes.js
@ -55,28 +55,8 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
|
||||
return links;
|
||||
}
|
||||
|
||||
|
||||
export const linkTest = () => {
|
||||
return {
|
||||
name: 'linky',
|
||||
nodes: [
|
||||
{ id:1, label: 1, x: -1, y: -1, z:-1, w: 0 },
|
||||
{ id:2, label: 2, x: 1, y: 1, z: 1, w: 0 },
|
||||
],
|
||||
links: [
|
||||
{ id: 1, source: 1, target: 2 }
|
||||
],
|
||||
options: [ { name: '--' }],
|
||||
description: `link`,
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
|
||||
// too small and simple to calculate
|
||||
|
||||
|
||||
|
||||
export const cell5 = () => {
|
||||
const c1 = Math.sqrt(5) / 4;
|
||||
return {
|
||||
@ -443,15 +423,6 @@ export const cell120_inscribed = () => {
|
||||
links.push(...links600);
|
||||
}
|
||||
|
||||
const CELL5S = CELLINDEX.CELL120_CELL5.cell5s;
|
||||
|
||||
for( const c5 in CELL5S ) {
|
||||
const nodes5 = nodes.filter((n) => CELL5S[c5].includes(n.id));
|
||||
const links5 = auto_detect_edges(nodes5, 5);
|
||||
links5.map((l) => l.label = 8);
|
||||
links.push(...links5);
|
||||
}
|
||||
|
||||
return {
|
||||
name: '120-cell',
|
||||
nodes: nodes,
|
||||
@ -459,44 +430,17 @@ export const cell120_inscribed = () => {
|
||||
options: [
|
||||
{ name: "none", links: [ 0 ]},
|
||||
{ name: "one inscribed 600-cell", links: [ 0, 1 ] },
|
||||
{ name: "five inscribed 600-cells", links: [ 0, 1, 2, 3, 4, 5 ] },
|
||||
{ name: "120 inscribed 5-cells", links: [ 0, 8 ] },
|
||||
{ name: "five inscribed 600-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
|
||||
],
|
||||
description: `The 120-cell is the four-dimensional analogue of the
|
||||
dodecahedron, and consists of 120 dodecahedra joined at 720 faces,
|
||||
with three dodecahedra around each edge. It is dual to the 600-cell,
|
||||
and five 600-cells can be inscribed in its vertices. The converse
|
||||
of this allows 120 5-cells (each of which has one vertex in each
|
||||
of the 5 600-cells) to be inscribed in the 120-cell.`,
|
||||
and five 600-cells can be inscribed in its vertices.`,
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
export const cell120_inscribed_cell5 = () => {
|
||||
const nodes = make_120cell_vertices();
|
||||
const links = auto_detect_edges(nodes, 4);
|
||||
|
||||
for( const cstr in CELLINDEX.INDEX120 ) {
|
||||
label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
|
||||
}
|
||||
|
||||
links.map((l) => l.label = 0);
|
||||
|
||||
|
||||
|
||||
|
||||
return {
|
||||
name: '120-cell-5-cell',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
options: [
|
||||
{ name: "5-cells", links: [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] },
|
||||
],
|
||||
description: `The 120-cell with one of its 5-cells.`,
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
function partition_coord(i, coords, invert) {
|
||||
|
||||
@ -1,66 +0,0 @@
|
||||
import * as THREE from 'three';
|
||||
|
||||
const EPSILON = 0.001;
|
||||
|
||||
class TaperedLink extends THREE.Group {
|
||||
|
||||
constructor(baseMaterial, color_i, n1, n2, r1, r2) {
|
||||
super();
|
||||
const geometry = new THREE.ConeGeometry( 1, 1, 16, true );
|
||||
const cplane = new THREE.Plane(new THREE.Vector3(0, -1, 0), 0.5);
|
||||
this.color_i = color_i;
|
||||
this.material = baseMaterial.clone();
|
||||
this.material.clippingPlanes = [ cplane ];
|
||||
this.object = new THREE.Mesh( geometry, this.material );
|
||||
this.add( this.object );
|
||||
this.update(n1, n2, r1, r2);
|
||||
}
|
||||
|
||||
update(n1, n2, r1, r2) {
|
||||
const kraw = r1 - r2;
|
||||
let k = ( Math.abs(kraw) < EPSILON ) ? EPSILON : kraw;
|
||||
let nbase = n1.v3;
|
||||
let napex = n2.v3;
|
||||
let rbase = r1;
|
||||
let rapex = r2;
|
||||
if( k < 0 ) {
|
||||
nbase = n2.v3;
|
||||
napex = n1.v3;
|
||||
rbase = r2;
|
||||
rapex = r1;
|
||||
k = -k;
|
||||
}
|
||||
|
||||
const l = nbase.distanceTo(napex);
|
||||
const lapex = l * rapex / k;
|
||||
const h = l + lapex;
|
||||
this.scale.copy(new THREE.Vector3(rbase, rbase, h));
|
||||
const h_offset = 0.5 * h / l;
|
||||
const pos = new THREE.Vector3();
|
||||
pos.lerpVectors(nbase, napex, h_offset);
|
||||
|
||||
this.position.copy(pos); // the group, not the cone!!
|
||||
|
||||
this.lookAt(nbase);
|
||||
this.children[0].rotation.x = 3 * Math.PI / 2.0;
|
||||
this.visible = true;
|
||||
const clipnorm = new THREE.Vector3();
|
||||
clipnorm.copy(napex);
|
||||
clipnorm.sub(nbase);
|
||||
clipnorm.negate();
|
||||
clipnorm.normalize();
|
||||
this.material.clippingPlanes[0].setFromNormalAndCoplanarPoint(
|
||||
clipnorm, napex
|
||||
);
|
||||
|
||||
|
||||
}
|
||||
|
||||
set_color(colors) {
|
||||
this.material.color = new THREE.Color(colors[this.color_i]);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
|
||||
export { TaperedLink };
|
||||
Loading…
x
Reference in New Issue
Block a user