Compare commits

..

No commits in common. "main" and "feature-faces" have entirely different histories.

17 changed files with 255 additions and 3513 deletions

View File

@ -1,137 +0,0 @@
// trying to go from faces to dodecahedra
function shared_vertices(f1, f2) {
return f1.nodes.filter((f) => f2.nodes.includes(f));
}
function adjacent_faces(f1, f2) {
// adjacent faces which share an edge, not just a vertex
const intersect = shared_vertices(f1, f2);
if( intersect.length < 2 ) {
return false;
}
if( intersect.length > 2 ) {
console.log(`warning: faces ${f1.id} and ${f2.id} have too many common vertices`);
}
return true;
}
function find_adjacent_faces(faces, face) {
const neighbours = faces.filter((f) => f.id !== face.id && adjacent_faces(f, face));
return neighbours;
}
function find_dodeca_mutuals(faces, f1, f2) {
// for any two adjacent faces, find their common neighbours where
// all three share exactly one vertex (this, I think, guarantees that
// all are on the same dodecahedron)
const n1 = find_adjacent_faces(faces, f1);
const n2 = find_adjacent_faces(faces, f2);
const common = n1.filter((f1) => n2.filter((f2) => f1.id === f2.id).length > 0 );
// there's one extra here - the third which has two nodes in common with
// both f1 and f2 - filter it out
const mutuals = common.filter((cf) => {
const shared = cf.nodes.filter((n) => f1.nodes.includes(n) && f2.nodes.includes(n));
return shared.length === 1
});
return mutuals;
}
function find_dodeca_next(faces, dodeca, f1, f2) {
// of a pair of mutuals, return the one we haven't already got
const m = find_dodeca_mutuals(faces, f1, f2);
if( dodeca.filter((f) => f.id === m[0].id ).length > 0 ) {
m.shift();
}
return m[0];
}
// from any two mutual faces, return all the faces in their dodecahedron
function make_dodecahedron(faces, f1, f2) {
const dodecahedron = [ f1, f2 ];
// take f1 as the 'center', get the other four around it from f2
const fs = find_dodeca_mutuals(faces, f1, f2);
const f3 = fs[0];
const f6 = fs[1];
dodecahedron.push(f3);
const f4 = find_dodeca_next(faces, dodecahedron, f1, f3);
dodecahedron.push(f4);
const f5 = find_dodeca_next(faces, dodecahedron, f1, f4);
dodecahedron.push(f5);
dodecahedron.push(f6);
// get the next ring
const f7 = find_dodeca_next(faces, dodecahedron, f6, f2);
dodecahedron.push(f7);
const f8 = find_dodeca_next(faces, dodecahedron, f2, f3);
dodecahedron.push(f8);
const f9 = find_dodeca_next(faces, dodecahedron, f3, f4);
dodecahedron.push(f9);
const f10 = find_dodeca_next(faces, dodecahedron, f4, f5);
dodecahedron.push(f10);
const f11 = find_dodeca_next(faces, dodecahedron, f5, f6);
dodecahedron.push(f11);
// get the last
const f12 = find_dodeca_next(faces, dodecahedron, f7, f8);
dodecahedron.push(f12);
return dodecahedron;
}
// for a face, pick an edge, and then find the other two faces which
// share this edge. These can be used as the starting points for the
// first face's two dodecahedra
function find_edge_neighbours(faces, face) {
const n1 = face.nodes[0];
const n2 = face.nodes[1];
return faces.filter((f) => f.id !== face.id && f.nodes.includes(n1) && f.nodes.includes(n2));
}
// each face is in two dodecahedra: this returns them both
function face_to_dodecahedra(faces, f) {
const edge_friends = find_edge_neighbours(faces, f);
const d1 = make_dodecahedron(faces, f, edge_friends[0]);
const d2 = make_dodecahedron(faces, f, edge_friends[1]);
return [ d1, d2 ];
}
// brute-force calculation of all dodecahedra
function dd_fingerprint(dodecahedron) {
const ids = dodecahedron.map((face) => face.id);
ids.sort()
return ids.join(',');
}
export function make_120cell_dodecahedra(faces) {
const dodecas = [];
const seen = {};
for( const face of faces ) {
const dds = face_to_dodecahedra(faces, face);
for( const dd of dds ) {
const fp = dd_fingerprint(dd);
if( ! (fp in seen) ) {
console.log(`added dodeca ${fp}`);
dodecas.push(dd);
seen[fp] = 1;
}
}
}
return dodecas;
}

View File

@ -1,188 +0,0 @@
export const LAYER_NAMES = {
0: "North pole",
1: "Arctic circle",
2: "North temperate",
3: "Tropic of Cancer",
4: "Equator",
5: "Tropic of Capricorn",
6: "South temperate",
7: "Antarctic circle (all)"
};
export const INDEX120 = {
"1": [
27,38,48,49,61,68,74,87,95,98,105,120, 126,131,140,149,156,165,174,
179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,
265,272,274,279,284,285,289,296,300,301,306,311,313,320,324,325,331,
334,339,342,347,350,356,357,362,367,369,376,378,383,388,389,393,400,
403,406,413,414,419,420,425,427,438,440,444,448,449,453,458,460,469,
471,473,474,487,488,490,494,499,503,511,512,513,514,525,527,530,532,
539,543,546,550,555,558,563,566,572,573,580,581,585,592,593,600
],
"2":[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,28,
30,31,34,35,37,40,41,44,46,47,50,51,53,56,57,60,62,63,66,67,69,72,73,
76,78,79,82,83,85,88,90,91,93,96,97,100,102,103,106,107,109,112,113,
116,118,119,122,123,125,128,129,132,134,135,138,139,141,144,145,148,
150,151,154,155,157,160,161,164,166,167,170,171,173,176,177,180,182,
183,186,187,189,192,193,196,198,199,202,203,205,208,209,212,214,215
],
"3":[
26,39,45,52,64,65,75,86,94,99,108,117,127,130,137,152,153,168,175,
178,188,197,206,211,219,222,227,230,235,238,244,245,251,254,257,264,
268,269,273,280,283,286,292,293,299,302,305,312,316,317,321,328,330,
335,338,343,348,349,355,358,363,366,370,375,377,384,385,392,394,399,
404,405,415,416,417,418,426,428,437,439,441,445,452,456,457,459,470,
472,475,476,485,486,491,495,498,502,509,510,515,516,526,528,529,531,
538,542,547,551,554,559,562,567,569,576,577,584,588,589,596,597
],
"4":[
32,33,43,54,58,71,77,84,92,101,110,115,121,136,143,146,159,162,169,
184,190,195,204,213,220,221,228,229,236,237,242,247,249,256,260,261,
266,271,276,277,281,288,290,295,297,304,308,309,315,318,322,327,329,
336,340,341,346,351,354,359,361,368,371,374,379,382,387,390,396,397,
401,408,409,410,423,424,430,432,433,435,443,447,450,454,461,463,466,
468,477,478,483,484,489,493,500,504,507,508,517,518,522,524,533,535,
540,544,545,549,553,560,561,568,570,575,578,583,587,590,595,598
],
"5":[
29,36,42,55,59,70,80,81,89,104,111,114,124,133,142,147,158,163,172,
181,191,194,201,216,217,224,225,232,233,240,243,246,250,255,259,262,
267,270,275,278,282,287,291,294,298,303,307,310,314,319,323,326,332,
333,337,344,345,352,353,360,364,365,372,373,380,381,386,391,395,398,
402,407,411,412,421,422,429,431,434,436,442,446,451,455,462,464,465,
467,479,480,481,482,492,496,497,501,505,506,519,520,521,523,534,536,
537,541,548,552,556,557,564,565,571,574,579,582,586,591,594,599
]
};
export const LAYERS120 = {
"0": [154,266,158,222,218,250,254,162,268,156,160,252,256,166,270,272,
164,220,224,168],
"1": [2,318,314,30,414,510,362,26,506,410,338,458,462,110,
106,6,350,346,34,482,418,474,330,442,450,98,90,14,
364,28,508,476,394,570,572,124,122,478,348,32,480,
512,396,576,574,126,128,8,352,38,422,486,334,454,
446,94,102,514,366,518,342,470,466,114,118,16,368,
36,484,516,398,580,578,130,132,412,316,420,332,452,
444,92,100,4,320,416,340,464,460,108,112,40,488,424,
336,448,456,104,96,520,400,582,584,136,134,344,468,472,120,116],
"2":[246,242,42,170,426,50,434,178,226,322,46,430,174,54,182,438,326,
230,78,558,526,62,494,542,590,142,74,554,386,300,298,202,290,206,
522,58,538,490,138,586,236,234,186,60,540,188,282,378,66,546,194,
68,196,548,382,286,498,82,562,530,146,594,76,556,204,80,208,560,
388,292,588,44,428,492,140,524,64,544,380,238,190,240,192,284,
592,496,432,48,528,144,70,198,550,72,552,200,288,384,502,534,566,
86,598,150,390,302,210,304,214,294,84,212,564,88,568,216,296,392,
596,500,436,52,532,148,324,244,172,248,180,228,176,56,440,184,232,
328,504,536,152,600],
"3":[369,273,275,371,17,353,257,261,357,9,401,305,306,402,21,307,308,
403,22,404,259,263,355,11,359,277,279,373,19,375,309,310,405,23,
406,258,262,354,10,358,274,276,370,18,372,356,260,264,360,12,407,
311,312,408,24,374,278,280,376,20],"4":[229,325,173,45,429,493,
141,525,589,289,385,557,77,205,201,137,521,553,73,585,285,381,
193,65,545,593,145,497,529,225,321,433,49,177,139,587,491,281,377,
539,59,187,283,379,189,61,541,197,287,199,237,239,191,293,389,213,
149,533,565,85,597,295,391,211,147,531,563,83,595,227,323,171,43,
427,523,151,503,535,231,327,439,55,183,599,383,551,71,87,215,567,
169,241,245,181,489,425,41,185,233,235,195,537,57,591,543,63,495,
143,549,69,501,179,499,435,51,175,431,47,527,203,291,387,555,75,
207,299,297,559,79,437,53,209,561,81,301,303,547,67,243,247],
"5":[457,337,461,105,109,469,341,465,117,113,89,97,441,449,329,93,445,
101,453,333,573,395,125,127,575,121,569,393,123,571,451,331,443,
99,91,129,577,131,579,397,107,459,111,339,463,95,447,335,103,455,
133,135,581,583,399,115,119,467,471,343
],
"6":[1,417,313,409,413,317,421,5,475,345,473,481,349,483,33,513,507,
13,363,511,7,487,351,485,37,517,15,519,367,515,3,423,319,415,39,
25,505,509,477,29,411,27,479,347,31,365,419,35,315,361
],
"7":[217,153,221,157,265,161,165,269,249,253,251,255,267,159,155,
163,219,271,223,167]
};
// Schoute's partition via https://arxiv.org/abs/1010.4353
export const PARTITION600 = {
"2,0,0,0": 1,
"0,2,0,0": 1,
"0,0,2,0": 1,
"0,0,0,2": 1,
"1,1,1,1": 1,
"1,1,-1,-1": 1,
"1,-1,1,-1": 1,
"1,-1,-1,1": 1,
"1,-1,-1,-1": 1,
"1,-1,1,1": 1,
"1,1,-1,1": 1,
"1,1,1,-1": 1,
"k,0,-t,-1": 2,
"0,k,1,-t": 2,
"t,-1,k,0": 2,
"1,t,0,k": 2,
"t,k,0,-1": 2,
"1,0,k,t": 2,
"k,-t,-1,0": 2,
"0,1,-t,k": 2,
"1,k,t,0": 2,
"t,0,-1,k": 2,
"0,t,-k,-1": 2,
"k,-1,0,-t": 2,
"t,0,1,k": 3,
"0,t,-k,1": 3,
"1,-k,-t,0": 3,
"k,1,0,-t": 3,
"0,k,1,t": 3,
"t,1,-k,0": 3,
"k,0,t,-1": 3,
"1,-t,0,k": 3,
"t,-k,0,-1": 3,
"0,1,-t,-k": 3,
"1,0,-k,t": 3,
"k,t,1,0": 3,
"t,0,-1,-k": 4,
"0,t,k,-1": 4,
"1,-k,t,0": 4,
"k,1,0,t": 4,
"t,1,k,0": 4,
"0,k,-1,-t": 4,
"1,-t,0,-k": 4,
"k,0,-t,1": 4,
"0,1,t,k": 4,
"t,-k,0,1": 4,
"k,t,-1,0": 4,
"1,0,k,-t": 4,
"k,0,t,1": 5,
"0,k,-1,t": 5,
"t,-1,-k,0": 5,
"1,t,0,-k": 5,
"1,0,-k,-t": 5,
"t,k,0,1": 5,
"0,1,t,-k": 5,
"k,-t,1,0": 5,
"t,0,1,-k": 5,
"1,k,-t,0": 5,
"k,-1,0,t": 5,
"0,t,k,1": 5
};
export const LAYERS600 = {
"0":[2,42,46,50,54,106,110,44,48,52,56,108,112],
"1":[10,12,14,16,18,20,22,24,34,36,38,40,98,102,100,104,90,92,94,96],
"2":[26,58,74,28,76,30,60,32,62,78,80,64],
"3":[3,4,5,6,7,8,65,113,81,66,114,82,67,115,83,68,116,84,69,117,85,70,118,86,71,119,87,72,120,88],
"4":[25,29,27,31,57,61,59,63,73,75,77,79],
"5":[97,101,99,103,33,35,37,39,89,91,93,95,9,11,13,15,17,19,21,23],
"6":[41,105,49,43,51,45,107,47,109,53,55,111],
"7":[1]
};

View File

@ -1,37 +0,0 @@
import ColorScheme from 'color-scheme';
import Color from 'color';
export const get_colours = (basis) => {
const basis_c = Color(basis);
const hslb = basis_c.hsl();
const hue = hslb['color'][0];
const saturation = hslb['color'][1];
const luminance = hslb['color'][2];
const scheme = new ColorScheme;
scheme.from_hue(hue).scheme("tetrade").distance(0.75);
const colours = scheme.colors().slice(1, 9);
colours.reverse();
const hsl = colours.map((c) => Color("#" + c).hsl());
const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber());
resaturated.unshift(basis);
return resaturated;
}
// basic colours where 0 = blue
// 1 - dark blue
// 2 - white
// 3 - light cyan
// 4 - light orange
// 5 - dark orange
export const get_plain_colours = (basis) => {
return [
basis,
0xffffff,
0x00ff00,
0xff0000,
0x0000ff,
0xff9900,
0x000000,
]
}

View File

@ -1,12 +0,0 @@
# Indexing manually ideas
- a list of all the faces (and maybe dodecahedra) which lets me assign
labels to them and lights up the interface
- where faces / vertices are repeated in the table, assigning a vertex in one
spot changes it everywhere else
separately - take the links generated by this codebase and apply them to
the d3.js forcemap code I wrote for the 24-cell

View File

@ -1,244 +0,0 @@
Steps forward -
1. algorithm which, given a face, finds the two dodecahedra it belongs to
2. using this, generate a list of all 120 dodecahedra:
1.
For a face: there are five edges, and ten other faces sharing an edge.
These edges are in two sets: one for each dodecahedron. The sets are defined
by them sharing vertices which aren't in the first face.
Go around a set of five, by pairs: for each pair, find the other neighbour -
this gives the next five faces.
There's only one face left, which is defined by the shared other vertices of
the last five.
2. have tried manual labelling and it will drive me crazy before I finish
3. Automated approach based on what I've got so far:
- should be possible to colour a single dodecahedron from a single face and
one other vertex (to pick a chirality)
- write a function to do this - the compound-of-four-tetrahedra map can be
more or less hard coded: follow the pattern 1-2-3-4-5, 3-4-5-1-2, etc out
from the inner ring, and map the original face's permutation
From this:
- colour the first dodecahedron, picking a chirality
- the next vertices from each of this dodecahedron's vertices have colours
which come from the first dodeca
- these can be used to colour the next layer of dodecahedra
- and so on
Alternatively:
- do it by the discrete Hopf fibration, one fibre at a time
/// old shit below that didn't work VVVV
Chords: 1.74806 - the 120-cell has 7200 chords of this length
Looking for a way to partition the 600 vertices of the 120 cell into five
disjoint 600-cells, each of which has 120 vertices.
(there are 10 such 600-cells so two ways to do the partition I guess)
a 600-cell has 720 edges! optimistically this means that each chord in the
collection of 7200 belongs to one and only one of the 600-cells.
the way forward:
I need to take the 7200 chords (pairs of nodes) and divide them into sets
which are connected to one another - with any luck, each of these will be
one of the 10 600-cells
Then need to sort these 10 sets of 120 vertices into the two sets of 5
collate chords by node
Each 120-cell vertex has 24 of the chord3s from it - as a 600-cell has 12
edges to each vertex, this suggests that each 120-vertex belongs to two
600-cells with a disjoint set of vertices
Next algorithm - gather each 600-cell
use the chords as the basis for this.
n1 -> 24 chords -> add these 24 neighbours
bad luck - traversing chord3s from the first vertex reaches all 600 vertices-
which isn't suprising as the two 5 disjoint sets overlap. Sigh.
Use the angles between the chords? seems a bit complex
Get the angles from the 600-cell model. Use these to separate out the sets of
24 chords from a point on the 120-cell.
Notes from dinner:
- all of the 60-degree angles are chords joining the vertices of the tetrahedra
- there should be two sets of these
for eg - this works for the chords from 1!
[ 25, 41 ],
[ 25, 97 ],
[ 25, 109 ],
[ 25, 157 ],
[ 25, 161 ],
[ 41, 97 ],
[ 41, 109 ],
[ 41, 173 ],
[ 41, 177 ],
[ 97, 113 ],
[ 97, 161 ],
[ 97, 177 ],
[ 37, 53 ],
[ 37, 93 ],
[ 37, 113 ],
[ 37, 157 ],
[ 37, 161 ],
[ 53, 93 ],
[ 53, 113 ],
[ 53, 173 ],
[ 53, 177 ],
[ 173, 177 ]
[ 93, 109 ],
[ 93, 157 ],
[ 93, 173 ],
[ 109, 157 ],
[ 109, 173 ],
[ 113, 161 ],
[ 113, 177 ],
[ 157, 161 ],
[ 29, 45 ], 5
[ 29, 101 ], 101
[ 29, 105 ], 105
[ 29, 153 ], 153
[ 29, 165 ], 165
[ 45, 101 ],
[ 45, 105 ],
[ 45, 169 ], 169
[ 45, 181 ], 181
[ 101, 117 ], 117
[ 101, 165 ],
[ 101, 181 ],
[ 105, 153 ],
[ 105, 169 ],
[ 33, 49 ], 33 49
[ 33, 89 ], 89
[ 33, 117 ],
[ 33, 153 ],
[ 33, 165 ],
[ 49, 89 ],
[ 49, 117 ],
[ 49, 169 ],
[ 49, 181 ],
[ 169, 181 ],
[ 89, 105 ],
[ 89, 153 ],
[ 89, 169 ],
[ 117, 165 ],
[ 117, 181 ],
[ 153, 165 ],
So each of these is one of the two icosahedral pyramids from node 1.
Doing this manually for the rest of the partition is possible, but could it
be automated based on angles?
Plan for Sunday:
* use the existing label_subgraph to make a function which partitions the
60-angle chords into two groups (like I did manually above)
// this is done and seems to work
* test this labelling manually (ie colour one set of 60-angle vertices)
// done this with the manual labels and it looks good
* make another labeling routine which can fill out the rest of the 600-cell
from the starting dodecahedron, by only following chords which are at 60
to the entering chord
Then the big algorithm does the following:
- start from node 1, find 60-angles, pick one partition at random, label that 600-cell
- find the next unlabelled node
- find 60-angles, partition them, pick a partition with no unlabelled cells and label that 600-cell
- repeat the previous step for the remaining three 600-cells
Alternative, more manual option: just write the second labelling routine and
do the rest by hand
[ 25, 41 ],
[ 25, 97 ],
[ 25, 109 ],
[ 25, 157 ],
[ 25, 161 ],
[ 41, 97 ],
[ 41, 109 ],
[ 41, 173 ],
[ 41, 177 ],
[ 97, 113 ],
[ 97, 161 ],
[ 97, 177 ],
[ 37, 53 ],
[ 37, 93 ],
[ 37, 113 ],
[ 37, 157 ],
[ 37, 161 ],
[ 53, 93 ],
[ 53, 113 ],
[ 53, 173 ],
[ 53, 177 ],
[ 173, 177 ]
[ 93, 109 ],
[ 93, 157 ],
[ 93, 173 ],
[ 109, 157 ],
[ 109, 173 ],
[ 113, 161 ],
[ 113, 177 ],
[ 157, 161 ],
25 41 97 109
157 161 173 177
113 37 53 93
Another idea - look at colouring the vertices of a dodecahedron according to
the four compound tetrahedra and see if this can be repeated automatically to
neighbouring cells

View File

@ -1,8 +1,8 @@
import * as THREE from 'three';
const HYPERPLANE = 2.0;
const W_FORESHORTENING = 0.04;
const HYPERPLANE = 2;
class FourDShape extends THREE.Group {
@ -15,10 +15,10 @@ class FourDShape extends THREE.Group {
this.nodes3 = {};
this.links = structure.links;
this.faces = ( "faces" in structure ) ? structure.faces : [];
this.node_scale = 1;
this.link_scale = 1;
this.node_size = structure.geometry.node_size;
this.link_size = structure.geometry.link_size;
this.geom_scale = 1;
this.hyperplane = HYPERPLANE;
this.foreshortening = W_FORESHORTENING;
this.initShapes();
}
@ -34,7 +34,7 @@ class FourDShape extends THREE.Group {
}
}
makeNode(material, v3, scale) {
makeNode(material, v3) {
const geometry = new THREE.SphereGeometry(this.node_size);
const sphere = new THREE.Mesh(geometry, material);
sphere.position.copy(v3);
@ -43,45 +43,33 @@ class FourDShape extends THREE.Group {
}
makeLink(material, link) {
const n1 = this.nodes3[link.source];
const n2 = this.nodes3[link.target];
const s1 = n1.scale;
const s2 = n2.scale;
const length = n1.v3.distanceTo(n2.v3);
const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target].v3;
const length = n1.distanceTo(n2);
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,
16, 1, true
);
centre.lerpVectors(n1, n2, 0.5);
const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 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);
edge.lookAt(n2);
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 = n1.scale;
const s2 = n2.scale;
const length = n1.v3.distanceTo(n2.v3);
updateLink(link) {
const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target].v3;
const length = n1.distanceTo(n2);
const centre = new THREE.Vector3();
centre.lerpVectors(n1.v3, n2.v3, 0.5);
// take the average of the ends as the thickness - as a workaround,
// because I haven't worked out how to reshape tapered links without
// having to reassign a new geometry to every link
const link_mean = this.link_scale * (s1 + s2) * 0.5;
link.object.scale.copy(new THREE.Vector3(link_mean, link_mean, length));
centre.lerpVectors(n1, n2, 0.5);
link.object.scale.copy(new THREE.Vector3(this.geom_scale, this.geom_scale, length));
link.object.position.copy(centre);
link.object.lookAt(n2.v3);
link.object.lookAt(n2);
link.object.children[0].rotation.x = Math.PI / 2.0;
link.object.visible = (!links_show || link.label in links_show);
}
@ -110,42 +98,23 @@ class FourDShape extends THREE.Group {
}
fourDtoV3_old(x, y, z, w, rotations) {
fourDtoV3(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);
const k = this.hyperplane / (this.hyperplane + v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
fourDscale(w) {
return this.hyperplane / ( this.hyperplane + w );
}
fourDrotate(x, y, z, w, rotations) {
const v4 = new THREE.Vector4(x, y, z, w);
for ( const m4 of rotations ) {
v4.applyMatrix4(m4);
}
return v4;
}
fourDtoV3(v4) {
const k = this.fourDscale(v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
initShapes() {
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 v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
const material = this.getMaterial(n, this.node_ms);
this.nodes3[n.id] = {
v3: v3,
scale: k,
label: n.label,
object: this.makeNode(material, v3, k)
object: this.makeNode(material, v3)
};
}
for( const l of this.links ) {
@ -159,22 +128,17 @@ class FourDShape extends THREE.Group {
}
render3(rotations, nodes_show, links_show) {
this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
render3(rotations) {
this.scalev3 = new THREE.Vector3(this.geom_scale, this.geom_scale, this.geom_scale);
for( const n of this.nodes4 ) {
const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
const k = this.fourDscale(v4.w);
const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
const s4 = k * this.node_scale * this.foreshortening;
const s3 = new THREE.Vector3(s4, s4, s4);
const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
this.nodes3[n.id].v3 = v3;
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 || n.label in nodes_show );
this.nodes3[n.id].object.scale.copy(this.scalev3);
}
for( const l of this.links ) {
this.updateLink(l, links_show);
this.updateLink(l);
}
for( const f of this.faces ) {
@ -182,6 +146,7 @@ class FourDShape extends THREE.Group {
}
}
}
export { FourDShape };

145
gui.js
View File

@ -1,107 +1,49 @@
import { GUI } from 'lil-gui';
const DEFAULTS = {
nodesize: 0.25,
nodeopacity: 1,
linksize: 0.2,
linkopacity: 0.75,
link2opacity: 0.75,
shape: '120-cell',
option: 'none',
visibility: 5,
inscribed: false,
inscribe_all: false,
color: 0x3293a9,
background: 0xd4d4d4,
hyperplane: 0.93,
zoom: 1,
xRotate: 'YW',
yRotate: 'XW',
dtheta: 0,
damping: false,
captions: true,
dpsi: 0,
}
const DEFAULT_SHAPE = '120-cell';
const DEFAULT_COLOR = 0x3293a9;
const DEFAULT_BG = 0x808080;
class FourDGUI {
constructor(shapes, changeShape, setColor, setBackground, setNodeOpacity,setLinkOpacity, setVisibility, showDocs) {
constructor(createShape, setColor, setBackground) {
this.gui = new GUI();
const SHAPE_NAMES = shapes.map((s) => s.name);
this.parseLinkParams();
const guiObj = this;
this.params = {
shape: this.link['shape'],
option: this.link['option'],
inscribed: this.link['inscribed'],
inscribe_all: this.link['inscribe_all'],
linksize: this.link['linksize'],
linkopacity: this.link['linkopacity'],
link2opacity: this.link['linkopacity'],
nodesize: this.link['nodesize'],
nodeopacity: this.link['nodeopacity'],
depth: this.link['depth'],
color: this.link['color'],
background: this.link['background'],
hyperplane: this.link['hyperplane'],
zoom: this.link['zoom'],
xRotate: this.link['xRotate'],
yRotate: this.link['yRotate'],
shape: this.link['shape'] || DEFAULT_SHAPE,
thickness: this.link['thickness'] || 1,
color: this.link['color'] || DEFAULT_COLOR,
background: this.link['background'] || DEFAULT_BG,
hyperplane: this.link['hyperplane'] || 2,
xRotate: this.link['xRotate'] || 'YW',
yRotate: this.link['yRotate'] || 'XZ',
damping: false,
captions: true,
dtheta: this.link['dtheta'],
dpsi: this.link['dpsi'],
dtheta: this.link['dtheta'] || 0,
dpsi: this.link['dpsi'] || 0,
"copy link": function () { guiObj.copyUrl() }
};
let options_ctrl;
this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
const options = this.getShapeOptions(shapes, shape);
options_ctrl = options_ctrl.options(options).onChange((option) => {
setVisibility(option)
});
options_ctrl.setValue(options[0])
changeShape(shape)
});
const options = this.getShapeOptions(shapes, this.params['shape']);
options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((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);
this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
this.gui.add(this.params, 'linksize', 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, 'shape',
[ '5-cell', '16-cell', 'tesseract', '24-cell', '120-cell', '600-cell' ]
).onChange(createShape)
this.gui.add(this.params, 'hyperplane', 1.5, 4);
this.gui.add(this.params, 'thickness', 0.1, 4);
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(showDocs);
this.gui.add(this.params, 'damping');
this.gui.add(this.params, 'copy link');
}
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 {
return [];
}
}
numParam(param, parser) {
numParam(param, parser, dft) {
const value = this.urlParams.get(param);
if( value ) {
const n = parser(value);
@ -109,7 +51,7 @@ class FourDGUI {
return n;
}
}
return DEFAULTS[param];
return dft;
}
stringToHex(cstr) {
@ -125,49 +67,36 @@ class FourDGUI {
parseLinkParams() {
this.linkUrl = new URL(window.location.toLocaleString());
this.link = {};
const guiObj = this;
this.urlParams = this.linkUrl.searchParams;
for( const param of [ "shape", "xRotate", "yRotate", "option" ]) {
for( const param of [ "shape", "xRotate", "yRotate" ]) {
const value = this.urlParams.get(param);
if( value ) {
this.link[param] = value;
} else {
this.link[param] = DEFAULTS[param];
}
}
for( const param of [ "inscribed", "inscribe_all"] ) {
this.link[param] = ( this.urlParams.get(param) === 'y' );
}
this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
this.link['zoom'] = this.numParam('zoom', parseFloat);
this.link['linksize'] = this.numParam('linksize', 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);
this.link['dtheta'] = this.numParam('dtheta', parseFloat);
const guiObj = this;
this.link['hyperplane'] = this.numParam('hyperplane', parseFloat, 2);
this.link['thickness'] = this.numParam('thickness', parseFloat, 1);
this.link['color'] = this.numParam(
'color', (s) => guiObj.stringToHex(s), DEFAULT_COLOR
);
this.link['background'] = this.numParam(
'background', (s) => guiObj.stringToHex(s), DEFAULT_BG
);
this.link['dpsi'] = this.numParam('dpsi', parseFloat, 0);
this.link['dtheta'] = this.numParam('dtheta', parseFloat, 0);
}
copyUrl() {
const url = new URL(this.linkUrl.origin + this.linkUrl.pathname);
url.searchParams.append("shape", this.params.shape);
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("nodesize", this.params.nodesize.toString());
url.searchParams.append("nodeopacity", this.params.nodesize.toString());
url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
url.searchParams.append("link2opacity", this.params.link2opacity.toString());
url.searchParams.append("thickness", this.params.thickness.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());
url.searchParams.append("zoom", this.params.zoom.toString());
url.searchParams.append("xRotate", this.params.xRotate);
url.searchParams.append("yRotate", this.params.yRotate);
url.searchParams.append("dtheta", this.params.dtheta.toString());
@ -217,4 +146,4 @@ class FourDGUI {
}
export { FourDGUI, DEFAULTS };
export { FourDGUI };

View File

@ -5,28 +5,9 @@
<title>FourD</title>
<style>
body { margin: 0; }
div#description {
position: fixed;
top: 0;
left: 0;
width: 20%;
z-index: 2;
font-family: sans-serif;
padding: 1em;
}
div#info {
position: fixed;
bottom:0;
right: 0;
z-index: 2;
border:0.5em;
font-family: sans-serif }
</style>
</head>
<body>
<script type="module" src="/main.js"></script>
<div id="description"></div>
<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>

View File

@ -1,294 +0,0 @@
// bad stuff
function find_chords(chords, n) {
return chords.filter((c) => c[0].id === n.id || c[1].id === n.id);
}
function find_neighbours(chords, n) {
const c = find_chords(chords, n);
return c.map((c) => c[0].id === n.id ? c[1] : c[0])
}
// for a list of pairs [n1, n2] (these are nodes which share a common angle
// from a center), find all the groups of nodes which don't appear in a pair
// together
function partition_nodes(pairs) {
let groups = [];
const seen = new Set();
for( const pair of pairs ) {
// both nodes are in a group already
if( seen.has(pair[0]) && seen.has(pair[1]) ) {
continue;
}
let already = false;
// check if either node is already in a group
for( const group of groups ) {
if( group.has(pair[0]) ) {
group.add(pair[1]);
seen.add(pair[1]);
already = true;
continue;
} else if( group.has(pair[1]) ) {
group.has(pair[0]);
seen.has(pair[0]);
already = true;
continue;
}
}
// if neither of the pair was in a former group, start a new group
if( !already ) {
groups.push(new Set(pair));
}
// collapse any groups which now have common elements
groups = collapse_groups(groups);
}
return groups;
}
// given a list of groups, if any have common elements, collapse them
function collapse_groups(groups) {
const new_groups = [ ];
for( group of groups ) {
let collapsed = false;
for( new_group of new_groups ) {
const i = intersection(group, new_group);
if( i.size > 0 ) {
for( const e of group ) {
new_group.add(e);
}
collapsed = true;
break;
}
}
if( !collapsed ) {
new_groups.push(new Set(group));
}
}
return new_groups;
}
function intersection(s1, s2) {
const i = new Set();
for( const e of s1 ) {
if( s2.has(e) ) {
i.add(e)
}
}
return i;
}
function union(s1, s2) {
const u = new Set(s1);
for( const e of s2 ) {
u.add(e);
}
return u;
}
function vector_angle(n1, n2, n3) {
const v1 = new THREE.Vector4(n1.x, n1.y, n1.z, n1.w);
const v2 = new THREE.Vector4(n2.x, n2.y, n2.z, n2.w);
const v3 = new THREE.Vector4(n3.x, n3.y, n3.z, n3.w);
v2.sub(v1);
v3.sub(v1);
const dp = v2.dot(v3);
return Math.acos(dp / ( v2.length() * v3.length()));
}
function neighbour_angles_orig(chords, n) {
const ns = find_neighbours(chords, n);
const angles = {};
for( let i = 0; i < ns.length - 1; i++ ) {
for( let j = i + 1; j < ns.length; j++ ) {
const n2 = ns[i];
const n3 = ns[j];
const a = THREE.MathUtils.radToDeg(vector_angle(n, n2, n3));
const af = (a).toFixed(3);
if( ! (af in angles) ) {
angles[af] = [];
}
angles[af].push([n2.id, n3.id]);
}
}
return angles;
}
function neighbour_angles(chords, n, angle) {
const ns = find_neighbours(chords, n);
const pairs = [];
for( let i = 0; i < ns.length - 1; i++ ) {
for( let j = i + 1; j < ns.length; j++ ) {
const n2 = ns[i];
const n3 = ns[j];
const a = THREE.MathUtils.radToDeg(vector_angle(n, n2, n3));
const af = (a).toFixed(3);
if( af === angle ) {
pairs.push([n2.id, n3.id]);
}
}
}
return pairs;
}
function make_120_partition(nodes, n) {
const chords = find_all_chords(nodes);
const chord3 = chords["1.74806"]; // these are edges of the 600-cells;
const pairs60 = neighbour_angles(chord3, n, "60.000");
const icosas = partition_nodes(pairs60);
n.label = 1;
const angles = icosa_nodes(nodes, icosas[0]);
label_120_partition_r(nodes, chord3, 1, n, angles);
}
// recursive function to label a single 600-cell vertex partition of the
// 120-cell by following icosahedral nets
// this doesn't work! completely - labels only 108-112
function label_120_partition_r(nodes, chords, label, origin, neighbours) {
console.log(`label_120_partition_r ${origin.id}`);
console.log(neighbours.map((n) => n.id).join(', '));
// first try to label everything
const unlabelled = [];
for( const n of neighbours ) {
if( n.label === 0 ) {
console.log(`Labelled ${n.id} ${label}`);
n.label = label;
unlabelled.push(n);
} else if( n.label !== label ) {
console.log(`node ${n.id} is already in group ${n.label}`);
//return false;
}
}
for( const n of unlabelled ) {
// the angles represent two icosahedral pyramids - partition them and
// pick the one which is at 60 to the edge we arrived on
//console.log(`looking for more neighbors for ${n}`);
const pairs60 = neighbour_angles(chords, n, "60.000");
const icosas = partition_nodes(pairs60);
const icosa = choose_icosa(nodes, origin, n, icosas);
const icosa_n = icosa_nodes(nodes, icosa);
console.log(`recursing to ${nice_icosa(nodes,icosa)}`);
return label_120_partition_r(nodes, chords, label, n, icosa_n);
}
}
// given a pair of icosa-sets, pick the one which is at the right angle to
// the incoming vector
function choose_icosa(nodes, origin, n1, icosas) {
for( const icosa of icosas ) {
const inodes = icosa_nodes(nodes, icosa);
const a60 = inodes.map((ni) => {
const a = THREE.MathUtils.radToDeg(vector_angle(n1, origin, ni));
return a.toFixed(3);
});
if( a60.filter((a) => a === "60.000").length > 0 ) {
return icosa;
}
}
console.log("No icosa found!");
return undefined;
}
function icosa_nodes(nodes, icosa) {
return Array.from(icosa).map((nid) => node_by_id(nodes, nid)).sort((a, b) => a.id - b.id);
}
function node_by_id(nodes, nid) {
const ns = nodes.filter((n) => n.id === nid);
return ns[0];
}
function enumerate_icosas(nodes) {
const chords = find_all_chords(nodes);
const chord3 = chords["1.74806"]; // these are edges of the 600-cells;
for( const n of nodes ) {
const pairs60 = neighbour_angles(chord3, n, "60.000");
const icosas = partition_nodes(pairs60);
for( const icosa of icosas ) {
const inodes = icosa_nodes(nodes, icosa);
console.log(icosa_to_csv(n.id, inodes).join(','));
}
}
}
function icosa_to_csv(nid, icosa) {
const cols = [ nid ];
const ia = icosa.map((n) => n.id);
for( let i = 1; i < 601; i++ ) {
if( ia.includes(i) ) {
cols.push(i);
} else {
cols.push('')
}
}
return cols;
}
function start_icosas(nodes, chords, origin) {
const pairs60 = neighbour_angles(chords, origin, "60.000");
return partition_nodes(pairs60).map((i) => nice_icosa(nodes, i));
}
function next_icosa(nodes, chords, origin, nid) {
const n = node_by_id(nodes, nid);
const pairs60 = neighbour_angles(chords, n, "60.000");
const icosas = partition_nodes(pairs60);
const icosa = choose_icosa(nodes, origin, n, icosas);
return nice_icosa(nodes, icosa);
}
function nice_icosa(nodes, icosa) {
return icosa_nodes(nodes, icosa).map((n) => n.id).join(', ');
}
function find_by_chord(nodesid, n, d) {
const EPSILON = 0.02;
return Object.keys(nodesid).filter((n1) => {
const d2 = dist2(nodesid[n1], nodesid[n]);
return Math.abs(d2 - d ** 2) < EPSILON;
});
}
function has_chord(n1, n2, d) {
const d2 = dist2(n1, n2);
const EPSILON = 0.01;
return Math.abs(d2 - d ** 2) < EPSILON;
}
function find_all_chords(nodes) {
const chords = {};
for( let i = 0; i < nodes.length - 1; i++ ) {
for( let j = i + 1; j < nodes.length; j++ ) {
const n1 = nodes[i];
const n2 = nodes[j];
const chord = Math.sqrt(dist2(n1, n2)).toFixed(5);
if( !(chord in chords) ) {
chords[chord] = [];
}
chords[chord].push([n1, n2]);
}
}
return chords;
}

View File

@ -1,78 +0,0 @@
// New approach with tetrahedral coloring
function find_edges(links, nid) {
return links.filter((l) => l.source === nid || l.target === nid );
}
function find_adjacent(links, nid) {
return find_edges(links, nid).map((l) => {
if( l.source === nid ) {
return l.target;
} else {
return l.source;
}
});
}
function iterate_graph(nodes, links, n, fn) {
const queue = [];
const seen = {};
const nodes_id = {};
nodes.map((n) => nodes_id[n.id] = n);
queue.push(n.id);
seen[n.id] = true;
fn(n);
while( queue.length > 0 ) {
const v = queue.shift();
find_adjacent(links, v).map((aid) => {
if( !(aid in seen) ) {
seen[aid] = true;
queue.push(aid);
fn(nodes_id[aid]);
}
})
}
}
// stupid tetrahedral labelling
// keeps getting stuck
function naive_label_120cell(nodes, links, n) {
const nodes_id = {};
nodes.map((n) => nodes_id[n.id] = n);
iterate_graph(nodes, links, nodes[0], (n) => {
const cols = new Set();
const nbors = find_adjacent(links, n.id);
for( const nb of nbors ) {
if( nodes_id[nb].label > 0 ) {
cols.add(nodes_id[nb].label);
}
for( const nb2 of find_adjacent(links, nb) ) {
if( nb2 !== n.id && nodes_id[nb].label > 0 ) {
cols.add(nodes_id[nb2].label);
}
}
}
const pcols = [ 1, 2, 3, 4, 5 ].filter((c) => !cols.has(c));
if( pcols.length < 1 ) {
console.log(`Got stuck, no options at ${n.id}`);
return false;
} else {
n.label = pcols[0];
console.log(`found ${pcols.length} colors for node ${n.id}`);
console.log(`applied ${pcols[0]} to node ${n.id}`);
return true;
}
});
}

File diff suppressed because it is too large Load Diff

View File

@ -1,173 +0,0 @@
import * as POLYTOPES from './polytopes.js';
// face detection for the 600-cell
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 make_600cell() {
const nodes = POLYTOPES.make_600cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 12);
return {
nodes: nodes,
links: links
}
}
export function link_to_tetras(nodes, links, link) {
const n1 = link.source;
const n2 = link.target;
const nl1 = nodes_links(links, n1).filter((l) => l.id !== link.id);
const nl2 = nodes_links(links, n2).filter((l) => l.id !== link.id);
const p1 = new Set();
const p = new Set();
for( const nl of nl1 ) {
if( nl.source !== n1 ) {
p1.add(nl.source);
}
if( nl.target !== n1 ) {
p1.add(nl.target);
}
}
for( const nl of nl2 ) {
if( nl.source !== n2 && p1.has(nl.source) ) {
p.add(nl.source);
}
if( nl.target !== n2 && p1.has(nl.target) ) {
p.add(nl.target);
}
}
const lp = Array.from(p);
const seen = {};
const tetras = [];
for( const p1 of lp ) {
for( const p2 of lp ) {
if( p1 != p2 ) {
if( linked(links, p1, p2) ) {
const fp = fingerprint([n1, n2, p1, p2]);
if( !seen[fp] ) {
seen[fp] = true;
tetras.push({fingerprint: fp, nodes: [n1, n2, p1, p2]})
}
}
}
}
}
return tetras;
}
export function auto_600cell_cells(nodes, links) {
const seen = {};
const tetras = [];
links.map((link) => {
link_to_tetras(nodes, links, link).map((lt) => {
if( !seen[lt.fingerprint] ) {
seen[lt.fingerprint] = true;
tetras.push(lt.nodes);
}
})
});
return tetras;
}
function node_by_id(nodes, nid) {
const ns = nodes.filter((n) => n.id === nid);
return ns[0];
}
export function tetra_w(nodes, tetra) {
let w = 0;
for( const nid of tetra ) {
const node = node_by_id(nodes, nid);
w += node.w;
}
return w / 4;
}
export function sorted_600cells() {
const cell600 = make_600cell();
const tetras = auto_600cell_cells(cell600.nodes, cell600.links);
const layers = tetras.map((t) => { return { "nodes": t, w: tetra_w(cell600.nodes, t) } });
layers.sort((a, b) => b.w - a.w);
return layers;
}
// const cell600 = make_600cell();
// const layers = sorted_600cells(cell600.nodes, cell600.links);
// for( const cell of layers ) {
// // const fp = fingerprint(cell.nodes);
// console.log(`${cell.w} ${cell.nodes}`);
// }
export function make_layered_600cell() {
const tetras = sorted_600cells()
const LAYERS = [
[ "00", 20 ],
[ "01", 20 ],
[ "02", 30 ],
[ "03", 60 ],
[ "04", 60 ],
[ "05", 60 ],
[ "06", 20 ],
[ "07", 60 ],
[ "08", 20 ],
[ "09", 60 ],
[ "10", 60 ],
[ "11", 60 ],
[ "12", 30 ],
[ "13", 20 ],
[ "14", 20 ]
];
const vertices = {};
const seen = {};
let i = 0;
for( const layer of LAYERS ) {
const label = layer[0];
const n = layer[1];
vertices[label] = [];
console.log(`Layer ${label} starting at ${i}`);
for( const t of tetras.slice(i, i + n) ) {
console.log(t);
for( const n of t.nodes ) {
if( !seen[n] ) {
vertices[label].push(n);
seen[n] = true;
}
}
}
i += n;
}
return JSON.stringify(vertices);
}

160
main.js
View File

@ -4,12 +4,10 @@ import * as THREE from 'three';
import * as POLYTOPES from './polytopes.js';
import { rotfn } from './rotation.js';
import { FourDGUI, DEFAULTS } from './gui.js';
import { FourDGUI } from './gui.js';
import { FourDShape } from './fourDShape.js';
import { get_colours } from './colours.js';
const FACE_OPACITY = 0.3;
const CAMERA_K = 5;
// scene, lights and camera
@ -24,10 +22,7 @@ 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 = 4;
camera.position.z = 4;
const renderer = new THREE.WebGLRenderer({antialias: true});
renderer.setSize( window.innerWidth, window.innerHeight );
@ -35,30 +30,12 @@ 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);
scene.background = new THREE.Color(0x808080);
const material = new THREE.MeshStandardMaterial({ color: 0x3293a9 });
const node_ms = [ material ];
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;
}
);
const link_ms = [ material ];
const face_ms = [
@ -71,46 +48,24 @@ for( const face_m of face_ms ) {
}
const STRUCTURES = POLYTOPES.build_all();
const STRUCTURES_BY_NAME = {};
STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s);
const STRUCTURES = {
'5-cell': POLYTOPES.cell5(),
'16-cell': POLYTOPES.cell16(),
'tesseract': POLYTOPES.tesseract(),
'24-cell': POLYTOPES.cell24(),
'120-cell': POLYTOPES.cell120(),
'600-cell': POLYTOPES.cell600()
};
let shape = false;
let structure = false;
let node_show = [];
let link_show = [];
function createShape(name, option) {
function createShape(name) {
if( shape ) {
scene.remove(shape);
}
structure = STRUCTURES_BY_NAME[name];
shape = new FourDShape(node_ms, link_ms, face_ms, structure);
console.log(STRUCTURES[name]);
shape = new FourDShape(node_ms, link_ms, face_ms, STRUCTURES[name]);
scene.add(shape);
setVisibility(option ? option : structure.options[0].name);
}
function displayDocs(name) {
const docdiv = document.getElementById("description");
const description = STRUCTURES_BY_NAME[name].description;
if( description ) {
docdiv.innerHTML =`<p>${name}</p><p>${description}</p>`;
} else {
docdiv.innerHTML =`<p>${name}</p>`;
}
}
function showDocs(visible) {
console.log(`showDocs ${visible}`);
const docdiv = document.getElementById("description");
if( visible ) {
docdiv.style.display = '';
} else {
docdiv.style.display = 'none';
}
}
// initialise gui and read params from URL
@ -118,69 +73,14 @@ function showDocs(visible) {
// callbacks to do things which are triggered by controls: reset the shape,
// change the colors. Otherwise we just read stuff from gui.params.
function setColors(c) {
const nc = get_colours(c);
for( let i = 0; i < node_ms.length; i++ ) {
node_ms[i].color = new THREE.Color(nc[i]);
link_ms[i].color = new THREE.Color(nc[i]);
}
material.color = new THREE.Color(c);
}
function setBackground(c) {
scene.background = new THREE.Color(c)
}
function setLinkOpacity(o, primary) {
if( structure.nolink2opacity ) {
link_ms.map((lm) => lm.opacity = o);
} else {
if( primary ) {
link_ms[0].opacity = o;
} else {
link_ms.slice(1).map((lm) => lm.opacity = o);
}
}
}
function setNodeOpacity(o) {
node_ms.map((nm) => nm.opacity = o);
}
let gui;
function changeShape() {
createShape(gui.params.shape);
displayDocs(gui.params.shape);
}
function setVisibility(option_name) {
const option = structure.options.filter((o) => o.name === option_name);
if( option.length ) {
node_show = option[0].nodes;
link_show = option[0].links;
} else {
console.log(`Error: option '${option_name}' not found`);
}
}
gui = new FourDGUI(
STRUCTURES,
changeShape,
setColors,
setBackground,
setNodeOpacity,
setLinkOpacity,
setVisibility,
showDocs
const gui = new FourDGUI(
createShape,
(c) => { material.color = new THREE.Color(c) },
(c) => { scene.background = new THREE.Color(c) },
);
// these are here to pick up colour settings from the URL params
setColors(gui.params.color);
setBackground(gui.params.background);
material.color = new THREE.Color(gui.params.color);
scene.background = new THREE.Color(gui.params.background);
const dragK = 0.005;
const damping = 0.99;
@ -219,8 +119,7 @@ renderer.domElement.addEventListener("pointerup", (event) => {
dragging = false;
})
createShape(gui.params.shape, gui.params.option);
displayDocs(gui.params.shape);
createShape(gui.params.shape);
function animate() {
requestAnimationFrame( animate );
@ -238,14 +137,9 @@ function animate() {
rotfn[gui.params.xRotate](theta),
rotfn[gui.params.yRotate](psi)
];
shape.hyperplane = 1 / gui.params.hyperplane;
camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
shape.node_scale = gui.params.nodesize;
shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
shape.render3(rotations, node_show, link_show);
shape.hyperplane = gui.params.hyperplane;
shape.geom_scale = gui.params.thickness;
shape.render3(rotations);
renderer.render( scene, camera );
}

276
package-lock.json generated
View File

@ -4,11 +4,8 @@
"requires": true,
"packages": {
"": {
"name": "fourdjs",
"dependencies": {
"color": "^4.2.3",
"color-scheme": "^1.0.1",
"lil-gui": "^0.19.0",
"lil-gui": "^0.18.2",
"three": "^0.154.0"
},
"devDependencies": {
@ -16,9 +13,9 @@
}
},
"node_modules/@esbuild/android-arm": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.20.tgz",
"integrity": "sha512-fyi7TDI/ijKKNZTUJAQqiG5T7YjJXgnzkURqmGj13C6dCqckZBLdl4h7bkhHt/t0WP+zO9/zwroDvANaOqO5Sw==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.15.tgz",
"integrity": "sha512-wlkQBWb79/jeEEoRmrxt/yhn5T1lU236OCNpnfRzaCJHZ/5gf82uYx1qmADTBWE0AR/v7FiozE1auk2riyQd3w==",
"cpu": [
"arm"
],
@ -32,9 +29,9 @@
}
},
"node_modules/@esbuild/android-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.20.tgz",
"integrity": "sha512-Nz4rJcchGDtENV0eMKUNa6L12zz2zBDXuhj/Vjh18zGqB44Bi7MBMSXjgunJgjRhCmKOjnPuZp4Mb6OKqtMHLQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.15.tgz",
"integrity": "sha512-NI/gnWcMl2kXt1HJKOn2H69SYn4YNheKo6NZt1hyfKWdMbaGadxjZIkcj4Gjk/WPxnbFXs9/3HjGHaknCqjrww==",
"cpu": [
"arm64"
],
@ -48,9 +45,9 @@
}
},
"node_modules/@esbuild/android-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.20.tgz",
"integrity": "sha512-8GDdlePJA8D6zlZYJV/jnrRAi6rOiNaCC/JclcXpB+KIuvfBN4owLtgzY2bsxnx666XjJx2kDPUmnTtR8qKQUg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.15.tgz",
"integrity": "sha512-FM9NQamSaEm/IZIhegF76aiLnng1kEsZl2eve/emxDeReVfRuRNmvT28l6hoFD9TsCxpK+i4v8LPpEj74T7yjA==",
"cpu": [
"x64"
],
@ -64,9 +61,9 @@
}
},
"node_modules/@esbuild/darwin-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.20.tgz",
"integrity": "sha512-bxRHW5kHU38zS2lPTPOyuyTm+S+eobPUnTNkdJEfAddYgEcll4xkT8DB9d2008DtTbl7uJag2HuE5NZAZgnNEA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.15.tgz",
"integrity": "sha512-XmrFwEOYauKte9QjS6hz60FpOCnw4zaPAb7XV7O4lx1r39XjJhTN7ZpXqJh4sN6q60zbP6QwAVVA8N/wUyBH/w==",
"cpu": [
"arm64"
],
@ -80,9 +77,9 @@
}
},
"node_modules/@esbuild/darwin-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-x64/-/darwin-x64-0.18.20.tgz",
"integrity": "sha512-pc5gxlMDxzm513qPGbCbDukOdsGtKhfxD1zJKXjCCcU7ju50O7MeAZ8c4krSJcOIJGFR+qx21yMMVYwiQvyTyQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-x64/-/darwin-x64-0.18.15.tgz",
"integrity": "sha512-bMqBmpw1e//7Fh5GLetSZaeo9zSC4/CMtrVFdj+bqKPGJuKyfNJ5Nf2m3LknKZTS+Q4oyPiON+v3eaJ59sLB5A==",
"cpu": [
"x64"
],
@ -96,9 +93,9 @@
}
},
"node_modules/@esbuild/freebsd-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-arm64/-/freebsd-arm64-0.18.20.tgz",
"integrity": "sha512-yqDQHy4QHevpMAaxhhIwYPMv1NECwOvIpGCZkECn8w2WFHXjEwrBn3CeNIYsibZ/iZEUemj++M26W3cNR5h+Tw==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-arm64/-/freebsd-arm64-0.18.15.tgz",
"integrity": "sha512-LoTK5N3bOmNI9zVLCeTgnk5Rk0WdUTrr9dyDAQGVMrNTh9EAPuNwSTCgaKOKiDpverOa0htPcO9NwslSE5xuLA==",
"cpu": [
"arm64"
],
@ -112,9 +109,9 @@
}
},
"node_modules/@esbuild/freebsd-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-x64/-/freebsd-x64-0.18.20.tgz",
"integrity": "sha512-tgWRPPuQsd3RmBZwarGVHZQvtzfEBOreNuxEMKFcd5DaDn2PbBxfwLcj4+aenoh7ctXcbXmOQIn8HI6mCSw5MQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-x64/-/freebsd-x64-0.18.15.tgz",
"integrity": "sha512-62jX5n30VzgrjAjOk5orYeHFq6sqjvsIj1QesXvn5OZtdt5Gdj0vUNJy9NIpjfdNdqr76jjtzBJKf+h2uzYuTQ==",
"cpu": [
"x64"
],
@ -128,9 +125,9 @@
}
},
"node_modules/@esbuild/linux-arm": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm/-/linux-arm-0.18.20.tgz",
"integrity": "sha512-/5bHkMWnq1EgKr1V+Ybz3s1hWXok7mDFUMQ4cG10AfW3wL02PSZi5kFpYKrptDsgb2WAJIvRcDm+qIvXf/apvg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm/-/linux-arm-0.18.15.tgz",
"integrity": "sha512-dT4URUv6ir45ZkBqhwZwyFV6cH61k8MttIwhThp2BGiVtagYvCToF+Bggyx2VI57RG4Fbt21f9TmXaYx0DeUJg==",
"cpu": [
"arm"
],
@ -144,9 +141,9 @@
}
},
"node_modules/@esbuild/linux-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm64/-/linux-arm64-0.18.20.tgz",
"integrity": "sha512-2YbscF+UL7SQAVIpnWvYwM+3LskyDmPhe31pE7/aoTMFKKzIc9lLbyGUpmmb8a8AixOL61sQ/mFh3jEjHYFvdA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm64/-/linux-arm64-0.18.15.tgz",
"integrity": "sha512-BWncQeuWDgYv0jTNzJjaNgleduV4tMbQjmk/zpPh/lUdMcNEAxy+jvneDJ6RJkrqloG7tB9S9rCrtfk/kuplsQ==",
"cpu": [
"arm64"
],
@ -160,9 +157,9 @@
}
},
"node_modules/@esbuild/linux-ia32": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ia32/-/linux-ia32-0.18.20.tgz",
"integrity": "sha512-P4etWwq6IsReT0E1KHU40bOnzMHoH73aXp96Fs8TIT6z9Hu8G6+0SHSw9i2isWrD2nbx2qo5yUqACgdfVGx7TA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ia32/-/linux-ia32-0.18.15.tgz",
"integrity": "sha512-JPXORvgHRHITqfms1dWT/GbEY89u848dC08o0yK3fNskhp0t2TuNUnsrrSgOdH28ceb1hJuwyr8R/1RnyPwocw==",
"cpu": [
"ia32"
],
@ -176,9 +173,9 @@
}
},
"node_modules/@esbuild/linux-loong64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-loong64/-/linux-loong64-0.18.20.tgz",
"integrity": "sha512-nXW8nqBTrOpDLPgPY9uV+/1DjxoQ7DoB2N8eocyq8I9XuqJ7BiAMDMf9n1xZM9TgW0J8zrquIb/A7s3BJv7rjg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-loong64/-/linux-loong64-0.18.15.tgz",
"integrity": "sha512-kArPI0DopjJCEplsVj/H+2Qgzz7vdFSacHNsgoAKpPS6W/Ndh8Oe24HRDQ5QCu4jHgN6XOtfFfLpRx3TXv/mEg==",
"cpu": [
"loong64"
],
@ -192,9 +189,9 @@
}
},
"node_modules/@esbuild/linux-mips64el": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-mips64el/-/linux-mips64el-0.18.20.tgz",
"integrity": "sha512-d5NeaXZcHp8PzYy5VnXV3VSd2D328Zb+9dEq5HE6bw6+N86JVPExrA6O68OPwobntbNJ0pzCpUFZTo3w0GyetQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-mips64el/-/linux-mips64el-0.18.15.tgz",
"integrity": "sha512-b/tmngUfO02E00c1XnNTw/0DmloKjb6XQeqxaYuzGwHe0fHVgx5/D6CWi+XH1DvkszjBUkK9BX7n1ARTOst59w==",
"cpu": [
"mips64el"
],
@ -208,9 +205,9 @@
}
},
"node_modules/@esbuild/linux-ppc64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ppc64/-/linux-ppc64-0.18.20.tgz",
"integrity": "sha512-WHPyeScRNcmANnLQkq6AfyXRFr5D6N2sKgkFo2FqguP44Nw2eyDlbTdZwd9GYk98DZG9QItIiTlFLHJHjxP3FA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ppc64/-/linux-ppc64-0.18.15.tgz",
"integrity": "sha512-KXPY69MWw79QJkyvUYb2ex/OgnN/8N/Aw5UDPlgoRtoEfcBqfeLodPr42UojV3NdkoO4u10NXQdamWm1YEzSKw==",
"cpu": [
"ppc64"
],
@ -224,9 +221,9 @@
}
},
"node_modules/@esbuild/linux-riscv64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-riscv64/-/linux-riscv64-0.18.20.tgz",
"integrity": "sha512-WSxo6h5ecI5XH34KC7w5veNnKkju3zBRLEQNY7mv5mtBmrP/MjNBCAlsM2u5hDBlS3NGcTQpoBvRzqBcRtpq1A==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-riscv64/-/linux-riscv64-0.18.15.tgz",
"integrity": "sha512-komK3NEAeeGRnvFEjX1SfVg6EmkfIi5aKzevdvJqMydYr9N+pRQK0PGJXk+bhoPZwOUgLO4l99FZmLGk/L1jWg==",
"cpu": [
"riscv64"
],
@ -240,9 +237,9 @@
}
},
"node_modules/@esbuild/linux-s390x": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-s390x/-/linux-s390x-0.18.20.tgz",
"integrity": "sha512-+8231GMs3mAEth6Ja1iK0a1sQ3ohfcpzpRLH8uuc5/KVDFneH6jtAJLFGafpzpMRO6DzJ6AvXKze9LfFMrIHVQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-s390x/-/linux-s390x-0.18.15.tgz",
"integrity": "sha512-632T5Ts6gQ2WiMLWRRyeflPAm44u2E/s/TJvn+BP6M5mnHSk93cieaypj3VSMYO2ePTCRqAFXtuYi1yv8uZJNA==",
"cpu": [
"s390x"
],
@ -256,9 +253,9 @@
}
},
"node_modules/@esbuild/linux-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-x64/-/linux-x64-0.18.20.tgz",
"integrity": "sha512-UYqiqemphJcNsFEskc73jQ7B9jgwjWrSayxawS6UVFZGWrAAtkzjxSqnoclCXxWtfwLdzU+vTpcNYhpn43uP1w==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-x64/-/linux-x64-0.18.15.tgz",
"integrity": "sha512-MsHtX0NgvRHsoOtYkuxyk4Vkmvk3PLRWfA4okK7c+6dT0Fu4SUqXAr9y4Q3d8vUf1VWWb6YutpL4XNe400iQ1g==",
"cpu": [
"x64"
],
@ -272,9 +269,9 @@
}
},
"node_modules/@esbuild/netbsd-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/netbsd-x64/-/netbsd-x64-0.18.20.tgz",
"integrity": "sha512-iO1c++VP6xUBUmltHZoMtCUdPlnPGdBom6IrO4gyKPFFVBKioIImVooR5I83nTew5UOYrk3gIJhbZh8X44y06A==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/netbsd-x64/-/netbsd-x64-0.18.15.tgz",
"integrity": "sha512-djST6s+jQiwxMIVQ5rlt24JFIAr4uwUnzceuFL7BQT4CbrRtqBPueS4GjXSiIpmwVri1Icj/9pFRJ7/aScvT+A==",
"cpu": [
"x64"
],
@ -288,9 +285,9 @@
}
},
"node_modules/@esbuild/openbsd-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/openbsd-x64/-/openbsd-x64-0.18.20.tgz",
"integrity": "sha512-e5e4YSsuQfX4cxcygw/UCPIEP6wbIL+se3sxPdCiMbFLBWu0eiZOJ7WoD+ptCLrmjZBK1Wk7I6D/I3NglUGOxg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/openbsd-x64/-/openbsd-x64-0.18.15.tgz",
"integrity": "sha512-naeRhUIvhsgeounjkF5mvrNAVMGAm6EJWiabskeE5yOeBbLp7T89tAEw0j5Jm/CZAwyLe3c67zyCWH6fsBLCpw==",
"cpu": [
"x64"
],
@ -304,9 +301,9 @@
}
},
"node_modules/@esbuild/sunos-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/sunos-x64/-/sunos-x64-0.18.20.tgz",
"integrity": "sha512-kDbFRFp0YpTQVVrqUd5FTYmWo45zGaXe0X8E1G/LKFC0v8x0vWrhOWSLITcCn63lmZIxfOMXtCfti/RxN/0wnQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/sunos-x64/-/sunos-x64-0.18.15.tgz",
"integrity": "sha512-qkT2+WxyKbNIKV1AEhI8QiSIgTHMcRctzSaa/I3kVgMS5dl3fOeoqkb7pW76KwxHoriImhx7Mg3TwN/auMDsyQ==",
"cpu": [
"x64"
],
@ -320,9 +317,9 @@
}
},
"node_modules/@esbuild/win32-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/win32-arm64/-/win32-arm64-0.18.20.tgz",
"integrity": "sha512-ddYFR6ItYgoaq4v4JmQQaAI5s7npztfV4Ag6NrhiaW0RrnOXqBkgwZLofVTlq1daVTQNhtI5oieTvkRPfZrePg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/win32-arm64/-/win32-arm64-0.18.15.tgz",
"integrity": "sha512-HC4/feP+pB2Vb+cMPUjAnFyERs+HJN7E6KaeBlFdBv799MhD+aPJlfi/yk36SED58J9TPwI8MAcVpJgej4ud0A==",
"cpu": [
"arm64"
],
@ -336,9 +333,9 @@
}
},
"node_modules/@esbuild/win32-ia32": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/win32-ia32/-/win32-ia32-0.18.20.tgz",
"integrity": "sha512-Wv7QBi3ID/rROT08SABTS7eV4hX26sVduqDOTe1MvGMjNd3EjOz4b7zeexIR62GTIEKrfJXKL9LFxTYgkyeu7g==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/win32-ia32/-/win32-ia32-0.18.15.tgz",
"integrity": "sha512-ovjwoRXI+gf52EVF60u9sSDj7myPixPxqzD5CmkEUmvs+W9Xd0iqISVBQn8xcx4ciIaIVlWCuTbYDOXOnOL44Q==",
"cpu": [
"ia32"
],
@ -352,9 +349,9 @@
}
},
"node_modules/@esbuild/win32-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/win32-x64/-/win32-x64-0.18.20.tgz",
"integrity": "sha512-kTdfRcSiDfQca/y9QIkng02avJ+NCaQvrMejlsB3RRv5sE9rRoeBPISaZpKxHELzRxZyLvNts1P27W3wV+8geQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/win32-x64/-/win32-x64-0.18.15.tgz",
"integrity": "sha512-imUxH9a3WJARyAvrG7srLyiK73XdX83NXQkjKvQ+7vPh3ZxoLrzvPkQKKw2DwZ+RV2ZB6vBfNHP8XScAmQC3aA==",
"cpu": [
"x64"
],
@ -367,52 +364,10 @@
"node": ">=12"
}
},
"node_modules/color": {
"version": "4.2.3",
"resolved": "https://registry.npmjs.org/color/-/color-4.2.3.tgz",
"integrity": "sha512-1rXeuUUiGGrykh+CeBdu5Ie7OJwinCgQY0bc7GCRxy5xVHy+moaqkpL/jqQq0MtQOeYcrqEz4abc5f0KtU7W4A==",
"dependencies": {
"color-convert": "^2.0.1",
"color-string": "^1.9.0"
},
"engines": {
"node": ">=12.5.0"
}
},
"node_modules/color-convert": {
"version": "2.0.1",
"resolved": "https://registry.npmjs.org/color-convert/-/color-convert-2.0.1.tgz",
"integrity": "sha512-RRECPsj7iu/xb5oKYcsFHSppFNnsj/52OVTRKb4zP5onXwVF3zVmmToNcOfGC+CRDpfK/U584fMg38ZHCaElKQ==",
"dependencies": {
"color-name": "~1.1.4"
},
"engines": {
"node": ">=7.0.0"
}
},
"node_modules/color-name": {
"version": "1.1.4",
"resolved": "https://registry.npmjs.org/color-name/-/color-name-1.1.4.tgz",
"integrity": "sha512-dOy+3AuW3a2wNbZHIuMZpTcgjGuLU/uBL/ubcZF9OXbDo8ff4O8yVp5Bf0efS8uEoYo5q4Fx7dY9OgQGXgAsQA=="
},
"node_modules/color-scheme": {
"version": "1.0.1",
"resolved": "https://registry.npmjs.org/color-scheme/-/color-scheme-1.0.1.tgz",
"integrity": "sha512-4x+ya6+z6g9DaTFSfVzTZc8TSjxHuDT40NB43N3XPUkQlF6uujhwH8aeMeq8HBgoQQog/vrYgJ16mt/eVTRXwQ=="
},
"node_modules/color-string": {
"version": "1.9.1",
"resolved": "https://registry.npmjs.org/color-string/-/color-string-1.9.1.tgz",
"integrity": "sha512-shrVawQFojnZv6xM40anx4CkoDP+fZsw/ZerEMsW/pyzsRbElpsL/DBVW7q3ExxwusdNXI3lXpuhEZkzs8p5Eg==",
"dependencies": {
"color-name": "^1.0.0",
"simple-swizzle": "^0.2.2"
}
},
"node_modules/esbuild": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/esbuild/-/esbuild-0.18.20.tgz",
"integrity": "sha512-ceqxoedUrcayh7Y7ZX6NdbbDzGROiyVBgC4PriJThBKSVPWnnFHZAkfI1lJT8QFkOwH4qOS2SJkS4wvpGl8BpA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/esbuild/-/esbuild-0.18.15.tgz",
"integrity": "sha512-3WOOLhrvuTGPRzQPU6waSDWrDTnQriia72McWcn6UCi43GhCHrXH4S59hKMeez+IITmdUuUyvbU9JIp+t3xlPQ==",
"dev": true,
"hasInstallScript": true,
"bin": {
@ -422,34 +377,34 @@
"node": ">=12"
},
"optionalDependencies": {
"@esbuild/android-arm": "0.18.20",
"@esbuild/android-arm64": "0.18.20",
"@esbuild/android-x64": "0.18.20",
"@esbuild/darwin-arm64": "0.18.20",
"@esbuild/darwin-x64": "0.18.20",
"@esbuild/freebsd-arm64": "0.18.20",
"@esbuild/freebsd-x64": "0.18.20",
"@esbuild/linux-arm": "0.18.20",
"@esbuild/linux-arm64": "0.18.20",
"@esbuild/linux-ia32": "0.18.20",
"@esbuild/linux-loong64": "0.18.20",
"@esbuild/linux-mips64el": "0.18.20",
"@esbuild/linux-ppc64": "0.18.20",
"@esbuild/linux-riscv64": "0.18.20",
"@esbuild/linux-s390x": "0.18.20",
"@esbuild/linux-x64": "0.18.20",
"@esbuild/netbsd-x64": "0.18.20",
"@esbuild/openbsd-x64": "0.18.20",
"@esbuild/sunos-x64": "0.18.20",
"@esbuild/win32-arm64": "0.18.20",
"@esbuild/win32-ia32": "0.18.20",
"@esbuild/win32-x64": "0.18.20"
"@esbuild/android-arm": "0.18.15",
"@esbuild/android-arm64": "0.18.15",
"@esbuild/android-x64": "0.18.15",
"@esbuild/darwin-arm64": "0.18.15",
"@esbuild/darwin-x64": "0.18.15",
"@esbuild/freebsd-arm64": "0.18.15",
"@esbuild/freebsd-x64": "0.18.15",
"@esbuild/linux-arm": "0.18.15",
"@esbuild/linux-arm64": "0.18.15",
"@esbuild/linux-ia32": "0.18.15",
"@esbuild/linux-loong64": "0.18.15",
"@esbuild/linux-mips64el": "0.18.15",
"@esbuild/linux-ppc64": "0.18.15",
"@esbuild/linux-riscv64": "0.18.15",
"@esbuild/linux-s390x": "0.18.15",
"@esbuild/linux-x64": "0.18.15",
"@esbuild/netbsd-x64": "0.18.15",
"@esbuild/openbsd-x64": "0.18.15",
"@esbuild/sunos-x64": "0.18.15",
"@esbuild/win32-arm64": "0.18.15",
"@esbuild/win32-ia32": "0.18.15",
"@esbuild/win32-x64": "0.18.15"
}
},
"node_modules/fsevents": {
"version": "2.3.3",
"resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.3.tgz",
"integrity": "sha512-5xoDfX+fL7faATnagmWPpbFtwh/R77WmMMqqHGS65C3vvB0YHrgF+B1YmZ3441tMj5n63k0212XNoJwzlhffQw==",
"version": "2.3.2",
"resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
"integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
"dev": true,
"hasInstallScript": true,
"optional": true,
@ -460,15 +415,10 @@
"node": "^8.16.0 || ^10.6.0 || >=11.0.0"
}
},
"node_modules/is-arrayish": {
"version": "0.3.2",
"resolved": "https://registry.npmjs.org/is-arrayish/-/is-arrayish-0.3.2.tgz",
"integrity": "sha512-eVRqCvVlZbuw3GrM63ovNSNAeA1K16kaR/LRY/92w0zxQ5/1YzwblUX652i4Xs9RwAGjW9d9y6X88t8OaAJfWQ=="
},
"node_modules/lil-gui": {
"version": "0.19.0",
"resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.19.0.tgz",
"integrity": "sha512-02/Z7rPng3GXWFwkQVj1hQaJYo2fIEYctqe0ima5uI/N2HEagB9ZGCQKkVWr3UuKfTr0arto3Q9prTB8sxtJJw=="
"version": "0.18.2",
"resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.18.2.tgz",
"integrity": "sha512-DgdrLy3/KGC0PiQLKgOcJMPItP4xY4iWgJ9+91Zaxfr8GCTmMps05QS9w9jW7yspILlbscbquwjOwxmWnSx5Uw=="
},
"node_modules/nanoid": {
"version": "3.3.6",
@ -495,9 +445,9 @@
"dev": true
},
"node_modules/postcss": {
"version": "8.4.31",
"resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.31.tgz",
"integrity": "sha512-PS08Iboia9mts/2ygV3eLpY5ghnUcfLV/EXTOW1E2qYxJKGGBUtNjN76FYHnMs36RmARn41bC0AZmn+rR0OVpQ==",
"version": "8.4.27",
"resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.27.tgz",
"integrity": "sha512-gY/ACJtJPSmUFPDCHtX78+01fHa64FaU4zaaWfuh1MhGJISufJAH4cun6k/8fwsHYeK4UQmENQK+tRLCFJE8JQ==",
"dev": true,
"funding": [
{
@ -523,9 +473,9 @@
}
},
"node_modules/rollup": {
"version": "3.29.4",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-3.29.4.tgz",
"integrity": "sha512-oWzmBZwvYrU0iJHtDmhsm662rC15FRXmcjCk1xD771dFDx5jJ02ufAQQTn0etB2emNk4J9EZg/yWKpsn9BWGRw==",
"version": "3.26.3",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-3.26.3.tgz",
"integrity": "sha512-7Tin0C8l86TkpcMtXvQu6saWH93nhG3dGQ1/+l5V2TDMceTxO7kDiK6GzbfLWNNxqJXm591PcEZUozZm51ogwQ==",
"dev": true,
"bin": {
"rollup": "dist/bin/rollup"
@ -538,14 +488,6 @@
"fsevents": "~2.3.2"
}
},
"node_modules/simple-swizzle": {
"version": "0.2.2",
"resolved": "https://registry.npmjs.org/simple-swizzle/-/simple-swizzle-0.2.2.tgz",
"integrity": "sha512-JA//kQgZtbuY83m+xT+tXJkmJncGMTFT+C+g2h2R9uxkYIrE2yy9sgmcLhCnw57/WSD+Eh3J97FPEDFnbXnDUg==",
"dependencies": {
"is-arrayish": "^0.3.1"
}
},
"node_modules/source-map-js": {
"version": "1.0.2",
"resolved": "https://registry.npmjs.org/source-map-js/-/source-map-js-1.0.2.tgz",
@ -561,14 +503,14 @@
"integrity": "sha512-Uzz8C/5GesJzv8i+Y2prEMYUwodwZySPcNhuJUdsVMH2Yn4Nm8qlbQe6qRN5fOhg55XB0WiLfTPBxVHxpE60ug=="
},
"node_modules/vite": {
"version": "4.5.3",
"resolved": "https://registry.npmjs.org/vite/-/vite-4.5.3.tgz",
"integrity": "sha512-kQL23kMeX92v3ph7IauVkXkikdDRsYMGTVl5KY2E9OY4ONLvkHf04MDTbnfo6NKxZiDLWzVpP5oTa8hQD8U3dg==",
"version": "4.4.6",
"resolved": "https://registry.npmjs.org/vite/-/vite-4.4.6.tgz",
"integrity": "sha512-EY6Mm8vJ++S3D4tNAckaZfw3JwG3wa794Vt70M6cNJ6NxT87yhq7EC8Rcap3ahyHdo8AhCmV9PTk+vG1HiYn1A==",
"dev": true,
"dependencies": {
"esbuild": "^0.18.10",
"postcss": "^8.4.27",
"rollup": "^3.27.1"
"postcss": "^8.4.26",
"rollup": "^3.25.2"
},
"bin": {
"vite": "bin/vite.js"

View File

@ -1,12 +1,9 @@
{
"dependencies": {
"color": "^4.2.3",
"color-scheme": "^1.0.1",
"lil-gui": "^0.19.0",
"lil-gui": "^0.18.2",
"three": "^0.154.0"
},
"devDependencies": {
"vite": "^4.4.6"
},
"type": "module"
}
}

View File

@ -1,28 +1,23 @@
import * as PERMUTE from './permute.js';
import * as CELLINDEX from './cellindex.js';
function index_nodes(nodes, scale) {
function scale_and_index(nodes, scale) {
let i = 1;
for( const n of nodes ) {
n["id"] = i;
i++;
}
}
function scale_nodes(nodes, scale) {
for( const n of nodes ) {
for( const a of [ 'x', 'y', 'z', 'w' ] ) {
n[a] = scale * n[a];
}
}
return nodes;
}
function dist2(n1, n2) {
return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
}
export function auto_detect_edges(nodes, neighbours, debug=false) {
function auto_detect_edges(nodes, neighbours, debug=false) {
const seen = {};
const nnodes = nodes.length;
const links = [];
@ -58,15 +53,15 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
// too small and simple to calculate
export const cell5 = () => {
const c1 = Math.sqrt(5) / 4;
const r5 = Math.sqrt(5);
const r2 = Math.sqrt(2) / 2;
return {
name: '5-cell',
nodes: [
{id:1, label: 1, x: c1, y: c1, z: c1, w: -0.25 },
{id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
{id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
{id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
{id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
{id:1, x: r2, y: r2, z: r2, w: -r2 / r5 },
{id:2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
{id:3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
{id:4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
{id:5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
],
links: [
{ id:1, source:1, target: 2},
@ -80,12 +75,10 @@ export const cell5 = () => {
{ id:9, source:3, target: 5},
{ id:10, source:4, target: 5},
],
options: [ { name: '--' }],
description: `Five tetrahedra joined at ten faces with three
tetrahedra around each edge. The 5-cell is the simplest regular
four-D polytope and the four-dimensional analogue of the tetrahedron.
A corresponding polytope, or simplex, exists for every n-dimensional
space.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
};
@ -93,139 +86,53 @@ export const cell5 = () => {
export const cell16 = () => {
let nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
nodes = nodes.filter((n) => n.x * n.y * n.z * n.w > 0);
nodes[0].label = 1;
nodes[3].label = 2;
nodes[5].label = 3;
nodes[6].label = 4;
nodes[7].label = 1;
nodes[4].label = 2;
nodes[2].label = 3;
nodes[1].label = 4;
index_nodes(nodes);
scale_nodes(nodes, 0.5);
scale_and_index(nodes, 0.75);
const links = auto_detect_edges(nodes, 6);
return {
name: '16-cell',
nodes: nodes,
links: links,
options: [ { name: '--' }],
description: `Sixteen tetrahedra joined at 32 faces with four
tetrahedra around each edge. The 16-cell is the four-dimensional
analogue of the octahedron and is dual to the tesseract. Every
n-dimensional space has a corresponding polytope in this family.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
};
export const tesseract = () => {
const nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
index_nodes(nodes);
for( const n of nodes ) {
if( n.x * n.y * n.z * n.w > 0 ) {
n.label = 2;
} else {
n.label = 1;
}
}
scale_nodes(nodes, 0.5);
const nodes = scale_and_index(PERMUTE.coordinates([1, 1, 1, 1], 0), Math.sqrt(2) / 2);
const links = auto_detect_edges(nodes, 4);
links.map((l) => { l.label = 0 });
for( const p of [ 1, 2 ] ) {
const nodes16 = nodes.filter((n) => n.label === p);
const links16 = auto_detect_edges(nodes16, 6);
links16.map((l) => l.label = p);
links.push(...links16);
}
return {
name: 'Tesseract',
nodes: nodes,
links: links,
options: [
{ name: 'none', links: [ 0 ] },
{ name: 'one 16-cell', links: [ 0, 1 ] },
{ name: 'both 16-cells', links: [ 0, 1, 2 ] },
],
description: `The most well-known four-dimensional shape, the
tesseract is analogous to the cube, and is constructed by placing two
cubes in parallel hyperplanes and joining their corresponding
vertices. It consists of eight cubes joined at 32 face with three
cubes around each edge, and is dual to the 16-cell. Every
n-dimensional space has a cube analogue or measure polytope.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
}
const CELL24_INDEXING = {
x: { y: 1, z: 3, w: 2 },
y: { z: 2, w: 3 },
z: { w: 1 }
};
function node_by_id(nodes, nid) {
const ns = nodes.filter((n) => n.id === nid);
return ns[0];
}
export const cell24 = () => {
const nodes = PERMUTE.coordinates([0, 0, 1, 1], 0);
for( const n of nodes ) {
const axes = ['x', 'y', 'z', 'w'].filter((a) => n[a] !== 0);
n.label = CELL24_INDEXING[axes[0]][axes[1]];
}
scale_nodes(nodes, Math.sqrt(2) / 2);
index_nodes(nodes);
const links = auto_detect_edges(nodes, 8);
links.map((l) => l.label = 0);
for( const p of [ 1, 2, 3 ] ) {
const nodes16 = nodes.filter((n) => n.label === p);
const links16 = auto_detect_edges(nodes16, 6);
links16.map((l) => l.label = p);
links.push(...links16);
}
// links.map((l) => {
// const ls = [ l.source, l.target ].map((nid) => node_by_id(nodes, nid).label);
// for ( const c of [1, 2, 3] ) {
// if( ! ls.includes(c) ) {
// l.label = c
// }
// }
// });
const nodes = scale_and_index(PERMUTE.coordinates([0, 0, 1, 1], 0), 1);
const links = auto_detect_edges(nodes, 6);
return {
name: '24-cell',
nodes: nodes,
links: links,
base: {},
options: [
{ name: 'none', links: [ 0 ] },
{ name: 'one 16-cell', links: [ 0, 1 ] },
{ name: 'three 16-cells', links: [ 0, 1, 2, 3 ] }
],
description: `A unique object without an exact analogue in higher
or lower dimensions, the 24-cell is made of twenty-four octahedra
joined at 96 faces, with three around each edge. The 24-cell is
self-dual.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
}
// face detection for the 120-cell
// NOTE: all of these return node ids, not nodes
@ -304,7 +211,7 @@ function auto_120cell_faces(links) {
export function make_120cell_vertices() {
function make_120cell_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const r5 = Math.sqrt(5);
const phi2 = phi * phi;
@ -321,546 +228,52 @@ export function make_120cell_vertices() {
PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
].flat();
index_nodes(nodes);
scale_nodes(nodes, 0.25 * Math.sqrt(2));
return nodes;
return scale_and_index(nodes, 0.5);
}
function label_nodes(nodes, ids, label) {
nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
}
function label_faces_120cell(nodes, faces, cfaces, label) {
const ns = new Set();
for( const fid of cfaces ) {
const face = faces.filter((f)=> f.id === fid );
if( face.length > 0 ) {
for ( const nid of face[0].nodes ) {
ns.add(nid);
}
}
}
label_nodes(nodes, Array.from(ns), label);
}
function link_labels(nodes, link) {
const n1 = nodes.filter((n) => n.id === link.source);
const n2 = nodes.filter((n) => n.id === link.target);
return [ n1[0].label, n2[0].label ];
}
// version of the 120-cell where nodes are partitioned by
// layer and the links follow that
export const cell120_layered = (max) => {
export const cell120 = () => {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
nodes.map((n) => n.label = 9); // make all invisible by default
for (const cstr in CELLINDEX.LAYERS120 ) {
label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
}
links.map((l) => {
const labels = link_labels(nodes, l);
if( labels[0] >= labels[1] ) {
l.label = labels[0];
} else {
l.label = labels[1];
}
});
const options = [];
const layers = [];
for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
layers.push(i);
options.push({
name: CELLINDEX.LAYER_NAMES[i],
links: [...layers],
nodes: [...layers]
})
}
const faces = auto_120cell_faces(links);
return {
name: '120-cell layered',
nodes: nodes,
links: links,
nolink2opacity: true,
options: options,
description: `This version of the 120-cell lets you explore its
structure by building each layer from the 'north pole' onwards.`,
geometry: {
node_size: 0.02,
link_size: 0.02
},
faces: faces
}
}
export const cell120_inscribed = () => {
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);
for( const p of [ 1, 2, 3, 4, 5 ]) {
const nodes600 = nodes.filter((n) => n.label === p);
const links600 = auto_detect_edges(nodes600, 12);
links600.map((l) => l.label = p);
links.push(...links600);
}
return {
name: '120-cell',
nodes: nodes,
links: links,
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 ] }
],
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.`,
}
}
function partition_coord(i, coords, invert) {
const j = invert ? -i : i;
if( j >= 0 ) {
return coords[j];
}
return "-" + coords[-j];
}
function partition_fingerprint(n, coords, invert) {
const p = ['x','y','z','w'].map((a) => partition_coord(n[a], coords, invert));
const fp = p.join(',');
return fp;
}
function label_vertex(n, coords, partition) {
const fp = partition_fingerprint(n, coords, false);
if( fp in partition ) {
return partition[fp];
} else {
const ifp = partition_fingerprint(n, coords, true);
if( ifp in partition ) {
return partition[ifp];
}
console.log(`Map for ${fp} ${ifp} not found`);
return 0;
}
}
function map_coord(i, coords, values) {
if( i >= 0 ) {
return values[coords[i]];
}
return -values[coords[-i]];
}
export function make_600cell_vertices() {
const coords = {
0: '0',
1: '1',
2: '2',
3: 't',
4: 'k'
};
const t = 0.5 * (1 + Math.sqrt(5));
const values = {
'0': 0,
'1': 1,
'2': 2,
't': t,
'k': 1 / t
};
function make_600cell_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const nodes = [
PERMUTE.coordinates([0, 0, 0, 2], 0),
PERMUTE.coordinates([1, 1, 1, 1], 0),
PERMUTE.coordinates([3, 1, 4, 0], 0, true)
].flat();
for( const n of nodes ) {
n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
}
for( const n of nodes ) {
for( const a of [ 'x', 'y', 'z', 'w'] ) {
n[a] = map_coord(n[a], coords, values);
}
}
index_nodes(nodes);
scale_nodes(nodes, 0.5);
return nodes;
PERMUTE.coordinates([phi, 1, 1 / phi, 0], 0, true)
].flat();
return scale_and_index(nodes, 0.75);
}
function get_node(nodes, id) {
const ns = nodes.filter((n) => n.id === id);
if( ns ) {
return ns[0]
} else {
return undefined;
}
}
function audit_link_labels(nodes, links) {
for( const l of links ) {
const n1 = get_node(nodes, l.source);
const n2 = get_node(nodes, l.target);
if( n1.label === n2.label ) {
console.log(`link ${l.id} joins ${n1.id} ${n2.id} with label ${n2.label}`);
}
}
}
export const cell600 = () => {
const nodes = make_600cell_vertices();
const links = auto_detect_edges(nodes, 12);
links.map((l) => l.label = 0);
for( const p of [1, 2, 3, 4, 5]) {
const nodes24 = nodes.filter((n) => n.label === p);
const links24 = auto_detect_edges(nodes24, 8);
links24.map((l) => l.label = p);
links.push(...links24);
}
return {
name: '600-cell',
nodes: nodes,
links: links,
options: [
{ name: "none", links: [ 0 ]},
{ name: "one 24-cell", links: [ 0, 1 ] },
{ name: "five 24-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
],
description: `The 600-cell is the four-dimensional analogue of the
icosahedron, and consists of 600 tetrahedra joined at 1200 faces
with five tetrahedra around each edge. It is dual to the 120-cell.
Its 120 vertices can be partitioned into five sets which form the
vertices of five inscribed 24-cells.`,
}
}
export const cell600_layered = () => {
const nodes = make_600cell_vertices();
const links = auto_detect_edges(nodes, 12);
nodes.map((n) => n.label = 9); // make all invisible by default
for (const cstr in CELLINDEX.LAYERS600 ) {
label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
}
links.map((l) => {
const labels = link_labels(nodes, l);
if( labels[0] >= labels[1] ) {
l.label = labels[0];
} else {
l.label = labels[1];
geometry: {
node_size: 0.02,
link_size: 0.02
}
});
const options = [];
const layers = [];
for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
layers.push(i);
options.push({
name: CELLINDEX.LAYER_NAMES[i],
links: [...layers],
nodes: [...layers]
})
}
return {
name: '600-cell layered',
nodes: nodes,
links: links,
nolink2opacity: true,
options: options,
description: `This version of the 600-cell lets you explore its
structure by building each layer from the 'north pole' onwards.`,
}
}
export const snub24cell = () => {
const nodes600 = make_600cell_vertices();
const links600 = auto_detect_edges(nodes600, 12);
const nodes = nodes600.filter((n) => n.label != 1);
const links = links600.filter((l) => {
const sn = node_by_id(nodes, l.source);
const tn = node_by_id(nodes, l.target);
return sn && tn;
});
links.map((l) => l.label = 0);
return {
name: 'Snub 24-cell',
nodes: nodes,
links: links,
options: [ { name: "--" } ],
description: `The snub 24-cell is a semiregular polytope which
connects the 24-cell with the 600-cell. It consists of 24 icosahedra
and 120 tetrahedra, and is constructed by removing one of the
five inscribed 24-cells from a 600-cell.`
}
}
function make_dodecahedron_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const phiinv = 1 / phi;
const nodes = [
{ x: 1, y: 1, z: 1, w: 0, label: 4 },
{ x: 1, y: 1, z: -1, w: 0, label: 3 },
{ x: 1, y: -1, z: 1, w: 0, label: 3 },
{ x: 1, y: -1, z: -1, w: 0, label: 2 },
{ x: -1, y: 1, z: 1, w: 0, label: 3 },
{ x: -1, y: 1, z: -1, w: 0, label: 1 },
{ x: -1, y: -1, z: 1, w: 0, label: 5 },
{ x: -1, y: -1, z: -1, w: 0, label: 3 },
{ x: 0, y: phi, z: phiinv, w: 0, label: 5 },
{ x: 0, y: phi, z: -phiinv, w: 0 , label: 2 },
{ x: 0, y: -phi, z: phiinv, w: 0, label: 4 },
{ x: 0, y: -phi, z: -phiinv, w: 0 , label: 1 },
{ x: phiinv, y: 0, z: phi, w: 0 , label: 2},
{ x: phiinv, y: 0, z: -phi, w: 0 , label: 4},
{ x: -phiinv, y: 0, z: phi, w: 0 , label: 1},
{ x: -phiinv, y: 0, z: -phi, w: 0 , label: 5},
{ x: phi, y: phiinv, z:0, w: 0 , label: 1},
{ x: phi, y: -phiinv, z:0, w: 0 , label: 5},
{ x: -phi, y: phiinv, z:0, w: 0 , label: 4},
{ x: -phi, y: -phiinv, z:0, w: 0 , label: 2},
];
scale_nodes(nodes, 1 / Math.sqrt(3));
index_nodes(nodes);
return nodes;
}
export const dodecahedron = () => {
const nodes = make_dodecahedron_vertices();
const links = auto_detect_edges(nodes, 3);
links.map((l) => l.label = 0);
for( const p of [ 1, 2, 3, 4, 5 ]) {
const tetran = nodes.filter((n) => n.label === p);
const tetral = auto_detect_edges(tetran, 3);
tetral.map((l) => l.label = p);
links.push(...tetral);
}
return {
name: 'Dodecahedron',
nodes: nodes,
links: links,
options: [
{ name: "none", links: [ 0 ]},
{ name: "one tetrahedron", links: [ 0, 1 ] },
{ name: "five tetrahedra", links: [ 0, 1, 2, 3, 4, 5 ] }
],
description: `The dodecahedron is a three-dimensional polyhedron
which is included here so that you can see the partition of its
vertices into five interlocked tetrahedra. This structure is the
basis for the partition of the 120-cell's vertices into five
600-cells.`
}
}
export const tetrahedron = () => {
const r2 = Math.sqrt(2);
const r3 = Math.sqrt(3);
return {
name: 'Tetrahedron',
nodes: [
{id:1, label: 1, x: 2 * r2 / 3, y: 0, z: -1/3, w: 0 },
{id:2, label: 2, x: -r2 / 3, y: r2 / r3, z: -1/3, w: 0 },
{id:3, label: 3, x: -r2 / 3, y: -r2 / r3, z: -1/3, w: 0 },
{id:4, label: 4, x: 0, y: 0, z: 1, w: 0 },
],
links: [
{ id:1, source:1, target: 2},
{ id:2, source:1, target: 3},
{ id:3, source:1, target: 4},
{ id:4, source:2, target: 3},
{ id:5, source:2, target: 4},
{ id:6, source:3, target: 4},
],
options: [ { name: '--' }],
description: `The simplest three-dimensional polytope, consisting of four triangles joined at six edges. The 5-cell is its four-dimensional analogue.`,
};
};
export const octahedron = () => {
const nodes = [
{id: 1, label: 1, x: 1, y: 0, z: 0, w: 0},
{id: 2, label: 1, x: -1, y: 0, z: 0, w: 0},
{id: 3, label: 2, x: 0, y: 1, z: 0, w: 0},
{id: 4, label: 2, x: 0, y: -1, z: 0, w: 0},
{id: 5, label: 3, x: 0, y: 0, z: 1, w: 0},
{id: 6, label: 3, x: 0, y: 0, z: -1, w: 0},
];
const links = [
{id:1, source: 1, target: 3},
{id:2, source: 1, target: 4},
{id:3, source: 1, target: 5},
{id:4, source: 1, target: 6},
{id:5, source: 2, target: 3},
{id:6, source: 2, target: 4},
{id:7, source: 2, target: 5},
{id:8, source: 2, target: 6},
{id:9, source: 3, target: 5},
{id:10, source: 3, target: 6},
{id:11, source: 4, target: 5},
{id:12, source: 4, target: 6},
]
links.map((l) => { l.label = 0 });
return {
name: 'Octahedron',
nodes: nodes,
links: links,
options: [ { name: '--' }],
description: `The three-dimensional cross-polytope, the 16-cell is its four-dimensional analogue.`,
};
}
export const cube = () => {
const 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},
{id: 3, label: 2, x: 1, y: -1, z: 1, w: 0},
{id: 4, label: 1, x: -1, y: -1, z: 1, w: 0},
{id: 5, label: 2, x: 1, y: 1, z: -1, w: 0},
{id: 6, label: 1, x: -1, y: 1, z: -1, w: 0},
{id: 7, label: 1, x: 1, y: -1, z: -1, w: 0},
{id: 8, label: 2, x: -1, y: -1, z: -1, w: 0},
];
scale_nodes(nodes, 1/Math.sqrt(3));
const links = auto_detect_edges(nodes, 3);
links.map((l) => { l.label = 0 });
return {
name: 'Cube',
nodes: nodes,
links: links,
options: [ { name: '--' }],
description: `The three-dimensional measure polytope, the tesseract is its four-dimensional analogue.`,
};
}
function make_icosahedron_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const nodes = [
{ x: 0, y: 1, z: phi, w: 0, label: 1 },
{ x: 0, y: -1, z: phi, w: 0, label: 1 },
{ x: 0, y: 1, z: -phi, w: 0, label: 1 },
{ x: 0, y: -1, z: -phi, w: 0, label: 1 },
{ x: 1, y: phi, z: 0, w: 0, label: 2 },
{ x: -1, y: phi, z: 0, w: 0, label: 2 },
{ x: 1, y: -phi, z: 0, w: 0, label: 2 },
{ x: -1, y: -phi, z: 0, w: 0, label: 2 },
{ x: phi, y: 0, z: 1, w: 0, label: 3},
{ x: phi, y: 0, z: -1, w: 0, label: 3},
{ x: -phi, y: 0, z: 1, w: 0, label: 3},
{ x: -phi, y: 0, z: -1, w: 0, label: 3},
];
scale_nodes(nodes, 1/Math.sqrt((5 + Math.sqrt(5)) / 2));
index_nodes(nodes);
return nodes;
}
export const icosahedron = () => {
const nodes = make_icosahedron_vertices();
const links = auto_detect_edges(nodes, 5);
links.map((l) => l.label = 0);
return {
name: 'Icosahedron',
nodes: nodes,
links: links,
options: [
{ name: "--"},
],
description: `The icosahedron is a twenty-sided polyhedron and is dual to the dodecahedron. Its four-dimensional analogue is the 600-cell.`
}
}
export const build_all = () => {
return [
tetrahedron(),
octahedron(),
cube(),
icosahedron(),
dodecahedron(),
cell5(),
cell16(),
tesseract(),
cell24(),
snub24cell(),
cell600(),
cell600_layered(),
cell120_inscribed(),
cell120_layered()
];
}
export const radii = (shape) => {
return shape.nodes.map(n => Math.sqrt(n.x * n.x + n.y * n.y + n.z * n.z + n.w * n.w))
}

View File

@ -3,14 +3,5 @@
import { defineConfig, loadEnv } from 'vite';
export default defineConfig({
base: '/fourjs/',
build: {
rollupOptions: {
output: {
manualChunks: {
threejs: [ 'three' ]
}
}
}
}
base: '/fourjs/'
})