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Basic function to colour a single dodecahedron defined by an face and 

a neighbouring vertex
feature-120-cell-index
Mike Lynch 2023-08-26 13:54:44 +10:00
parent 8a926f0552
commit 3b806c3796
1 changed files with 61 additions and 41 deletions
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102
testbed.js
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@ -360,17 +360,6 @@ function make_dodecahedron(faces, f1, f2) {
return dodecahedron; return dodecahedron;
} }
// goal - a version of the above which collates the nodes to
// a standard 'layout' on the dodecahedron, so that it's then easy
// to colour them automatically
function faces_to_dodecahedron(faces, f1, f2) { function faces_to_dodecahedron(faces, f1, f2) {
const dodecahedron = [ f1, f2 ]; const dodecahedron = [ f1, f2 ];
@ -407,6 +396,17 @@ function faces_to_dodecahedron(faces, f1, f2) {
return dodecahedron; return dodecahedron;
} }
// from a face and one neighbouring node, return a dodecahedron
function face_plus_to_dodecahedron(faces, f1, node) {
const neighbours = find_adjacent_faces(faces, f1);
const nodens = neighbours.filter((f) => f.nodes.includes(node));
return faces_to_dodecahedron(faces, f1, nodens[0]); // does it matter which?
}
// for three faces, return their common vertex (if they have one) // for three faces, return their common vertex (if they have one)
function find_dodeca_vertex(f1, f2, f3) { function find_dodeca_vertex(f1, f2, f3) {
@ -420,45 +420,65 @@ function find_dodeca_vertex(f1, f2, f3) {
} }
} }
const VERTEX_MAP = [
[ 0, 1, 5 ],
[ 0, 1, 2 ],
[ 0, 2, 3 ],
[ 0, 3, 4 ],
[ 0, 4, 5 ],
[ 1, 5, 6 ],
[ 1, 2, 7 ],
[ 2, 3, 8 ],
[ 3, 4, 9 ],
[ 4, 5, 10 ],
[ 1, 6, 7 ],
[ 2, 7, 8 ],
[ 3, 8, 9 ],
[ 4, 9, 10 ],
[ 5, 6, 10 ],
[ 6, 7, 11 ],
[ 7, 8, 11 ],
[ 8, 9, 11 ],
[ 9, 10, 11 ],
[ 6, 10, 11 ],
];
function dodecahedron_vertices(dodeca) {
const VERTEX_MAP = [
[ 0, 1, 5 ], function dodecahedron_vertices(faces) {
[ 0, 1, 2 ], const face_sets = VERTEX_MAP.map((vs) => vs.map((v) => faces[v]));
[ 0, 2, 3 ], return face_sets.map((fs) => find_dodeca_vertex(...fs));
[ 0, 3, 4 ],
[ 0, 4, 5 ],
[ 1, 5, 6 ],
[ 1, 2, 7 ],
[ 2, 3, 8 ],
[ 3, 4, 9 ],
[ 4, 5, 10 ],
[ 1, 6, 7 ],
[ 2, 7, 8 ],
[ 3, 8, 9 ],
[ 4, 9, 10 ],
[ 5, 6, 10 ],
[ 6, 7, 11 ],
[ 7, 8, 11 ],
[ 8, 9, 11 ],
[ 9, 10, 11 ],
[ 6, 10, 11 ],
];
return VERTEX_MAP.map((vs) => find_dodeca_vertex(...vs.map((v) => dd[v])));
} }
function dodecahedron_colours(vertices, left) { // p is the permutation of the first face
const PARTITION = [
function dodecahedron_colours(vertices, p) {
const LEFT_PART = [
1, 2, 3, 4, 5, 3, 4, 5, 1, 2, 5, 1, 2, 3, 4, 2, 3, 4, 5, 1, 1, 2, 3, 4, 5, 3, 4, 5, 1, 2, 5, 1, 2, 3, 4, 2, 3, 4, 5, 1,
]; ];
const colours = { 1: [], 2: [], 3: [], 4: [], 5: [] }; const RIGHT_PART = [
1, 2, 3, 4, 5, 4, 5, 1, 2, 3, 3, 4, 5, 1, 2, 1, 2, 3, 4, 5,
];
const part = LEFT_PART;
const colours = {};
for( let i = 0; i < 20; i++ ) { for( let i = 0; i < 20; i++ ) {
colours[PARTITION[i]].push(vertices[i]); const v = vertices[i];
const colour = p[part[i] - 1];
colours[v] = colour;
} }
return colours; return colours;
} }
// p is the permutation of the first face
function colour_one_dodecahedron(faces, face, node, p) {
const dd = face_plus_to_dodecahedron(faces, face, node);
const vertices = dodecahedron_vertices(dd);
return dodecahedron_colours(vertices, p);
}
@ -502,9 +522,9 @@ function make_120cell_cells(faces) {
//console.log(`added dodeca ${fp}`); //console.log(`added dodeca ${fp}`);
const d = { const d = {
id: i, id: i,
faces: dd faces: dd,
nodes: dodecahedron_vertices(dd),
} }
dodeca_nodes(d);
dodecas.push(d); dodecas.push(d);
i += 1; i += 1;
seen[fp] = 1; seen[fp] = 1;