Added dodecahedron with compound of five cubes, refactored the
inscribed polytopes into one functionfeature-3d-shapes
Mike Lynch
parent
6e8cfa8763
commit
c8ce499b22
4
gui.js
4
gui.js
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@ -7,7 +7,7 @@ const DEFAULTS = {
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nodesize: 1.25,
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linkopacity: 0.5,
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link2opacity: 0.5,
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shape: '120-cell',
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shape: 'five-cubes',
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inscribed: false,
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inscribe_all: false,
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color: 0x3293a9,
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@ -45,7 +45,7 @@ class FourDGUI {
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};
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this.gui.add(this.params, 'shape',
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[ 'dodecahedron', '5-cell', '16-cell', 'tesseract',
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[ 'dodecahedron', 'five-cubes', '5-cell', '16-cell', 'tesseract',
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'24-cell', '600-cell', '120-cell' ]
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).onChange(changeShape)
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this.gui.add(this.params, 'inscribed').onChange(changeShape);
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3
main.js
3
main.js
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@ -65,6 +65,7 @@ const STRUCTURES = {
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'tesseract': POLYTOPES.tesseract(),
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'24-cell': POLYTOPES.cell24(),
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'dodecahedron': POLYTOPES.dodecahedron(),
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'five-cubes': POLYTOPES.five_cubes(),
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'120-cell': POLYTOPES.cell120(),
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'600-cell': POLYTOPES.cell600(),
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};
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@ -75,6 +76,7 @@ const INSCRIBED = {
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'120-cell': POLYTOPES.cell120_inscribed(),
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'600-cell': POLYTOPES.cell600_inscribed(),
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'dodecahedron': POLYTOPES.dodecahedron_inscribed(),
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'five-cubes': POLYTOPES.five_cubes_inscribed(),
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};
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const ALL_INSCRIBED = {
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@ -83,6 +85,7 @@ const ALL_INSCRIBED = {
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'120-cell': POLYTOPES.cell120_all_inscribed(),
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'600-cell': POLYTOPES.cell600_all_inscribed(),
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'dodecahedron': POLYTOPES.dodecahedron_all_inscribed(),
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'five-cubes': POLYTOPES.five_cubes_all_inscribed(),
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}
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let shape = false;
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111
polytopes.js
111
polytopes.js
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@ -327,6 +327,8 @@ function make_120cell_vertices() {
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].flat();
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index_nodes(nodes);
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scale_nodes(nodes, 0.5);
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label_120cell(nodes);
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return nodes;
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}
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@ -413,20 +415,18 @@ export const cell120 = () => {
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}
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const cell120_some_inscribed = (ps) => {
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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label_120cell(nodes);
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const inscribed_polytope = (vertex_fn, edges, inscr_edges, parts) => {
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const nodes = vertex_fn();
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const links = auto_detect_edges(nodes, edges);
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const all_links = links;
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all_links.map((l) => l.label = 0);
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for( const p of ps) {
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const nodes600 = nodes.filter((n) => n.label === p);
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const links600 = auto_detect_edges(nodes600, 12);
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links600.map((l) => l.label = p);
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all_links.push(...links600);
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for( const p of parts ) {
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const nodes_in = nodes.filter((n) => n.label === p);
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const links_in = auto_detect_edges(nodes_in, inscr_edges);
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links_in.map((l) => l.label = p);
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all_links.push(...links_in);
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}
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return {
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@ -439,8 +439,13 @@ const cell120_some_inscribed = (ps) => {
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}
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}
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export const cell120_inscribed = () => cell120_some_inscribed([1]);
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export const cell120_all_inscribed = () => cell120_some_inscribed([1,2,3,4,5]);
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export const cell120_inscribed = () => inscribed_polytope(
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make_120cell_vertices, 4, 12, [1]
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);
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export const cell120_all_inscribed = () => inscribed_polytope(
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make_120cell_vertices, 4, 12, [1,2,3,4,5]
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);
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// Schoute's partition via https://arxiv.org/abs/1010.4353
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@ -628,36 +633,12 @@ export const cell600 = () => {
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}
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}
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const cell600_some_inscribed = (ps) => {
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const nodes = make_600cell_vertices();
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const links = auto_detect_edges(nodes, 12);
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const all_links = links;
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all_links.map((l) => l.label = 0);
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for( const p of ps) {
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const nodes24 = nodes.filter((n) => n.label === p);
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const links24 = auto_detect_edges(nodes24, 8);
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links24.map((l) => l.label = p);
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all_links.push(...links24);
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}
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return {
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nodes: nodes,
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links: all_links,
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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}
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}
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export const cell600_inscribed = () => cell600_some_inscribed([1]);
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export const cell600_all_inscribed = () => cell600_some_inscribed([1,2,3,4,5]);
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export const cell600_inscribed = () => inscribed_polytope(
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make_600cell_vertices, 12, 8, [1]
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);
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export const cell600_all_inscribed = () => inscribed_polytope(
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make_600cell_vertices, 12, 8, [1,2,3,4,5]
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);
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function make_dodecahedron_vertices() {
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@ -708,18 +689,42 @@ export const dodecahedron = () => {
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}
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}
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const dodecahedron_some_inscribed = (ps) => {
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export const dodecahedron_inscribed = () => inscribed_polytope(
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make_dodecahedron_vertices, 3, 3, [1]
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);
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export const dodecahedron_all_inscribed = () => inscribed_polytope(
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make_dodecahedron_vertices, 3, 3, [1,2,3,4,5]
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);
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// this can't be done with inscribed_polytope because each vertex
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// belongs to two cubes
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export const dodecahedron_five_cubes = (parts) => {
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const nodes = make_dodecahedron_vertices();
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const links = auto_detect_edges(nodes, 3);
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const all_links = links;
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all_links.map((l) => l.label = 0);
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for( const p of ps) {
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const tetran = nodes.filter((n) => n.label === p);
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const tetral = auto_detect_edges(tetran, 3);
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tetral.map((l) => l.label = p);
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all_links.push(...tetral);
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}
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const CUBES = {
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1: [ 1, 2, 3, 4, 5, 6, 7, 8 ],
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2: [ 4, 5, 10, 11, 13, 16, 17, 20],
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3: [ 2, 7, 9, 12, 13, 16, 18, 19],
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4: [ 1, 8, 10, 11, 14, 15, 18, 19],
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5: [ 3, 6, 9, 12, 14, 15, 17, 20]
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};
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if( parts.length > 0 ) {
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// console.log(parts);
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//console.log(parts.map(String));
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//nodes.map((n) => n.label = 0);
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for( const label of parts.map(String) ) {
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console.log(`label = ${label}`);
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const cube = nodes.filter((n) => CUBES[label].includes(n.id));
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const cubel = auto_detect_edges(cube, 3);
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cubel.map((l) => l.label = Number(label));
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all_links.push(...cubel);
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}
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}
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return {
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nodes: nodes,
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@ -727,11 +732,11 @@ const dodecahedron_some_inscribed = (ps) => {
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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}
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}
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}
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export const dodecahedron_inscribed = () => dodecahedron_some_inscribed([1]);
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export const dodecahedron_all_inscribed = () => dodecahedron_some_inscribed([1,2,3,4,5]);
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export const five_cubes = () => dodecahedron_five_cubes([]);
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export const five_cubes_inscribed = () => dodecahedron_five_cubes([1]);
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export const five_cubes_all_inscribed = () => dodecahedron_five_cubes([1,2,3,4,5]);
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36
testbed.js
36
testbed.js
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@ -913,16 +913,32 @@ function make_dodecahedron_vertices() {
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const phiinv = 1 / phi;
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const nodes = [
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{ x: 1, y: 1, z: 1, w: 0 },
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{ x: 1, y: 1, z: -1, w: 0 },
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{ x: 1, y: -1, z: 1, w: 0 },
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{ x: 1, y: -1, z: -1, w: 0 },
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{ x: -1, y: 1, z: 1, w: 0 },
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{ x: -1, y: 1, z: -1, w: 0 },
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{ x: -1, y: -1, z: 1, w: 0 },
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{ x: -1, y: -1, z: -1, w: 0 }
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].flat();
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scale_nodes(nodes, 0.5);
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{ x: 1, y: 1, z: 1, w: 0, label: 4 },
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{ x: 1, y: 1, z: -1, w: 0, label: 3 },
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{ x: 1, y: -1, z: 1, w: 0, label: 3 },
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{ x: 1, y: -1, z: -1, w: 0, label: 2 },
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{ x: -1, y: 1, z: 1, w: 0, label: 3 },
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{ x: -1, y: 1, z: -1, w: 0, label: 1 },
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{ x: -1, y: -1, z: 1, w: 0, label: 5 },
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{ x: -1, y: -1, z: -1, w: 0, label: 3 },
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{ x: 0, y: phi, z: phiinv, w: 0, label: 5 },
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{ x: 0, y: phi, z: -phiinv, w: 0 , label: 2 },
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{ x: 0, y: -phi, z: phiinv, w: 0, label: 4 },
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{ x: 0, y: -phi, z: -phiinv, w: 0 , label: 1 },
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{ x: phiinv, y: 0, z: phi, w: 0 , label: 2},
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{ x: phiinv, y: 0, z: -phi, w: 0 , label: 4},
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{ x: -phiinv, y: 0, z: phi, w: 0 , label: 1},
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{ x: -phiinv, y: 0, z: -phi, w: 0 , label: 5},
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{ x: phi, y: phiinv, z:0, w: 0 , label: 1},
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{ x: phi, y: -phiinv, z:0, w: 0 , label: 5},
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{ x: -phi, y: phiinv, z:0, w: 0 , label: 4},
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{ x: -phi, y: -phiinv, z:0, w: 0 , label: 2},
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];
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index_nodes(nodes);
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return nodes;
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}
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