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Added dodecahedron with compound of five cubes, refactored the 

inscribed polytopes into one function
feature-3d-shapes
Mike Lynch 2023-09-16 17:05:07 +10:00
parent 6e8cfa8763
commit c8ce499b22
4 changed files with 89 additions and 65 deletions
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4
gui.js
View File

@ -7,7 +7,7 @@ const DEFAULTS = {
nodesize: 1.25, nodesize: 1.25,
linkopacity: 0.5, linkopacity: 0.5,
link2opacity: 0.5, link2opacity: 0.5,
shape: '120-cell', shape: 'five-cubes',
inscribed: false, inscribed: false,
inscribe_all: false, inscribe_all: false,
color: 0x3293a9, color: 0x3293a9,
@ -45,7 +45,7 @@ class FourDGUI {
}; };
this.gui.add(this.params, 'shape', this.gui.add(this.params, 'shape',
[ 'dodecahedron', '5-cell', '16-cell', 'tesseract', [ 'dodecahedron', 'five-cubes', '5-cell', '16-cell', 'tesseract',
'24-cell', '600-cell', '120-cell' ] '24-cell', '600-cell', '120-cell' ]
).onChange(changeShape) ).onChange(changeShape)
this.gui.add(this.params, 'inscribed').onChange(changeShape); this.gui.add(this.params, 'inscribed').onChange(changeShape);

3
main.js
View File

@ -65,6 +65,7 @@ const STRUCTURES = {
'tesseract': POLYTOPES.tesseract(), 'tesseract': POLYTOPES.tesseract(),
'24-cell': POLYTOPES.cell24(), '24-cell': POLYTOPES.cell24(),
'dodecahedron': POLYTOPES.dodecahedron(), 'dodecahedron': POLYTOPES.dodecahedron(),
'five-cubes': POLYTOPES.five_cubes(),
'120-cell': POLYTOPES.cell120(), '120-cell': POLYTOPES.cell120(),
'600-cell': POLYTOPES.cell600(), '600-cell': POLYTOPES.cell600(),
}; };
@ -75,6 +76,7 @@ const INSCRIBED = {
'120-cell': POLYTOPES.cell120_inscribed(), '120-cell': POLYTOPES.cell120_inscribed(),
'600-cell': POLYTOPES.cell600_inscribed(), '600-cell': POLYTOPES.cell600_inscribed(),
'dodecahedron': POLYTOPES.dodecahedron_inscribed(), 'dodecahedron': POLYTOPES.dodecahedron_inscribed(),
'five-cubes': POLYTOPES.five_cubes_inscribed(),
}; };
const ALL_INSCRIBED = { const ALL_INSCRIBED = {
@ -83,6 +85,7 @@ const ALL_INSCRIBED = {
'120-cell': POLYTOPES.cell120_all_inscribed(), '120-cell': POLYTOPES.cell120_all_inscribed(),
'600-cell': POLYTOPES.cell600_all_inscribed(), '600-cell': POLYTOPES.cell600_all_inscribed(),
'dodecahedron': POLYTOPES.dodecahedron_all_inscribed(), 'dodecahedron': POLYTOPES.dodecahedron_all_inscribed(),
'five-cubes': POLYTOPES.five_cubes_all_inscribed(),
} }
let shape = false; let shape = false;

109
polytopes.js
View File

@ -327,6 +327,8 @@ function make_120cell_vertices() {
].flat(); ].flat();
index_nodes(nodes); index_nodes(nodes);
scale_nodes(nodes, 0.5); scale_nodes(nodes, 0.5);
label_120cell(nodes);
return nodes; return nodes;
} }
@ -413,20 +415,18 @@ export const cell120 = () => {
} }
const cell120_some_inscribed = (ps) => { const inscribed_polytope = (vertex_fn, edges, inscr_edges, parts) => {
const nodes = make_120cell_vertices(); const nodes = vertex_fn();
const links = auto_detect_edges(nodes, 4); const links = auto_detect_edges(nodes, edges);
label_120cell(nodes);
const all_links = links; const all_links = links;
all_links.map((l) => l.label = 0); all_links.map((l) => l.label = 0);
for( const p of ps) { for( const p of parts ) {
const nodes600 = nodes.filter((n) => n.label === p); const nodes_in = nodes.filter((n) => n.label === p);
const links600 = auto_detect_edges(nodes600, 12); const links_in = auto_detect_edges(nodes_in, inscr_edges);
links600.map((l) => l.label = p); links_in.map((l) => l.label = p);
all_links.push(...links600); all_links.push(...links_in);
} }
return { return {
@ -439,8 +439,13 @@ const cell120_some_inscribed = (ps) => {
} }
} }
export const cell120_inscribed = () => cell120_some_inscribed([1]);
export const cell120_all_inscribed = () => cell120_some_inscribed([1,2,3,4,5]); export const cell120_inscribed = () => inscribed_polytope(
make_120cell_vertices, 4, 12, [1]
);
export const cell120_all_inscribed = () => inscribed_polytope(
make_120cell_vertices, 4, 12, [1,2,3,4,5]
);
// Schoute's partition via https://arxiv.org/abs/1010.4353 // Schoute's partition via https://arxiv.org/abs/1010.4353
@ -628,36 +633,12 @@ export const cell600 = () => {
} }
} }
export const cell600_inscribed = () => inscribed_polytope(
make_600cell_vertices, 12, 8, [1]
const cell600_some_inscribed = (ps) => { );
const nodes = make_600cell_vertices(); export const cell600_all_inscribed = () => inscribed_polytope(
const links = auto_detect_edges(nodes, 12); make_600cell_vertices, 12, 8, [1,2,3,4,5]
);
const all_links = links;
all_links.map((l) => l.label = 0);
for( const p of ps) {
const nodes24 = nodes.filter((n) => n.label === p);
const links24 = auto_detect_edges(nodes24, 8);
links24.map((l) => l.label = p);
all_links.push(...links24);
}
return {
nodes: nodes,
links: all_links,
geometry: {
node_size: 0.02,
link_size: 0.02
},
}
}
export const cell600_inscribed = () => cell600_some_inscribed([1]);
export const cell600_all_inscribed = () => cell600_some_inscribed([1,2,3,4,5]);
function make_dodecahedron_vertices() { function make_dodecahedron_vertices() {
@ -708,17 +689,41 @@ export const dodecahedron = () => {
} }
} }
const dodecahedron_some_inscribed = (ps) => { export const dodecahedron_inscribed = () => inscribed_polytope(
make_dodecahedron_vertices, 3, 3, [1]
);
export const dodecahedron_all_inscribed = () => inscribed_polytope(
make_dodecahedron_vertices, 3, 3, [1,2,3,4,5]
);
// this can't be done with inscribed_polytope because each vertex
// belongs to two cubes
export const dodecahedron_five_cubes = (parts) => {
const nodes = make_dodecahedron_vertices(); const nodes = make_dodecahedron_vertices();
const links = auto_detect_edges(nodes, 3); const links = auto_detect_edges(nodes, 3);
const all_links = links; const all_links = links;
all_links.map((l) => l.label = 0); all_links.map((l) => l.label = 0);
for( const p of ps) { const CUBES = {
const tetran = nodes.filter((n) => n.label === p); 1: [ 1, 2, 3, 4, 5, 6, 7, 8 ],
const tetral = auto_detect_edges(tetran, 3); 2: [ 4, 5, 10, 11, 13, 16, 17, 20],
tetral.map((l) => l.label = p); 3: [ 2, 7, 9, 12, 13, 16, 18, 19],
all_links.push(...tetral); 4: [ 1, 8, 10, 11, 14, 15, 18, 19],
5: [ 3, 6, 9, 12, 14, 15, 17, 20]
};
if( parts.length > 0 ) {
// console.log(parts);
//console.log(parts.map(String));
//nodes.map((n) => n.label = 0);
for( const label of parts.map(String) ) {
console.log(`label = ${label}`);
const cube = nodes.filter((n) => CUBES[label].includes(n.id));
const cubel = auto_detect_edges(cube, 3);
cubel.map((l) => l.label = Number(label));
all_links.push(...cubel);
}
} }
return { return {
@ -727,11 +732,11 @@ const dodecahedron_some_inscribed = (ps) => {
geometry: { geometry: {
node_size: 0.02, node_size: 0.02,
link_size: 0.02 link_size: 0.02
}, }
} }
} }
export const five_cubes = () => dodecahedron_five_cubes([]);
export const dodecahedron_inscribed = () => dodecahedron_some_inscribed([1]); export const five_cubes_inscribed = () => dodecahedron_five_cubes([1]);
export const dodecahedron_all_inscribed = () => dodecahedron_some_inscribed([1,2,3,4,5]); export const five_cubes_all_inscribed = () => dodecahedron_five_cubes([1,2,3,4,5]);

36
testbed.js
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@ -913,16 +913,32 @@ function make_dodecahedron_vertices() {
const phiinv = 1 / phi; const phiinv = 1 / phi;
const nodes = [ const nodes = [
{ x: 1, y: 1, z: 1, w: 0 }, { x: 1, y: 1, z: 1, w: 0, label: 4 },
{ x: 1, y: 1, z: -1, w: 0 }, { x: 1, y: 1, z: -1, w: 0, label: 3 },
{ x: 1, y: -1, z: 1, w: 0 }, { x: 1, y: -1, z: 1, w: 0, label: 3 },
{ x: 1, y: -1, z: -1, w: 0 }, { x: 1, y: -1, z: -1, w: 0, label: 2 },
{ x: -1, y: 1, z: 1, w: 0 },
{ x: -1, y: 1, z: -1, w: 0 }, { x: -1, y: 1, z: 1, w: 0, label: 3 },
{ x: -1, y: -1, z: 1, w: 0 }, { x: -1, y: 1, z: -1, w: 0, label: 1 },
{ x: -1, y: -1, z: -1, w: 0 } { x: -1, y: -1, z: 1, w: 0, label: 5 },
].flat(); { x: -1, y: -1, z: -1, w: 0, label: 3 },
scale_nodes(nodes, 0.5);
{ 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},
];
index_nodes(nodes);
return nodes; return nodes;
} }