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Hour of nutty hacking and it's labelling 105 nodes

experiments-120-cell
Mike Lynch 2023-08-06 13:41:01 +10:00
parent 62bc994788
commit c3766b749b
1 changed files with 92 additions and 24 deletions
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116
permute_testbed.js
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@ -373,21 +373,6 @@ function find_neighbours(chords, n) {
function label_subgraph(chords, label, n) {
const neighbours = find_neighbours(chords, n);
for( const n1 of neighbours ) {
if( n1.label === 0 ) {
n1.label = label;
console.log(`Added ${n1.id} to group ${label}`);
label_subgraph(chords, label, n1);
} else {
if( n1.label !== label ) {
console.log(`node ${n1.id} is already in group ${n1.label}`);
}
}
}
}
// 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
@ -418,7 +403,6 @@ function partition_nodes(pairs) {
// if neither of the pair was in a former group, start a new group
if( !already ) {
groups.push(new Set(pair));
console.log(`new group ${groups}`)
}
// collapse any groups which now have common elements
groups = collapse_groups(groups);
@ -479,7 +463,7 @@ function vector_angle(n1, n2, n3) {
return Math.acos(dp / ( v2.length() * v3.length()));
}
function neighbour_angles(chords, n) {
function neighbour_angles_orig(chords, n) {
const ns = find_neighbours(chords, n);
const angles = {};
for( let i = 0; i < ns.length - 1; i++ ) {
@ -497,15 +481,99 @@ function neighbour_angles(chords, n) {
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);
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
function label_120_partition_r(nodes, chords, label, origin, neighbours) {
console.log(`label_120_partition_r`);
console.log(origin);
console.log(neighbours.map((n) => n.id));
for( const n of neighbours ) {
if( n.label === 0 ) {
n.label = label;
console.log(`Added ${n.id} to group ${label}`);
// 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);
return label_120_partition_r(nodes, chords, label, n, icosa_n);
} else {
if( n.label !== label ) {
console.log(`node ${n.id} is already in group ${n.label}`);
return false;
}
}
}
}
// 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));
}
function node_by_id(nodes, nid) {
const ns = nodes.filter((n) => n.id === nid);
return ns[0];
}
const nodes = make_120cell_vertices();
const chords = find_all_chords(nodes)
const chord3 = chords["1.74806"];
const angle_groups = neighbour_angles(chord3, nodes[0]);
const pairs60 = angle_groups['60.000'];
// const chords = find_all_chords(nodes);
// const chord3 = chords["1.74806"]; // these are edges of the 600-cells;
// const pairs60 = neighbour_angles(chord3, nodes[0], "60.000");
// const icosas = partition_nodes(pairs60);