Stuck an abstraction between permutations and real coordinates for
the 600-cell so that I can label them
This commit is contained in:
Mike Lynch
parent
bee04c7e65
commit
0fdf8a40e4
@ -324,22 +324,10 @@ function find_peers(nodesid, seen, n, d) {
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}
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}
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function peer(n1, n2, d) {
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const d2 = dist2(n1, n2);
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const EPSILON = 0.01;
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function partition_from_node(nodesid, start, d) {
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return Math.abs(d2 - d ** 2) < EPSILON;
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const group = [];
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const looping = true;
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let ns = find_peers(nodesid, group, start, d);
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console.log(`0 ${ns}`);
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let i = 1;
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while( ns.length > 0 && i < ns.length ) {
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group.push(...ns);
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ns = find_peers(nodesid, group, ns[i], d);
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console.log(`${i} ${ns}`);
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i++;
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}
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return group;
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}
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}
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@ -351,15 +339,27 @@ function partition_nodes_by_distance(nodes, d) {
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for( const node of nodes ) {
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for( const node of nodes ) {
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nodesid[node.id] = node;
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nodesid[node.id] = node;
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}
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}
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let tick = 0;
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while( Object.keys(nodesid).length > 0 ) {
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while( Object.keys(nodesid).length > 0 ) {
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const start = Object.keys(nodesid)[0];
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const start = Object.keys(nodesid)[0];
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console.log(`Start node = ${start}`);
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console.log(`Start node = ${start}`);
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const group = partition_from_node(nodesid, start, d);
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const group = [ start ];
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if( group.length < 1 ) {
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for( const n2 of Object.keys(nodesid) ) {
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console.log("something went wrong, empty neighbour group");
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console.log(`group [ ${group} ] / n2 ${n2}`);
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break;
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const n3 = [];
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if( !group.includes(n2) ) {
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console.log(`group: ${group}`);
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for( const g of group ) {
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if( peer(nodesid[g], nodesid[n2], d) ) {
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console.log(`Match`);
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//n3.push(n2);
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}
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}
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}
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}
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console.log(`n3 = ${n3}`);
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group.push(...n3);
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}
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process.exit();
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for( const g of group ) {
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for( const g of group ) {
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delete nodesid[g];
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delete nodesid[g];
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}
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}
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@ -387,5 +387,6 @@ const cell600 = () => {
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}
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}
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const nodes = make_600cell_vertices();
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197
polytopes.js
197
polytopes.js
@ -180,111 +180,126 @@ export const cell120 = () => {
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}
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}
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}
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}
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// Schoute's partition via https://arxiv.org/abs/1010.4353
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const partition600 = {
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"2,0,0,0": 1,
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"0,2,0,0": 1,
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"0,0,2,0": 1,
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"0,0,0,2": 1,
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"1,1,1,1": 1,
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"1,1,-1,-1": 1,
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"1,-1,1,-1": 1,
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"1,-1,-1,1": 1,
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"1,-1,-1,-1": 1,
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"1,-1,1,1": 1,
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"1,1,-1,1": 1,
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"1,1,1,-1": 1,
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"k,0,-t,-1": 2,
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"0,k,1,-t": 2,
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"t,-1,k,0": 2,
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"1,t,0,k": 2,
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"t,k,0,-1": 2,
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"1,0,k,t": 2,
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"k,-t,-1,0": 2,
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"0,1,-t,k": 2,
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"1,k,t,0": 2,
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"t,0,-1,k": 2,
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"0,t,-k,-1": 2,
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"k,-1,0,-t": 2,
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"t,0,1,k": 3,
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"0,t,-k,1": 3,
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"1,-k,-t,0": 3,
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"k,1,0,-t": 3,
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"0,k,1,t": 3,
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"t,1,-k,0": 3,
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"k,0,t,-1": 3,
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"1,-t,0,k": 3,
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"t,-k,0,-1": 3,
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"0,1,-t,-k": 3,
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"1,0,-k,t": 3,
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"k,t,1,0": 3,
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"t,0,-1,k": 4,
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"0,t,k,-1": 4,
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"1,-k,t,0": 4,
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"k,1,0,t": 4,
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"t,1,k,0": 4,
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"0,k,-1,-t": 4,
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"1,-t,0,-k": 4,
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"k,0,-t,1": 4,
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"0,1,t,k": 4,
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"t,-k,0,1": 4,
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"k,t,-1,0": 4,
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"1,0,k,-t": 4,
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"k,0,t,1": 5,
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"0,k,-1,t": 5,
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"t,-1,-k,0": 5,
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"1,t,0,-k": 5,
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"1,0,-k,-t": 5,
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"t,k,0,1": 5,
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"0,1,t,-k": 5,
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"k,-t,1,0": 5,
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"t,0,1,-k": 5,
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"1,k,-t,0": 5,
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"k,-1,0,t": 5,
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"0,t,k,1": 5
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};
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// permute unique indices ->
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// use these to label nodes ->
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// assign actual values to indices ->
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function map_coord(i, coords, values) {
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if( i >= 0 ) {
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return values[coords[i]];
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}
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return -values[coords[-i]];
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}
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function make_600cell_vertices() {
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function make_600cell_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const coords = {
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0: '0',
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1: '1',
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2: '2',
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3: 't',
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4: 'k'
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};
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const t = 0.5 * (1 + Math.sqrt(5));
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const values = {
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'0': 0,
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'1': 1,
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'2': 2,
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't': t,
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'k': 1 / t
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};
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const nodes = [
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const nodes = [
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PERMUTE.coordinates([0, 0, 0, 2], 0),
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PERMUTE.coordinates([0, 0, 0, 2], ),
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PERMUTE.coordinates([1, 1, 1, 1], 1),
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PERMUTE.coordinates([1, 1, 1, 1], 0),
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PERMUTE.coordinates([phi, 1, 1 / phi, 0], 1, true)
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PERMUTE.coordinates([3, 1, 4, 0], 1, true)
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].flat();
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].flat();
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for( const n of nodes ) {
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for( const a of [ 'x', 'y', 'z', 'w'] ) {
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n[a] = map_coord(n[a], coords, values);
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}
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}
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index_nodes(nodes);
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index_nodes(nodes);
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const groups = partition_nodes_by_distance(nodes, 2);
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//const groups = partition_nodes_by_distance(nodes, 2);
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scale_nodes(nodes, 0.75);
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scale_nodes(nodes, 0.75);
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return nodes;
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return nodes;
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}
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}
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// Trying to do this with an algorithm, not just a lookup table.
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// I think that all of the vertices which belong to the same 24-cell group
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// are 2 units apart.
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function partition_nodes_by_distance_bad(nodes, d) {
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const groups = [];
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const EPSILON = 0.002;
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for( const n1 of nodes ) {
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let matched = false;
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for( const group of groups ) {
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for( const n2 of group ) {
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const d2 = dist2(n1, n2);
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// console.log(`comparing ${n1.id} ${n2.id}`);
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// console.log(n1);
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// console.log(n2);
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// console.log(`${d2} ${Math.abs(d2 - d**2)}`);
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if( Math.abs(d2 - d ** 2) < EPSILON ) {
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group.push(n1);
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matched = true;
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// console.log(`Matched ${n1.id} ${n2.id} ${d2}`);
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break;
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}
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}
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if( matched ) {
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break;
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}
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}
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if(! matched ) {
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// console.log(`unmatched node ${n1.id}`);
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groups.push([ n1 ]);
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}
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}
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console.log(`Build ${groups.length} groups`);
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console.log(groups);
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return groups;
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}
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// find all nodes in nodesid which are d away from n (and are not n)
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function nodes_by_distance(nodesid, n, d) {
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const EPSILON = 0.02;
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const neighbours = Object.keys(nodesid).filter((n1id) => {
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if( n1id !== n.id ) {
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const d2 = dist2(nodesid[n1id], nodesid[n]);
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console.log(`${n} ${n1id} ${d2}`);
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return Math.abs(d2 - d ** 2) < EPSILON;
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} else {
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return false;
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}
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});
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console.log(`neighbours at ${d} ${neighbours}`);
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return neighbours;
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}
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function partition_nodes_by_distance(nodes, d) {
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const groups = [];
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const nodesid = {};
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const EPSILON = 0.02;
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for( const node of nodes ) {
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nodesid[node.id] = node;
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}
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while( Object.keys(nodesid).length > 0 ) {
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const start = Object.keys(nodesid)[0];
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const group = [ start ];
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const neighbours = nodes_by_distance(nodesid, n, d).filter((n2) => !(n2 in group));
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if( neighbours ) {
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group.push(...neighbours);
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}
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const group = partition_r(nodesid, [ start ], start, d);
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console.log(group);
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for( const g of group ) {
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delete nodesid[g];
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}
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groups.push(group);
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}
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}
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