fourdjs/explore_120cell.js

import * as POLYTOPES from './polytopes.js';

// exploring more inscriptions of the 120-cell


export function nodes_links(links, nodeid) {
    return links.filter((l) => l.source === nodeid || l.target === nodeid);
}


export function linked(links, n1, n2) {
    const ls = nodes_links(nodes_links(links, n1), n2);
    if( ls.length ) {
        return ls[0]
    } else {
        return false;
    }
}


function fingerprint(ids) {
    const sids = [...ids];
    sids.sort();
    return sids.join(',');
}

export function dist(n1, n2) {
    return Math.sqrt((n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2);
}


export function make_120cell() {
    const nodes = POLYTOPES.make_120cell_vertices();
    const links = POLYTOPES.auto_detect_edges(nodes, 4);
    return {
    	nodes: nodes,
    	links: links
    }
}

function round_dist(raw) {
    return Math.floor(raw * 100000) / 100000;
}

export function distance_groups(cell120) {
    // get list of other nodes by distance
    // sort them and dump them out
    const dists = {};

    cell120.nodes.map((n) => {
        const draw = dist(cell120.nodes[0], n);
        const dtrunc = round_dist(draw);
        if( !(dtrunc in dists) ) {
            dists[dtrunc] = [];
        }
        dists[dtrunc].push(n);
    });
    return dists; 
}

function distance_group(cell120, n0, chord) {
    const nodes = []
    cell120.nodes.map((n) => {
        const d = round_dist(dist(n0, n));
        if( d == chord ) {
            nodes.push(n);
        }
    });
    // filter and return those whose chord is also the same
    const equidistant = [];
    for( const n1 of nodes ) {
        for( const n2 of nodes ) {
            if( n2.id > n1.id ) {
                if( round_dist(dist(n1, n2)) == chord ) {
                    equidistant.push([n1, n2]);
                }
            }
        }
    }
    return equidistant;
}


export function chord_survey() {
    const cell120 = POLYTOPES.cell120_inscribed();

    const dgroups = distance_groups(cell120);

    const dists = Object.keys(dgroups);

    dists.sort();

    for( const d of dists ) {
        const g0 = dgroups[d][0];
        dgroups[d].map((g) => {
            console.log(`${g0.id}-${g.id}: ${round_dist(dist(g0, g))}`);
        });
    }
}

// how to proceed: start with the 120-cell that has five 600-cells inscribed
// in it. Take the 120 nodes from one of those 600-cells, and construct a 5-cell
// from each such that all of the vertices are on different 600-cells.

// collect them and output by label because every 5-cell is on all 5 600-cells

function overlap(c1, c2) {
    for( const l in c1 ) {
        if( c1[l] === c2[l] ) {
            return true;
        }
    }
    return false;
}


export function gather_5cells() {
    const cell120 = POLYTOPES.cell120_inscribed();
    const CHORD5 = round_dist(Math.sqrt(2.5));
    const bins = [];
    cell120.nodes.filter((n) => n.label === 1).map((n) => {
        const g = distance_group(cell120, n, CHORD5);
        const cells = [ ];
        for( const pair of g ) {
            let seen = false;
            for( const cell of cells ) {
                const c = Object.values(cell);
                if( c.includes(pair[0].id) || c.includes(pair[1].id) ) {
                    if( !c.includes(pair[0].id) ) { 
                        cell[pair[0].label] = pair[0].id;
                    }
                    if( !c.includes(pair[1].id) ) {
                        cell[pair[1].label] = pair[1].id;
                    }
                    seen = true;
                    break;
                }
            }
            if( !seen ) {
                const cell = {};
                cell[1]= n.id;
                cell[pair[0].label] = pair[0].id;
                cell[pair[1].label] = pair[1].id;
                cells.push(cell);
           }
        }
        //console.log(`From ${n.id}`);
        //console.log(cells);
        for( const cell of cells ) {
            let binned = false;
            for( const bin of bins ) {
                const overlaps = bin.filter((b) => overlap(b, cell));
                if( overlaps.length === 0 ) {
                    bin.push(cell);
                    binned = true;
                    break;
                }
            }
            if( !binned ) {
                console.log(`new bin for ${JSON.stringify(cell)}`);
                bins.push([ cell ]);
            }
        }
        //console.log(bins);
    })
    ;
}

gather_5cells();