cellindex.js

@@ -104,12 +104,16 @@ export const LAYERS120 =  {
 		163,219,271,223,167]
 };
 
+// just one for now
+
 export const CELL120_CELL5 = {
-    "1": [ 258, 1, 510, 304, 431 ],
+    "1": [ 1, 258, 304, 431, 510 ],
-    "2": [ 185, 93, 222, 295, 372 ],
+    "2": [ 1, 260, 302, 427, 506 ],
-}
+    "3": [1, 264, 298, 435, 514],
-
+    "4": [1, 330, 334, 387, 391],
-
+    "5": [1, 491, 503, 574, 578],
+    "6": [1, 495, 499, 570, 582 ],
+};
 
 // Schoute's partition via https://arxiv.org/abs/1010.4353
 

explore_120cell.js

@@ -1,24 +1,10 @@
 
-// TODO - try visualising the 5-cells from a vertex on the layered 120-cell
-// and get an intuition for how they work with the dodecahedral structure
-
-// Another new approach -
-// pick a starting 5-cell
-// look at the neighbours on the 120-cell of all of its 5 vertices
-// try to find abother 5-cell with these neighbours
-// if there's only one, add that to the list and keep going
-// if there's more than one, are they disjoint with each other?
 
 import * as POLYTOPES from './polytopes.js';
 
 // exploring more inscriptions of the 120-cell
 
 
-function choice(a) {
-    const r = Math.floor(Math.random() * a.length);
-    return a[r];
-}
-
 export function nodes_links(links, nodeid) {
     return links.filter((l) => l.source === nodeid || l.target === nodeid);
 }
@@ -114,6 +100,11 @@ export function chord_survey() {
     }
 }
 
+// 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 ) {
@@ -125,13 +116,13 @@ function overlap(c1, c2) {
 }
 
 
-export function gather_5cells(cell120) {
+export function gather_5cells() {
+    const cell120 = POLYTOPES.cell120_inscribed();
     const CHORD5 = round_dist(Math.sqrt(2.5));
     const bins = [];
-    const all = [];
     cell120.nodes.filter((n) => n.label === 1).map((n) => {
-        const cells = [ ];
         const g = distance_group(cell120, n, CHORD5);
+        const cells = [ ];
         for( const pair of g ) {
             let seen = false;
             for( const cell of cells ) {
@@ -155,163 +146,26 @@ export function gather_5cells(cell120) {
                 cells.push(cell);
            }
         }
-        all.push(...cells);
+        //console.log(`From ${n.id}`);
-   });
+        //console.log(cells);
-    return all;
-}
-
-function audit_5cells(cells) {
-    // this verifies that for each label (a 600-cell set), each of its 
-    // vertices is in exactly 7 5-cells. It checks out.
-    
-    ['1','2','3','4','5'].map((l) => {
-        const sets = {};
         for( const cell of cells ) {
-            const lv = cell[l];
+            let binned = false;
-            if( !(lv in sets) ) {
+            for( const bin of bins ) {
-                sets[lv] = [];
+                const overlaps = bin.filter((b) => overlap(b, cell));
+                if( overlaps.length === 0 ) {
+                    bin.push(cell);
+                    binned = true;
+                    break;
                 }
-            sets[lv].push(cell);
             }
-        for( const lv in sets ) {
+            if( !binned ) {
-            const ok = ( sets[lv].length === 7 ) ? 'ok' : 'miss';
+                console.log(`new bin for ${JSON.stringify(cell)}`);
-            console.log(`${l},${lv},${sets[lv].length},${ok}`);
+                bins.push([ cell ]);
             }
-    });
+        }
+        //console.log(bins);
+    })
+    ;
 }
 
-function try_120_5_cells_fails(cell120, cells, l) {
+gather_5cells();
-    // iterate over every vertex in the 600-cell defined by label l,
-    // get all 7 5-cells including that vertex, and add them if they are
-    // disjoint with what we already have
-
-    // this always runs out of disjoint nodes early
-
-    const vertices = cell120.nodes.filter((n) => n.label === l);
-
-    const cellset = [];
-    for( const v of vertices ) {
-        console.log(`Vertex ${v.id}`);
-        const vcells = cells.filter((c) => c[l] === v.id);
-        const overlap_any = (cs, c) => {
-            for( const seen of cs ) {
-                if( overlap(seen, c) ) {
-                    console.log("overlap");
-                    console.log(c);
-                    return true;
- 
-                }
-            }
-            return false;
-        }
-        const disjoint = vcells.filter((c) => ! overlap_any(cellset, c));
-        console.log(`Found ${disjoint.length} disjoint cells`);
-        if( disjoint.length > 0 ) {
-            cellset.push(choice(disjoint));
-        }
-    }
-    console.log(`Found total of ${cellset.length} disjoint cells`);
-    //console.log(cellset);
-}
-
-function overlap_any(cs, c) {
-    for( const seen of cs ) {
-        if( overlap(seen, c) ) {
-            return true;
-        }
-    }
-    return false;
-}
-
-
-function explore_disjoint(cell120, all5, l) {
-    const a = all5[0];
-
-    const overlaps = all5.filter((c) => overlap(c, a));
-
-    console.log(a);
-
-    console.log(overlaps.length);
-    console.log(overlaps);
-}
-
-// select a five-cell from a starting vertex v
-// find a neighbor of v vn on its 600 cell, find all of the 5-cells which include
-// vn. Then see if we can find any from that set which are similiar neighbours to 
-// the other four vertices in the first 5-cell 
-
-// the idea is that the 600-cells are a guide to finding the right subset of 
-// 5-cells 
-
-function neighbours600(cell120, vid) {
-    const v = cell120.nodes.filter((node) => node.id === vid)[0];
-    const label = v.label; 
-    const links = cell120.links.filter((l) => {
-        return l.label === v.label && (l.source === v.id || l.target == v.id );
-    });
-    const nodes = links.map((l) => {
-        if( l.source === v.id ) {
-            return l.target;
-        } else {
-            return l.source;
-        }
-    });
-    return nodes;
-}
-
-function cell120node(cell120, nid) {
-    return cell120.nodes.filter((n) => n.id === nid)[0];
-}
-
-function node_dist(cell120, aid, bid) {
-    const a = cell120node(cell120, aid);
-    const b = cell120node(cell120, bid);
-    return dist(a, b);
-}
-
-
-
-function follow_600(cell120, all5) {
-    const v = cell120.nodes[0];
-    console.log("Start vertex:");
-    console.log(v);
-    const v5s = all5.filter((c5) => c5[v.label] === v.id);
-    console.log(`Vertex ${v.id} belongs to these 5-cells:`);
-    console.log(v5s);
-    const n600s = neighbours600(cell120, v.id);
-    const n600id = n600s[0];
-    const n600 = cell120node(cell120, n600id); 
-    console.log("One 600-cell neighbour:");
-    console.log(n600);
-    const DIST600 = round_dist(node_dist(cell120, v.id, n600id));
-    const nv5s = all5.filter((c5) => c5[v.label] === n600id);
-    console.log(`Vertex ${n600id} belongs to these 5-cells:`); 
-    console.log(nv5s);
-    console.log("Distances for each pair of 5-cells from the two sets:");
-    for( const v5a of v5s ) {
-        for( const v5b of nv5s ) {
-            let match = true;
-            const d = {};
-            for( const label in v5a ) {
-                d[label] = round_dist(node_dist(cell120, v5a[label], v5b[label]));
-                if( d[label] != DIST600 ) {
-                    match = false;
-                }
-            }
-            if( match ) {
-                console.log("--- pair ---");
-                console.log(v5a);
-                console.log(v5b);
-            }
-        }
-    }
-}
-
-
-
-
-const cell120 = POLYTOPES.cell120_inscribed();
-const all5 = gather_5cells(cell120);
-
-follow_600(cell120, all5);
-

gui.js

@@ -28,10 +28,9 @@ const DEFAULTS = {
 
 class FourDGUI {
 
-	constructor(funcs) {
+	constructor(shapes, changeShape, setColor, setBackground, setNodeOpacity,setLinkOpacity, setVisibility, showDocs) {
-                this.shapes = funcs.shapes;
 		this.gui = new GUI();
-		const SHAPE_NAMES = this.shapes.map((s) => s.name);
+		const SHAPE_NAMES = shapes.map((s) => s.name);
 
 		this.parseLinkParams();
 		const guiObj = this;
@@ -56,52 +55,41 @@ class FourDGUI {
 			captions: true,
 			dtheta: this.link['dtheta'],
 			dpsi: this.link['dpsi'],
-			"copy link": function () { guiObj.copyUrl() },
+			"copy link": function () { guiObj.copyUrl() }
 		};
-		if( funcs.extras ) {
-    		    for( const label in funcs.extras ) {
-    		        console.log(label);
-    		        console.log(funcs.extras[label]);
-    		        this.params[label] = funcs.extras[label];
-    		    }
-		}
 		let options_ctrl;
 		this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
-			const options = this.getShapeOptions(shape);
+			const options = this.getShapeOptions(shapes, shape);
 			options_ctrl = options_ctrl.options(options).onChange((option) => {
-				funcs.setVisibility(option)
+				setVisibility(option)
 			});
 			options_ctrl.setValue(options[0])
-			funcs.changeShape(shape)
+			changeShape(shape)
 		});
-		const options = this.getShapeOptions(this.params['shape']);
+		const options = this.getShapeOptions(shapes, this.params['shape']);
 		options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
-			funcs.setVisibility(option)
+			setVisibility(option)
 		});
 		this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
 		this.gui.add(this.params, 'zoom', 0.1, 2.0);
 		this.gui.add(this.params, 'nodesize', 0, 1.5);
-		this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(funcs.setNodeOpacity);
+		this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
 		this.gui.add(this.params, 'linksize', 0, 2);
-		console.log(funcs.setLinkOpacity);
+		console.log(setLinkOpacity);
-		this.gui.add(this.params, 'linkopacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, true));
+		this.gui.add(this.params, 'linkopacity', 0, 1).onChange((v) => setLinkOpacity(v, true));
-		this.gui.add(this.params, 'link2opacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, false));
+		this.gui.add(this.params, 'link2opacity', 0, 1).onChange((v) => setLinkOpacity(v, false));
-		this.gui.addColor(this.params, 'color').onChange(funcs.setColor);
+		this.gui.addColor(this.params, 'color').onChange(setColor);
-		this.gui.addColor(this.params, 'background').onChange(funcs.setBackground);
+		this.gui.addColor(this.params, 'background').onChange(setBackground);
 		this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
 		this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
-		this.gui.add(this.params, 'captions').onChange(this.showDocs);
+		this.gui.add(this.params, 'captions').onChange(showDocs);
 		this.gui.add(this.params, 'damping');
 		this.gui.add(this.params, 'copy link');
-		if( funcs.extras ) {
+
-     		    for( const label in funcs.extras ) {
-    		        this.gui.add(this.params, label);
-     		    }
-                }
 	}
 
-	getShapeOptions(shape) {
+	getShapeOptions(shapes, shape) {
-		const spec = this.shapes.filter((s) => s.name === shape);
+		const spec = shapes.filter((s) => s.name === shape);
 		if( spec && spec[0].options ) {
 			return spec[0].options.map((o) => o.name);
 		} else {

main.js

@@ -200,20 +200,14 @@ function setVisibility(option_name) {
 
 
 gui = new FourDGUI(
-    {
+	STRUCTURES,
-	shapes: STRUCTURES,
+	changeShape,
-	changeShape: changeShape,
+	setColors,
-	setColors: setColors,
+	setBackground,
-	setBackground: setBackground,
+	setNodeOpacity,
-	setNodeOpacity: setNodeOpacity,
+	setLinkOpacity,
-	setLinkOpacity: setLinkOpacity,
+	setVisibility,
-	setVisibility: setVisibility,
+	showDocs
-	showDocs: showDocs,
-	extras: {
-    	    "Show an alert": function() { alert("hi there") },
-    	    "Show a different one": function() { alert('yowza')},
-	},
-    }
 );
 
 // these are here to pick up colour settings from the URL params

polytopes.js

@@ -463,27 +463,19 @@ export const cell120_inscribed = () => {
 
 export const cell120_inscribed_cell5 = () => {
 	const nodes  = make_120cell_vertices();
-	//const links = auto_detect_edges(nodes, 4);
+	const links = auto_detect_edges(nodes, 4);
 
   	for( const cstr in CELLINDEX.INDEX120 ) {
 		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
 	}
 
-	//links.map((l) => l.label = 0);
+	links.map((l) => l.label = 0);
-
-        const links = [];
-
-	for( const p of [ 1, 2 ]) {
-		const nodes600 = nodes.filter((n) => n.label === p);
-		const links600 = auto_detect_edges(nodes600, 12);
-		links600.map((l) => l.label = p);
-		links.push(...links600);
-	}
 
         for( const c5 in CELLINDEX.CELL120_CELL5 ) {
             const nodes5 = nodes.filter((n) => CELLINDEX.CELL120_CELL5[c5].includes(n.id));
+            console.log(`node5 = ${nodes5}`);
             const links5 = auto_detect_edges(nodes5, 4);
-            links5.map((l) => l.label = 0);
+            links5.map((l) => l.label = c5);
             links.push(...links5);
         }
 
@@ -492,7 +484,8 @@ export const cell120_inscribed_cell5 = () => {
 		nodes: nodes,
 		links: links,
 		options: [
-		    { name: "5-cells", links: [ 0, 1, 2, 3, 4, 5, 6 ] },
+			{ name: "none", links: [ 0 ]},
+			{ name: "one inscribed 5-cell", links: [ 0, 1 ] },
 		],
 		description: `The 120-cell with one of its 5-cells.`,
 	}