2c:null 2d:["$","title",null,{"children":"Stellating {7, 3} in Minkowski space | nanma80 | Observable"}] 32:T1399,getFaces = function(options = {}){ const group = new THREE.Group(); var faces = getFilteredFaces(zLimit); var showFaces = !convexHull; var edgeSize = 0.05; const faceMaterial = new THREE.MeshBasicMaterial( {color: faceColor, side: THREE.DoubleSide, transparent: false, opacity: 1}); const edgeMaterial = new THREE.LineBasicMaterial({color: convexHull ? convexHullColor : edgeColor } ); const highlightedEdgeMaterial = new THREE.LineBasicMaterial({color: highlightedEdgeColor } ); const highlightedFaceMaterial = new THREE.MeshBasicMaterial( {color: highlightedEdgeColor, side: THREE.DoubleSide, transparent: true, opacity: 0.3}); const coneMaterial = new THREE.MeshBasicMaterial( {color: coneColor, side: THREE.DoubleSide, transparent: true, opacity: 0.3}); var allStellatedEdges = []; var allStellatedVertices = []; faces.forEach(function(face) { var edges = face.map(function(v, i) { return [face[i], face[(i + 1) % face.length]] }); var stellatedEdges = edges.map(stellateEdge); var convexHullFace = []; // take convex hulls if(convexHull) { convexHullFace = getConvexHullFace(stellatedEdges); stellatedEdges = convexHullFace.map(function(v, i) { return [convexHullFace[i], convexHullFace[(i + 1) % convexHullFace.length]] }); } var stellatedVertices = stellatedEdges.map(function(e) { return e.map(function(v) { return new THREE.Vector3(v[1], v[2], -v[0]); }) }); if (showFaces) { var faceGeometry = new THREE.Geometry(); var vertices = (convexHull ? convexHullFace : face).map(function(v) { return new THREE.Vector3(v[1], v[2], -v[0]); }); faceGeometry.vertices = vertices; for(var i = 1; i <= faceGeometry.vertices.length - 2; i++) { faceGeometry.faces.push( new THREE.Face3( 0, i, i+1 ) ); } var mesh = new THREE.Mesh( faceGeometry, faceMaterial ); group.add(mesh); } for(var i = 0; i <= stellatedVertices.length - 1; i++) { const points = [stellatedVertices[i][0], stellatedVertices[i][1]]; const lineGeometry = new THREE.BufferGeometry().setFromPoints( points ); const line = new THREE.Line( lineGeometry, edgeMaterial ); const pointGeometry = new THREE.Geometry(); pointGeometry.vertices.push(stellatedVertices[i][0]); pointGeometry.vertices.push(stellatedVertices[i][1]); const pointMaterial = new THREE.PointsMaterial( { color: pointColor, size: 0.4} ); const threePoints = new THREE.Points( pointGeometry, pointMaterial ); group.add(line); group.add(threePoints); } if (highlightSomeFaces){ stellatedEdges.forEach(e => allStellatedVertices.push(...e)); allStellatedEdges.push(stellatedEdges); } }); if (showCones) { group.add(ConeFromTo(new THREE.Vector3(0, 0, coneSize), new THREE.Vector3(0, 0, 0), 0.1, coneMaterial)); group.add(ConeFromTo(new THREE.Vector3(0, 0, -coneSize), new THREE.Vector3(0, 0, 0), 0.1, coneMaterial)); } if (highlightSomeFaces && convexHull && allStellatedVertices.length > 0) { var highlightedVertex = allStellatedVertices.sort(function(a, b) {return vertexCost(a) - vertexCost(b) })[0]; var highlightedFaces = allStellatedEdges.filter(f => containsVertex(f, highlightedVertex)); highlightedFaces.forEach(function(stellatedEdges) { var stellatedVertices = stellatedEdges.map(function(e) { return e.map(function(v) { return new THREE.Vector3(v[1], v[2], -v[0]); }) }); for(var i = 0; i <= stellatedVertices.length - 1; i++) { const points = [stellatedVertices[i][0], stellatedVertices[i][1]]; const lineGeometry = new THREE.BufferGeometry().setFromPoints( points ); const line = new THREE.Line( lineGeometry, highlightedEdgeMaterial ); group.add(line); } var scalingFactor = 0.99; var stellatedVertices = stellatedEdges.map(function(e) { return e.map(function(v) { return new THREE.Vector3(v[1] * scalingFactor, v[2] * scalingFactor, -v[0] * scalingFactor); }) }); var faceGeometry = new THREE.Geometry(); faceGeometry.vertices = stellatedVertices.map(edge => edge[0]); for(var i = 1; i <= faceGeometry.vertices.length - 2; i++) { faceGeometry.faces.push( new THREE.Face3( 0, i, i+1 ) ); } var mesh = new THREE.Mesh( faceGeometry, highlightedFaceMaterial ); group.add(mesh); }); // const pointGeometry = new THREE.Geometry(); // pointGeometry.vertices.push(new THREE.Vector3(highlightedVertex[1], highlightedVertex[2], -highlightedVertex[0])); // const pointMaterial = new THREE.PointsMaterial( { color: pointColor, size: 2} ); // const threePoints = new THREE.Points( pointGeometry, pointMaterial ); // group.add(threePoints); } return group; }33:[] 30:{"id":"ca34615ac762e953","slug":"stellating-7-3-in-minkowski-space","title":"Stellating {7, 3} in Minkowski space","thumbnail":"8f85c70e5dbfb21df1235c23e2361689c279f2ee7e4a3a751daae7bb87c8abc1","access_level":"public","create_time":"$D2021-02-28T18:21:46.366Z","update_time":"$D2021-03-20T21:59:27.306Z","view_time":null,"first_public_time":"$D2021-03-03T07:22:20.981Z","has_unpublished_edits":null,"fork":{"id":"1d994fb7d9db7e27","slug":"near-miss-ball-and-stick-vzome-model","title":"Near-miss ball-and-stick vZome model","owner":{"id":"1ff257e2ac2cfcd3","login":"nanma80","name":""}},"stars":0,"starred":false,"owner":{"type":"team","id":"1ff257e2ac2cfcd3","login":"nanma80","name":"","avatar_url":"https://avatars-next.observableusercontent.com/11efa8d876ef2e51b4f61bda72b5eb802c951f91a040b67ca06616569276b529","tier":"starter_2024","bio":""},"version":1174,"publish_version":1174,"role":null,"authored":false,"authors":[{"type":"individual","id":"ccfea1fbe2bd217e","login":"nanma80","name":"","avatar_url":"https://avatars-next.observableusercontent.com/11efa8d876ef2e51b4f61bda72b5eb802c951f91a040b67ca06616569276b529","tier":null,"bio":""}],"members":[{"type":"individual","id":"ccfea1fbe2bd217e","login":"nanma80","name":"","avatar_url":"https://avatars-next.observableusercontent.com/11efa8d876ef2e51b4f61bda72b5eb802c951f91a040b67ca06616569276b529","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Stellating {7, 3} in Minkowski space","cells":[{"id":0,"value":"title = md`# Stellating {7, 3} in Minkowski space`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":981,"value":"html`

${rendering}

\n ${viewof convexHull}\n
\n ${viewof highlightSomeFaces} \n
\n ${viewof showCones}\n
\n ${viewof antipodal} \n

`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":997,"value":"html`

${viewof zLimit}

${viewof stellationRatio}

${viewof boostX}

${viewof boostY}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1146,"value":"md `\n----\n## Summary`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1151,"value":"md`\n| Shape | Construction | Parameters | Notes |\n|---|---|---|\n|{7,3}|Tile heptagons in H2|edge stellation ratio = 1||\n|{7/2,7}|First stellation of {7,3}|edge stellation ratio = 2.604||\n|{7,7/2}|Take the convex hull of each face of {7/2, 7}|edge stellation ratio = 2.604, check \"take the convex hull...\"|Dual of {7/2, 7}|\n|{7/3, inf}?|Second stellation of {7, 3}|edge stellation ratio = 9.098|Vertices are hyperideal. Central parts of edges in the hyperbolic plane|\n|Collection of {7}s|Take the convex hull of each face of {7/3, inf} |edge stellation ratio = 9.098, check \"take the convex hull...\"| The whole edges are outside of hyperbolic plane|\n|{7, inf}|Identify antipodal points of the collection of {7}s|edge stellation ratio = 9.098, check \"take the convex hull...\", check \"show the antipodal copy\", imagine antipodal points as the same|Each edge is shared by two faces, which is required as a polyhedron|\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"md `\n----\n## Code`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":673,"value":"function applyBoostX(v) {\n return [\n Math.cosh(boostX) * v[0] + Math.sinh(boostX) * v[1],\n Math.sinh(boostX) * v[0] + Math.cosh(boostX) * v[1],\n v[2]\n ];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":678,"value":"function applyBoostY(v) {\n return [\n Math.cosh(boostY) * v[0] + Math.sinh(boostY) * v[2],\n v[1],\n Math.sinh(boostY) * v[0] + Math.cosh(boostY) * v[2] \n ];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":600,"value":"function stellateEdge( edge ) {\n var center = edge[0].map(function(x, i) { return (edge[0][i] + edge[1][i]) / 2});\n var stellateSide = function(x, i) {\n return (x - center[i]) * stellationRatio + center[i]\n };\n return [edge[0].map(stellateSide), edge[1].map(stellateSide)];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":771,"value":"getFilteredFaces = function(limit){\n var faces = faces_7_3;\n // apply Lorentz boost\n faces = faces.map(function(face) {\n return face.map(applyBoostX).map(applyBoostY);\n });\n // filter by z limit\n faces = faces.filter(f => f.map(f => f[0]).reduce((a, b) => a + b, 0) < limit * 7);\n\n // console.log(faces.map(f => f.map( v => v.map(c => -c) )));\n if (antipodal) {\n faces = faces.concat(faces.map(f => f.map( v => v.map(c => -c) )));\n }\n return faces;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1094,"value":"containsVertex = function(edges, v) {\n var match = false;\n edges.forEach(edge => {\n if (match) return;\n edge.forEach(end => {\n if (match) return;\n var normsq = 0;\n for(var i = 0; i <= 2; i++) {\n normsq += (end[i] - v[i])**2;\n }\n if (normsq < 0.0001) {\n match = true;\n };\n })\n });\n return match;\n };","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1099,"value":"vertexCost = function(a) {return Math.abs(a[0] - 1.8) * 10 - 0.1 * a[2]};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1123,"value":"getConvexHullFace = function(stellatedEdges){\n if (stellationRatio <= stellationRatio1) {\n return [\n stellatedEdges[0][0], stellatedEdges[6][1], \n stellatedEdges[1][0], stellatedEdges[0][1], \n stellatedEdges[2][0], stellatedEdges[1][1], \n stellatedEdges[3][0], stellatedEdges[2][1], \n stellatedEdges[4][0], stellatedEdges[3][1], \n stellatedEdges[5][0], stellatedEdges[4][1], \n stellatedEdges[6][0], stellatedEdges[5][1]\n ];\n }\n else {\n return [\n stellatedEdges[0][0], stellatedEdges[5][1], \n stellatedEdges[1][0], stellatedEdges[6][1], \n stellatedEdges[2][0], stellatedEdges[0][1], \n stellatedEdges[3][0], stellatedEdges[1][1], \n stellatedEdges[4][0], stellatedEdges[2][1], \n stellatedEdges[5][0], stellatedEdges[3][1], \n stellatedEdges[6][0], stellatedEdges[4][1]\n ];\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":498,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":834,"value":"getRange = function(min, max, n) {\n return [...Array(n).keys()].map(k => ( max - min ) * k / n + min);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":877,"value":"function ConeFromTo(A, B, radius, material) {\n // from https://stackoverflow.com/a/51155933\n var vec = B.clone(); vec.sub(A);\n var h = vec.length();\n vec.normalize();\n var quaternion = new THREE.Quaternion();\n quaternion.setFromUnitVectors(new THREE.Vector3(0, 1, 0), vec);\n var geometry = new THREE.ConeGeometry( coneSize, coneSize, 32, 1, true, 0, 2.0 * Math.PI );\n geometry.translate(0, h / 2, 0);\n var object = new THREE.Mesh(geometry, material);\n object.applyQuaternion(quaternion);\n object.position.set(A.x, A.y, A.z);\n return object;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":926,"value":"md`----\n## Config`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":901,"value":"coneSize = zLimit * 1.6;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":729,"value":"viewof faceColor = color( { value: '#7ad18c', title: \"Face color\" } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":684,"value":"viewof edgeColor = color( { value: '#3f05e1', title: 'Edge color' } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1105,"value":"viewof highlightedEdgeColor = color( { value: '#ff0000', title: 'Highlighted edge color' } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":865,"value":"viewof pointColor = color( { value: '#da25cb', title: \"Point color\" } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":726,"value":"viewof convexHullColor = color( { value: '#e2a703', title: \"Convex hull color\" } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":883,"value":"viewof coneColor = color( { value: '#00d8f5', title: \"Cone color\" } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":964,"value":"md`----\n## Original controls`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1117,"value":"viewof highlightSomeFaces = checkbox({\n options: [{ value: true, label: \"Highlight the convex hull faces that contains a vertex\" }]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":555,"value":"viewof zLimit = slider({\n min: 2, \n max: 96, \n step: 1, \n value: 12, \n title: `z-limit: control the visibility of faces based on the z-value`,\n //description: `A larger number here includes more heptagonal faces. Value = 2 shows only one face.`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":821,"value":"viewof stellationRatio = {\n const ratios = getRange(1, stellationRatio1, 13).concat(getRange(stellationRatio1, stellationRatio2, 36)).concat([stellationRatio2]).map(a => a.toFixed(3));\n \n return slider({\n value: this ? this.input.value : 0, step: 1, max: ratios.length - 1,\n getValue: n => ratios[n.value],\n title: \"Edge stellation ratio\",\n description: `No stellation: 1. First stellation: ${stellationRatio1.toFixed(3)}. Second stellation: ${stellationRatio2.toFixed(3)}`\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":692,"value":"viewof convexHull = checkbox({\n options: [{ value: true, label: \"Take the convex hull of each heptagram\" }]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":907,"value":"viewof showCones = checkbox({\n options: [{ value: true, label: \"Show the light cone\" }]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":919,"value":"viewof antipodal = checkbox({\n options: [{ value: true, label: \"Show the antipodal copy\" }]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":667,"value":"viewof boostX = slider({\n min: -1.0,\n max: +1.0,\n value: 0,\n precision: 2,\n title: \"Lorentz Boost X\",\n description: '\"Hyperbolic\" rotation in the X-Z direction'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":670,"value":"viewof boostY = slider({\n min: -1.0,\n max: +1.0,\n value: 0,\n precision: 2,\n title: \"Lorentz Boost Y\",\n description: '\"Hyperbolic\" rotation in the Y-Z direction'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":404,"value":"rendering = reusable3dCanvas( this, \n getFaces(),\n { renderWidth: width * 0.78,\n camera: { aspect: 5/3, position: [0, 50, 20] }\n } )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":284,"value":"md`----\n## Data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"faces_7_3 = fetch(\n `https://raw.githubusercontent.com/nanma80/hyperbolic_tiling/master/data/h_7_3_8gen.json`\n).then(response => response.json()) ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":393,"value":"epsilon = 0.1 ** 8","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":643,"value":"stellationRatio1 = Math.tan(2*Math.PI/7)/Math.tan(Math.PI/7)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":647,"value":"stellationRatio2 = (Math.tan(3*Math.PI/7)/Math.tan(Math.PI/7))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":288,"value":"md`----\n## Dependencies`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":375,"value":"import {reusable3dCanvas, THREE} from '@vorth/reusable-three-js-canvas'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":162,"value":"import {slider, color, select, checkbox, button} from '@jashkenas/inputs'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1"}} 31:"$30:body"