tileSpecs = (() => { const SCALE = 2; const COLOR_PALETTE = [ "#e74c3c","#3498db","#f1c40f","#2ecc71","#9b59b6", "#e67e22","#1abc9c","#34495e","#d35400","#7f8c8d" ]; // --- Z^3 lattice signed-permutation isometries: all 48 (det = ±1) const Z3_MATRICES_ALL = (() => { const perms = (arr) => { if (arr.length <= 1) return [arr.slice()]; const out = []; for (let i = 0; i < arr.length; i++) { const rest = arr.slice(0, i).concat(arr.slice(i + 1)); for (const p of perms(rest)) out.push([arr[i], ...p]); } return out; }; const det3 = (M) => M[0][0]*(M[1][1]*M[2][2]-M[1][2]*M[2][1]) - M[0][1]*(M[1][0]*M[2][2]-M[1][2]*M[2][0]) + M[0][2]*(M[1][0]*M[2][1]-M[1][1]*M[2][0]); const mats = []; for (const p of perms([0,1,2])) { const P = [[0,0,0],[0,0,0],[0,0,0]]; for (let i = 0; i < 3; i++) P[i][p[i]] = 1; for (const sx of [-1,1]) for (const sy of [-1,1]) for (const sz of [-1,1]) { const S = [[sx,0,0],[0,sy,0],[0,0,sz]]; const M = [ [P[0][0]*S[0][0] + P[0][1]*S[1][0] + P[0][2]*S[2][0], P[0][0]*S[0][1] + P[0][1]*S[1][1] + P[0][2]*S[2][1], P[0][0]*S[0][2] + P[0][1]*S[1][2] + P[0][2]*S[2][2]], [P[1][0]*S[0][0] + P[1][1]*S[1][0] + P[1][2]*S[2][0], P[1][0]*S[0][1] + P[1][1]*S[1][1] + P[1][2]*S[2][1], P[1][0]*S[0][2] + P[1][1]*S[1][2] + P[1][2]*S[2][2]], [P[2][0]*S[0][0] + P[2][1]*S[1][0] + P[2][2]*S[2][0], P[2][0]*S[0][1] + P[2][1]*S[1][1] + P[2][2]*S[2][1], P[2][0]*S[0][2] + P[2][1]*S[1][2] + P[2][2]*S[2][2]], ]; const det = det3(M); mats.push({ M, det }); } } return mats; })(); const Z3_MATRICES_DET1 = Z3_MATRICES_ALL.filter(x => x.det === 1); const add3 = (a,b) => [a[0]+b[0], a[1]+b[1], a[2]+b[2]]; const sub3 = (a,b) => [a[0]-b[0], a[1]-b[1], a[2]-b[2]]; const dot3 = (a,b) => a[0]*b[0] + a[1]*b[1] + a[2]*b[2]; const cross3 = (a,b) => [a[1]*b[2]-a[2]*b[1], a[2]*b[0]-a[0]*b[2], a[0]*b[1]-a[1]*b[0]]; const norm3 = (a) => Math.sqrt(dot3(a, a)); const normalize3 = (a) => { const n = norm3(a); return n === 0 ? a : [a[0]/n, a[1]/n, a[2]/n]; }; // Generic function to compute solid angle of a cone spanned by three vectors const computeSolidAngle = (v1, v2, v3) => { const u = normalize3(v1); const v = normalize3(v2); const w = normalize3(v3); const triple = dot3(u, cross3(v, w)); const uv = dot3(u, v); const vw = dot3(v, w); const wu = dot3(w, u); const denom = 1 + uv + vw + wu; if (Math.abs(denom) < 1e-12) return 0; const numerator = Math.abs(triple); const ratio = numerator / denom; const clampedRatio = Math.max(-1e12, Math.min(1e12, ratio)); const omega = 2 * Math.atan(clampedRatio); return Math.abs(omega) < 1e-12 ? 0 : omega; }; const computeDihedralAngle = (v1, v2, v3, v4) => { const a = sub3(v3, v1); const b = sub3(v2, v1); const c = sub3(v4, v1); const n1 = cross3(a, b); const n2 = cross3(b, c); const n1_norm = norm3(n1); const n2_norm = norm3(n2); if (n1_norm < 1e-12 || n2_norm < 1e-12) return 0; const cosAngle = dot3(n1, n2) / (n1_norm * n2_norm); const clampedCos = Math.max(-1, Math.min(1, cosAngle)); const angle = Math.acos(clampedCos); return Math.PI - angle; }; const computeWeight48 = (angle, fullAngle) => { const exact = (angle / fullAngle) * 48; const rounded = Math.round(exact); if (Math.abs(exact - rounded) < 1e-6) return rounded; return Math.floor(exact); }; const getTetrahedronWeights = () => { const verts = [[0,0,0],[1,1,0],[1,0,1],[0,1,1]]; const v0 = verts[0]; const v1 = sub3(verts[1], v0); const v2 = sub3(verts[2], v0); const v3 = sub3(verts[3], v0); const solidAngle = computeSolidAngle(v1, v2, v3); const dihedralAngle = computeDihedralAngle(verts[0], verts[1], verts[2], verts[3]); const fullSphere = 4 * Math.PI; const fullCircle = 2 * Math.PI; return { vertexWeight: computeWeight48(solidAngle, fullSphere), edgeWeight: computeWeight48(dihedralAngle, fullCircle), faceWeight: 24, interiorWeight: 48 }; }; const getTetragonalDisphenoidWeights = () => { const verts = [[0,0,1],[0,0,-1],[1,1,0],[1,-1,0]]; const v0 = verts[0]; const v1 = sub3(verts[1], v0); const v2 = sub3(verts[2], v0); const v3 = sub3(verts[3], v0); const solidAngle = computeSolidAngle(v1, v2, v3); const longDihedral = computeDihedralAngle(verts[0], verts[1], verts[2], verts[3]); const shortDihedral = computeDihedralAngle(verts[0], verts[2], verts[1], verts[3]); const fullSphere = 4 * Math.PI; const fullCircle = 2 * Math.PI; return { vertexWeight: computeWeight48(solidAngle, fullSphere), longEdgeWeight: computeWeight48(longDihedral, fullCircle), shortEdgeWeight: computeWeight48(shortDihedral, fullCircle), faceWeight: 24, interiorWeight: 48 }; }; const computeTetrahedronWeights = (verts, isTetragonalDisphenoid = false) => { if (isTetragonalDisphenoid) return getTetragonalDisphenoidWeights(); return getTetrahedronWeights(); }; const computeHullFaces = (verts) => { const pts = verts.map(v => v.slice()); const N = pts.length; const sum = pts.reduce((acc,v)=>add3(acc,v), [0,0,0]); const faces = []; const seen = new Set(); for (let i=0;i 0) { ok = false; break; } if (d === 0) onPlane.push(m); } if (!ok || onPlane.length < 3) continue; const facePts = onPlane.map(idx => pts[idx]); const c = facePts.reduce((acc,v)=>add3(acc,v), [0,0,0]).map(x => x / facePts.length); const nz = (() => { const len = Math.sqrt(nn[0]*nn[0]+nn[1]*nn[1]+nn[2]*nn[2]); return [nn[0]/len, nn[1]/len, nn[2]/len]; })(); let xax = sub3(facePts[0].map(Number), c); const xlen = Math.sqrt(xax[0]*xax[0]+xax[1]*xax[1]+xax[2]*xax[2]) || 1; xax = [xax[0]/xlen, xax[1]/xlen, xax[2]/xlen]; const yax = cross3(nz, xax); const withAng = onPlane.map((idx) => { const v = sub3(pts[idx].map(Number), c); const ang = Math.atan2(dot3(v, yax), dot3(v, xax)); return { idx, ang }; }).sort((a,b)=>a.ang-b.ang); const ordered = withAng.map(o => o.idx); const h = ordered.slice().sort((a,b)=>a-b).join(","); if (!seen.has(h)) { seen.add(h); faces.push(ordered); } } return faces; }; const computeTetrahedronOccupancy = (vertsScaled, faces, isTetragonalDisphenoid = false) => { const weights = computeTetrahedronWeights( vertsScaled.map(v => [v[0]/SCALE, v[1]/SCALE, v[2]/SCALE]), isTetragonalDisphenoid ); const minB = [Infinity, Infinity, Infinity]; const maxB = [-Infinity, -Infinity, -Infinity]; for (const v of vertsScaled) { for (let i = 0; i < 3; i++) { minB[i] = Math.min(minB[i], v[i]); maxB[i] = Math.max(maxB[i], v[i]); } } const occ = []; const vertSet = new Set(vertsScaled.map(v => v.join(','))); let longEdges = []; let shortEdges = []; if (isTetragonalDisphenoid) { for (let i = 0; i < vertsScaled.length; i++) { for (let j = i + 1; j < vertsScaled.length; j++) { const v1 = vertsScaled[i]; const v2 = vertsScaled[j]; const dx = Math.abs(v1[0] - v2[0]); const dy = Math.abs(v1[1] - v2[1]); const dz = Math.abs(v1[2] - v2[2]); if (dx === 0 && dy === 0 && dz === 4) longEdges.push([i, j]); else shortEdges.push([i, j]); } } } for (let x = minB[0]; x <= maxB[0]; x++) { for (let y = minB[1]; y <= maxB[1]; y++) { for (let z = minB[2]; z <= maxB[2]; z++) { const p = [x, y, z]; const key = p.join(','); if (vertSet.has(key)) { occ.push([p, weights.vertexWeight]); continue; } let isEdge = false; if (isTetragonalDisphenoid) { for (const [i, j] of longEdges) { const v1 = vertsScaled[i]; const v2 = vertsScaled[j]; if (p[0]*2 === v1[0] + v2[0] && p[1]*2 === v1[1] + v2[1] && p[2]*2 === v1[2] + v2[2]) { occ.push([p, weights.longEdgeWeight]); isEdge = true; break; } } if (!isEdge) { for (const [i, j] of shortEdges) { const v1 = vertsScaled[i]; const v2 = vertsScaled[j]; if (p[0]*2 === v1[0] + v2[0] && p[1]*2 === v1[1] + v2[1] && p[2]*2 === v1[2] + v2[2]) { occ.push([p, weights.shortEdgeWeight]); isEdge = true; break; } } } } else { for (let i = 0; i < vertsScaled.length && !isEdge; i++) { for (let j = i + 1; j < vertsScaled.length && !isEdge; j++) { const v1 = vertsScaled[i]; const v2 = vertsScaled[j]; if (p[0]*2 === v1[0] + v2[0] && p[1]*2 === v1[1] + v2[1] && p[2]*2 === v1[2] + v2[2]) { occ.push([p, weights.edgeWeight]); isEdge = true; break; } } } } if (isEdge) continue; const EPS = 1e-7; const scaledVerts = vertsScaled.map(v => [v[0]/SCALE, v[1]/SCALE, v[2]/SCALE]); const pu = [p[0]/SCALE, p[1]/SCALE, p[2]/SCALE]; const [v0, v1, v2, v3] = scaledVerts; const v0v1 = sub3(v1, v0); const v0v2 = sub3(v2, v0); const v0v3 = sub3(v3, v0); const v0p = sub3(pu, v0); const d00 = dot3(v0v1, v0v1); const d01 = dot3(v0v1, v0v2); const d02 = dot3(v0v1, v0v3); const d03 = dot3(v0v1, v0p); const d11 = dot3(v0v2, v0v2); const d12 = dot3(v0v2, v0v3); const d13 = dot3(v0v2, v0p); const d22 = dot3(v0v3, v0v3); const d23 = dot3(v0v3, v0p); const denom = d00 * (d11 * d22 - d12 * d12) - d01 * (d01 * d22 - d12 * d02) + d02 * (d01 * d12 - d11 * d02); if (Math.abs(denom) < 1e-12) continue; const invDenom = 1 / denom; const u = (d11 * d22 - d12 * d12) * d03 - (d01 * d22 - d12 * d02) * d13 + (d01 * d12 - d11 * d02) * d23; const v = -(d01 * d22 - d12 * d02) * d03 + (d00 * d22 - d02 * d02) * d13 - (d00 * d12 - d01 * d02) * d23; const w = (d01 * d12 - d11 * d02) * d03 - (d00 * d12 - d01 * d02) * d13 + (d00 * d11 - d01 * d01) * d23; const baryU = u * invDenom; const baryV = v * invDenom; const baryW = w * invDenom; const baryT = 1 - baryU - baryV - baryW; if (baryU > -EPS && baryV > -EPS && baryW > -EPS && baryT > -EPS && baryU < 1+EPS && baryV < 1+EPS && baryW < 1+EPS && baryT < 1+EPS) { if (Math.abs(baryU) < EPS || Math.abs(baryV) < EPS || Math.abs(baryW) < EPS || Math.abs(baryT) < EPS) { occ.push([p, weights.faceWeight]); } else { occ.push([p, weights.interiorWeight]); } } } } } return occ; }; const scanConvexInterior = (verts, faces) => { const minB = [Infinity,Infinity,Infinity]; const maxB = [-Infinity,-Infinity,-Infinity]; for (const v of verts) for (let i=0;i<3;i++) { minB[i]=Math.min(minB[i],v[i]); maxB[i]=Math.max(maxB[i],v[i]); } const sum = verts.reduce((acc,v)=>add3(acc,v), [0,0,0]); const N = verts.length; const planes = []; for (const f of faces) { if (f.length < 3) continue; const v0 = verts[f[0]], v1 = verts[f[1]], v2 = verts[f[2]]; let n = cross3(sub3(v1,v0), sub3(v2,v0)); const test = dot3(n, sub3([N*v0[0],N*v0[1],N*v0[2]], sum)); if (test < 0) n = [-n[0],-n[1],-n[2]]; planes.push({ n, d: dot3(n, v0) }); } const interior = []; for (let x=minB[0]; x<=maxB[0]; x++) for (let y=minB[1]; y<=maxB[1]; y++) for (let z=minB[2]; z<=maxB[2]; z++) { const p = [x,y,z]; let inside = true, boundary = false; for (const pl of planes) { const val = dot3(pl.n, p); if (val > pl.d) { inside = false; break; } if (val === pl.d) boundary = true; } if (inside && !boundary) interior.push([p, 48]); } return interior; }; const createScaledTileData = (unitVerts, faceTemplate, autoHull=false, isTetragonalDisphenoid=false) => { const vertsScaled = unitVerts.map(v => v.map(c => Math.round(c * SCALE))); const faces = autoHull ? computeHullFaces(vertsScaled) : faceTemplate.map(f => f.v.slice()); const faceData = autoHull ? faces.map(f => ({ v: f, type: "default" })) : faceTemplate.map(f => ({ v: f.v.slice(), type: f.type })); let occ; if (unitVerts.length === 4 && faceTemplate.length === 4 && faceTemplate.every(f => f.v.length === 3)) { occ = computeTetrahedronOccupancy(vertsScaled, faces, isTetragonalDisphenoid); } else { occ = scanConvexInterior(vertsScaled, faceData.map(f => f.v)); } return { v: vertsScaled, f_data: faceData, occ, skip_winding: false }; }; const generatePolycubeData = (voxels) => { const voxelSet = new Set(voxels.map(v => v.map(Number).join(","))); const vox = voxels.map(v => v.map(Number)); const uniqueVerts = new Set(); for (const v of vox) { for (const dx of [0,1]) for (const dy of [0,1]) for (const dz of [0,1]) { uniqueVerts.add([v[0]+dx, v[1]+dy, v[2]+dz].join(",")); } } const vertsList = [...uniqueVerts].map(s => s.split(",").map(Number)) .sort((a,b)=>a[0]-b[0]||a[1]-b[1]||a[2]-b[2]); const vertMap = new Map(vertsList.map((v,i)=>[v.join(","), i])); const faceDefs = [ [[ 1,0,0], [[1,0,0],[1,1,0],[1,1,1],[1,0,1]]], [[-1,0,0], [[0,0,0],[0,0,1],[0,1,1],[0,1,0]]], [[ 0,1,0], [[0,1,0],[0,1,1],[1,1,1],[1,1,0]]], [[ 0,-1,0], [[0,0,0],[1,0,0],[1,0,1],[0,0,1]]], [[ 0,0,1], [[0,0,1],[1,0,1],[1,1,1],[0,1,1]]], [[ 0,0,-1], [[0,0,0],[0,1,0],[1,1,0],[1,0,0]]], ]; const faces = []; for (const v of vox) { const [vx,vy,vz] = v; for (const [nrm, deltas] of faceDefs) { const nb = [vx+nrm[0], vy+nrm[1], vz+nrm[2]].join(","); if (!voxelSet.has(nb)) { const idxs = deltas.map(([dx,dy,dz]) => vertMap.get([vx+dx,vy+dy,vz+dz].join(","))); faces.push(idxs); } } } const scaledVerts = vertsList.map(v => v.map(c => (c * SCALE)|0)); const occ = new Map(); for (const v of vertsList) occ.set(v.map(c => (c*SCALE)|0).join(","), 6); for (let i=0;i (c*SCALE/2)|0); occ.set(mid.join(","), 12); } } for (const v of vox) { const vs = v.map(c => (c*SCALE)|0); const roll = (arr, k) => arr.slice(k).concat(arr.slice(0,k)); for (let i=0;i<3;i++) { const a = add3(vs, roll([2,1,1], i)); const b = add3(vs, roll([0,1,1], i)); occ.set(a.join(","), 24); occ.set(b.join(","), 24); } occ.set([v[0]*SCALE+1, v[1]*SCALE+1, v[2]*SCALE+1].join(","), 48); } const occList = [...occ.entries()].map(([k,w]) => [k.split(",").map(Number), w]); const faceData = faces.map(f => ({ v: f.slice(), type: "default" })); return { v: scaledVerts, f_data: faceData, occ: occList, skip_winding: true }; }; class Prototile3D { constructor(name, vertices, face_data, occupancy_map, skip_winding=false, is_mirror=false) { this.name = name; this.is_mirror = is_mirror; this.verts = vertices.map(v => v.slice()); this.faces = face_data.map(f => f.v.slice()); this.face_types = face_data.map(f => f.type); this.occupancy_points = (occupancy_map || []).map(([pt,w]) => ({ pos: pt.slice(), weight: w })); if (!skip_winding) this._fixWinding(); this.unique_orientations = []; this.is_chiral = false; this._calcSymmetries(); if (!is_mirror) this._checkChirality(); } _fixWinding() { const inside = this.occupancy_points.length ? this.occupancy_points[0].pos : [ Math.round(this.verts.reduce((s,v)=>s+v[0],0)/this.verts.length), Math.round(this.verts.reduce((s,v)=>s+v[1],0)/this.verts.length), Math.round(this.verts.reduce((s,v)=>s+v[2],0)/this.verts.length), ]; const newFaces = []; for (const f of this.faces) { if (f.length < 3) { newFaces.push(f); continue; } const v0 = this.verts[f[0]], v1 = this.verts[f[1]], v2 = this.verts[f[2]]; let n = cross3(sub3(v1,v0), sub3(v2,v0)); const inward = sub3(inside, v0); if (dot3(n, inward) > 0) newFaces.push(f.slice().reverse()); else newFaces.push(f.slice()); } this.faces = newFaces; } _calcSymmetries() { const mul = (M,v) => ([ M[0][0]*v[0]+M[0][1]*v[1]+M[0][2]*v[2], M[1][0]*v[0]+M[1][1]*v[1]+M[1][2]*v[2], M[2][0]*v[0]+M[2][1]*v[1]+M[2][2]*v[2], ]); const buildFrom = (matList) => { const seen = new Set(); const out = []; for (let iso_idx = 0; iso_idx < matList.length; iso_idx++) { const { M, det } = matList[iso_idx]; let tVerts = this.verts.map(v => mul(M,v)); const shift = [Infinity,Infinity,Infinity]; for (const v of tVerts) for (let i=0;i<3;i++) shift[i]=Math.min(shift[i], v[i]); tVerts = tVerts.map(v => [v[0]-shift[0], v[1]-shift[1], v[2]-shift[2]]); const vIndex = new Map(tVerts.map((v,i)=>[v.join(","), i])); const tOcc = this.occupancy_points.map(pt => { const mp = mul(M, pt.pos); return { pos: [mp[0]-shift[0], mp[1]-shift[1], mp[2]-shift[2]], weight: pt.weight }; }); const newFaces = []; const newFaceTypes = []; for (let fi = 0; fi < this.faces.length; fi++) { const face = this.faces[fi]; const mapped = face.map(oldIdx => { const mv = mul(M, this.verts[oldIdx]); const key = [mv[0]-shift[0], mv[1]-shift[1], mv[2]-shift[2]].join(","); return vIndex.get(key); }); const fixed = (det === -1) ? mapped.slice().reverse() : mapped; newFaces.push(fixed); newFaceTypes.push(this.face_types[fi]); } const vHash = tVerts.map(v=>v.join(",")).sort().join("|"); const oHash = tOcc.map(p=>`${p.pos.join(",")}:${p.weight}`).sort().join("|"); const fHash = newFaces.map((f,i)=>`${f.slice().sort((a,b)=>a-b).join(",")}:${newFaceTypes[i]}`).sort().join("|"); const geomHash = `${vHash}@@${oHash}@@${fHash}`; if (seen.has(geomHash)) continue; seen.add(geomHash); out.push({ iso_idx, det, verts: tVerts, faces: newFaces, face_types: newFaceTypes, occupancy: tOcc, vertsForFace: (fIdx) => fIdx.map(i => tVerts[i]) }); } return out; }; this.orientations24 = buildFrom(Z3_MATRICES_DET1); this.unique_orientations = this.orientations24; } _checkChirality() { const mirror = this.verts.map(v => [-v[0], v[1], v[2]]); const minv = [Infinity,Infinity,Infinity]; for (const v of mirror) for (let i=0;i<3;i++) minv[i]=Math.min(minv[i], v[i]); const tVerts = mirror.map(v => sub3(v, minv)); const tOcc = this.occupancy_points.map(pt => ({ pos: sub3([-pt.pos[0], pt.pos[1], pt.pos[2]], minv), weight: pt.weight })); const vHash = tVerts.map(v=>v.join(",")).sort().join("|"); const oHash = tOcc.map(p=>`${p.pos.join(",")}:${p.weight}`).sort().join("|"); const mirrorHash = `${vHash}@@${oHash}`; const baseNoFaces = new Set(); for (const o of this.unique_orientations) { const vh = o.verts.map(v=>v.join(",")).sort().join("|"); const oh = o.occupancy.map(p=>`${p.pos.join(",")}:${p.weight}`).sort().join("|"); baseNoFaces.add(`${vh}@@${oh}`); } this.is_chiral = !baseNoFaces.has(mirrorHash); } get_mirror_copy() { if (!this.is_chiral) return null; const mirrorVerts = this.verts.map(v => [-v[0], v[1], v[2]]); const minv = [Infinity,Infinity,Infinity]; for (const v of mirrorVerts) for (let i=0;i<3;i++) minv[i]=Math.min(minv[i], v[i]); const tVerts = mirrorVerts.map(v => sub3(v, minv)); const mirrorOcc = this.occupancy_points.map(p => [sub3([-p.pos[0],p.pos[1],p.pos[2]], minv), p.weight]); const faceData = this.faces.map((f,i)=>({ v: f.slice(), type: this.face_types[i] })); return new Prototile3D(`reflected ${this.name}`, tVerts, faceData, mirrorOcc, false, true); } } const make_tile = (name, data) => { return new Prototile3D(name, data.v, data.f_data, data.occ, !!data.skip_winding, false); }; const gen_tetrahedron_data = () => { const verts = [[0,0,0],[1,1,0],[1,0,1],[0,1,1]]; return createScaledTileData( verts, [ { v:[0,1,2], type:"TET_FACE" }, { v:[0,2,3], type:"TET_FACE" }, { v:[0,3,1], type:"TET_FACE" }, { v:[1,3,2], type:"TET_FACE" } ], false, false ); }; const gen_tetragonal_disphenoid_data = () => { const verts = [[0,0,1],[0,0,-1],[1,1,0],[1,-1,0]]; return createScaledTileData( verts, [ { v:[0,2,3], type:"TD_FACE" }, { v:[1,3,2], type:"TD_FACE" }, { v:[0,3,1], type:"TD_FACE" }, { v:[0,1,2], type:"TD_FACE" } ], false, true ); }; const gen_octahedron_data = () => createScaledTileData( [[ 1,0,0],[-1,0,0],[0,1,0],[0,-1,0],[0,0,1],[0,0,-1]], [ {v:[0,2,4], type:"OCTA_FACE_A"}, {v:[2,1,4], type:"OCTA_FACE_B"}, {v:[1,3,4], type:"OCTA_FACE_A"}, {v:[3,0,4], type:"OCTA_FACE_B"}, {v:[0,5,2], type:"OCTA_FACE_B"}, {v:[2,5,1], type:"OCTA_FACE_A"}, {v:[1,5,3], type:"OCTA_FACE_B"}, {v:[3,5,0], type:"OCTA_FACE_A"}, ], false ); const gen_corner_tetra_data = () => createScaledTileData( [[0,0,0],[2,0,0],[0,2,0],[0,0,2],[1,1,0],[1,0,1],[0,1,1]], [ {v:[0,2,4], type:"CORNER_SIDE_L"}, {v:[0,4,1], type:"CORNER_SIDE_R"}, {v:[0,1,5], type:"CORNER_SIDE_L"}, {v:[0,5,3], type:"CORNER_SIDE_R"}, {v:[0,3,6], type:"CORNER_SIDE_L"}, {v:[0,6,2], type:"CORNER_SIDE_R"}, {v:[4,6,5], type:"CORNER_CENTER"}, {v:[1,5,4], type:"CORNER_OUTER"}, {v:[2,4,6], type:"CORNER_OUTER"}, {v:[3,6,5], type:"CORNER_OUTER"}, ], false ); const gen_cuboctahedron_data = () => { const set = new Set(); for (const x of [-1,1]) for (const y of [-1,1]) set.add([x,y,0].join(",")); for (const x of [-1,1]) for (const z of [-1,1]) set.add([x,0,z].join(",")); for (const y of [-1,1]) for (const z of [-1,1]) set.add([0,y,z].join(",")); return createScaledTileData([...set].map(s => s.split(",").map(Number)), [], true); }; const gen_elongated_square_bipyramid = () => { const verts = []; for (const x of [-1,1]) for (const y of [-1,1]) for (const z of [-1,1]) verts.push([x,y,z]); verts.push([0,0,2],[0,0,-2]); return createScaledTileData(verts, [], true); }; const gen_n_cross_data = (arm) => { const vox = [[0,0,0]]; const dirs = [[1,0,0],[-1,0,0],[0,1,0],[0,-1,0],[0,0,1],[0,0,-1]]; for (const d of dirs) for (let i=1;i<=arm;i++) vox.push([i*d[0], i*d[1], i*d[2]]); return generatePolycubeData(vox); }; const gen_n_semicross_data = (arm) => { const vox = [[0,0,0]]; const dirs = [[1,0,0],[0,1,0],[0,0,1]]; for (const d of dirs) for (let i=1;i<=arm;i++) vox.push([i*d[0], i*d[1], i*d[2]]); return generatePolycubeData(vox); }; const gen_double_ring_data = () => generatePolycubeData([ [0,0,0],[0,0,1], [1,0,0],[1,1,0],[1,1,1],[0,1,1], [-1,0,0],[-1,-1,0],[-1,-1,1],[0,-1,1] ]); const gen_buckled_ring_data = () => generatePolycubeData([[0,0,0],[1,0,0],[1,1,0],[1,1,1],[0,1,1],[0,0,1]]); const gen_large_buckled_ring_data = () => generatePolycubeData([ [0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0], [2,2,1],[2,2,2],[1,2,2],[0,2,2],[0,1,2],[0,0,2],[0,0,1] ]); const gen_tuning_fork = () => { const vox = []; for (let x=0;x<3;x++) for (let y=0;y<12;y++) { if (!(x===1 && (y<3 || (6<=y && y<9)))) vox.push([x,y,0]); } return generatePolycubeData(vox); }; const gen_twisted_h_data = () => generatePolycubeData([[0,0,0],[0,0,1],[1,0,1],[-1,0,1],[0,0,-1],[0,1,-1],[0,-1,-1]]); const gen_cube_data = () => generatePolycubeData([[0,0,0]]); const gen_s_tetracube = () => generatePolycubeData([[0,0,0],[1,0,0],[1,1,0],[1,1,1]]); const gen_knuckle_pentacube = () => generatePolycubeData([[0,0,0],[1,0,0],[-1,0,0],[0,1,0],[0,0,1]]); const gen_rhombic_robust = () => { const set = new Set(); const perms = (arr) => { if (arr.length<=1) return [arr.slice()]; const out=[]; for (let i=0;i-x).join(",")); } for (const sx of [-1,1]) for (const sy of [-1,1]) for (const sz of [-1,1]) set.add([sx,sy,sz].join(",")); return createScaledTileData([...set].map(s => s.split(",").map(Number)), [], true); }; const gen_trunc_oct_robust = () => { const set = new Set(); const perms = (arr) => { if (arr.length<=1) return [arr.slice()]; const out=[]; for (let i=0;i s.split(",").map(Number)), [], true); }; const gen_elongated_dodecahedron = () => { const verts = [[2,0,0],[-2,0,0],[0,2,0],[0,-2,0],[0,0,4],[0,0,-4]]; for (const x of [-1,1]) for (const y of [-1,1]) for (const z of [-1,1]) verts.push([x,y,2*z]); return createScaledTileData(verts, [], true); }; const gen_hex_prism = () => { const perms = (arr) => { if (arr.length<=1) return [arr.slice()]; const out=[]; for (let i=0;i createScaledTileData( [[0,0,0],[2,0,0],[2,2,0],[2,2,2],[1,1,0],[2,1,1]], [ {v:[0,1,4], type:"RIGHT_ISO_A"}, {v:[1,2,4], type:"RIGHT_ISO_B"}, {v:[1,2,5], type:"RIGHT_ISO_A"}, {v:[2,3,5], type:"RIGHT_ISO_B"}, {v:[0,1,3], type:"SCALENE_BACK"}, {v:[0,2,3], type:"SCALENE_SLANT"}, ], false ); const gen_gyrobifastigium_data = () => { const verts = [[1,1,0],[1,-1,0],[-1,-1,0],[-1,1,0],[0,1,2],[0,-1,2],[1,0,-2],[-1,0,-2]]; return createScaledTileData(verts, [], true); }; const gen_trunc_tetra_friauf = () => { const tips = [[0,0,0],[3,3,0],[3,0,3],[0,3,3]]; const verts = []; for (let i=0;i<4;i++) for (let j=0;j<4;j++) if (j!==i) { const a=tips[i], b=tips[j]; verts.push([a[0]+((b[0]-a[0])/3), a[1]+((b[1]-a[1])/3), a[2]+((b[2]-a[2])/3)]); } const uniq = new Map(); for (const v of verts) uniq.set(v.join(","), v); const temp = createScaledTileData([...uniq.values()], [], true); temp.f_data = temp.f_data.map(f => ({ ...f, type: (f.v.length===3 ? "TRI_FACE" : "HEX_FACE") })); return temp; }; const gen_rhombic_pyramid = () => createScaledTileData( [[2,0,0],[1,1,1],[0,0,2],[1,-1,1],[2,0,2]], [ {v:[0,1,2,3], type:"RHOMBIC_SPIKE_BASE"}, {v:[0,1,4], type:"SPIKE_WALL"}, {v:[1,2,4], type:"SPIKE_WALL"}, {v:[2,3,4], type:"SPIKE_WALL"}, {v:[3,0,4], type:"SPIKE_WALL"}, ], false ); const gen_letter_o_data = () => { const vox = []; for (let x = 0; x < 3; x++) for (let y = 0; y < 4; y++) { if (x === 1 && (y === 1 || y === 2)) continue; vox.push([x, y, 0]); } const data = generatePolycubeData(vox); const hollowSet = new Set(['1,1,0', '1,2,0']); const voxelSet = new Set(vox.map(v => v.join(','))); const dirs = [[1,0,0], [-1,0,0],[0,1,0], [0,-1,0],[0,0,1], [0,0,-1]]; const faceInfo = new Map(); const getFaceType = (vx, vy, vz, dx, dy, dz, neighbor) => { if (hollowSet.has(neighbor)) { if ((vy === 0 && dy === 1) || (vy === 3 && dy === -1)) return "inner_single"; else return "inner_double"; } const isOnPerimeter = (vx === 0 && dx === -1) || (vx === 2 && dx === 1) || (vy === 0 && dy === -1) || (vy === 3 && dy === 1) || (vz === 0 && dz === -1) || (vz === 0 && dz === 1); if (isOnPerimeter) return "outer_rim"; else return "outer_side"; }; for (const v of vox) { const [vx, vy, vz] = v; for (let d = 0; d < dirs.length; d++) { const [dx, dy, dz] = dirs[d]; const nb = [vx + dx, vy + dy, vz + dz]; const nbKey = nb.join(','); if (hollowSet.has(nbKey) || !voxelSet.has(nbKey)) { const faceType = getFaceType(vx, vy, vz, dx, dy, dz, nbKey); const key = `${vx},${vy},${vz},${dx},${dy},${dz}`; faceInfo.set(key, { voxel: v, normal: [dx, dy, dz], type: faceType }); } } } const faceCenter = (faceIndices, vertices) => { const verts = faceIndices.map(i => vertices[i]); const sum = verts.reduce((acc, v) => [acc[0]+v[0], acc[1]+v[1], acc[2]+v[2]], [0,0,0]); return sum.map(c => c / verts.length); }; const estimateNormal = (faceIndices, vertices) => { if (faceIndices.length < 3) return [0,0,0]; const v0 = vertices[faceIndices[0]], v1 = vertices[faceIndices[1]], v2 = vertices[faceIndices[2]]; const e1 = [v1[0]-v0[0], v1[1]-v0[1], v1[2]-v0[2]]; const e2 = [v2[0]-v0[0], v2[1]-v0[1], v2[2]-v0[2]]; const nx = e1[1]*e2[2] - e1[2]*e2[1], ny = e1[2]*e2[0] - e1[0]*e2[2], nz = e1[0]*e2[1] - e1[1]*e2[0]; const len = Math.sqrt(nx*nx + ny*ny + nz*nz); if (len < 0.0001) return [0,0,0]; return [nx/len, ny/len, nz/len]; }; for (let i = 0; i < data.f_data.length; i++) { const face = data.f_data[i]; const center = faceCenter(face.v, data.v); const normal = estimateNormal(face.v, data.v); let matched = false; for (const [key, info] of faceInfo.entries()) { const [vx, vy, vz, dx, dy, dz] = key.split(',').map(Number); const facePos = [vx + (dx > 0 ? 1 : dx < 0 ? 0 : 0.5), vy + (dy > 0 ? 1 : dy < 0 ? 0 : 0.5), vz + (dz > 0 ? 1 : dz < 0 ? 0 : 0.5)].map(p => p * 2); const dist = Math.sqrt(Math.pow(center[0] - facePos[0], 2) + Math.pow(center[1] - facePos[1], 2) + Math.pow(center[2] - facePos[2], 2)); const dot = normal[0]*dx + normal[1]*dy + normal[2]*dz; if (dist < 1.0 && dot > 0.7) { face.type = info.type; matched = true; break; } } if (!matched) { const voxelCenter = center.map(c => Math.round(c / 2)); const isNearPerimeter = voxelCenter[0] === 0 || voxelCenter[0] === 3 || voxelCenter[1] === 0 || voxelCenter[1] === 4 || voxelCenter[2] === 0 || voxelCenter[2] === 1; if (isNearPerimeter) face.type = "outer_rim"; else face.type = "outer_side"; } } return data; }; const gen_1cross_plus_data = () => generatePolycubeData([[0,0,0],[1,0,0], [-1,0,0],[0,1,0], [0,-1,0],[0,0,1], [0,0,-1],[2,0,0]]); // --- Barlow Packing Generators (FCC/HCP Voronoi Cells) --- const gen_barlow_polyhedra = () => { // 1. Rhombic Dodecahedron (FCC) // Vertices scaled x3 to avoid fractions during reflection // Standard RD vertices: perms of (±2,0,0) -> (±6,0,0) and (±1,±1,±1) -> (±3,±3,±3) const rd_verts = [ [3,3,3], [-3,-3,-3], // Poles [6,0,0], [0,6,0], [0,0,6], // Top Shoulders [-6,0,0], [0,-6,0], [0,0,-6], // Bottom Shoulders [3,3,-3], [3,-3,3], [-3,3,3], // Top Waist (Equator) [-3,-3,3], [-3,3,-3], [3,-3,-3] // Bottom Waist ]; const rd_data = createScaledTileData(rd_verts, [], true); // 2. Trapezo-Rhombic Dodecahedron (HCP) // Construct by taking Top Half of RD and Reflecting it across x+y+z=0 // Reflection formula: v' = v - 2 * (dot(v,n)/dot(n,n)) * n, where n=[1,1,1], dot(n,n)=3 // v' = v - 2/3 * sum(v) * [1,1,1] const trd_verts = []; // Add Top Half (including equator) trd_verts.push([3,3,3]); // Pole trd_verts.push([6,0,0], [0,6,0], [0,0,6]); // Top Shoulders trd_verts.push([3,3,-3], [3,-3,3], [-3,3,3]); // Top Waist (Equator) // Reflect Top Half to create Bottom Half const reflect = (v) => { const sum = v[0]+v[1]+v[2]; const k = (2 * sum) / 3; return [v[0]-k, v[1]-k, v[2]-k]; }; trd_verts.push(reflect([3,3,-3]), reflect([3,-3,3]), reflect([-3,3,3])); // Bottom Waist trd_verts.push(reflect([6,0,0]), reflect([0,6,0]), reflect([0,0,6])); // Bottom Shoulders trd_verts.push(reflect([3,3,3])); // Bottom Pole const trd_data = createScaledTileData(trd_verts, [], true); trd_data.f_data.forEach(f => { if (f.v.length === 4) f.type = "TRD_TRAP"; else f.type = "TRD_RHOMB"; }); return { rd: rd_data, trd: trd_data }; }; // --- Registry (complete) --- const TILING_REGISTRY = { "1_cross": { name:"1-Cross (Heptacube)", category:["Polycubes"], build: () => [make_tile("1-Cross", gen_n_cross_data(1))] }, "2_cross": { name:"2-Cross (Tridecacube)", category:["Polycubes"], build: () => [make_tile("2-Cross", gen_n_cross_data(2))] }, "3_cross": { name:"3-Cross (Nonadecacube)", category:["Polycubes"], build: () => [make_tile("3-Cross", gen_n_cross_data(3))] }, "t_cross": { name:"T-Cross", category:["Polycubes"], build: () => [make_tile("T-Cross", (() => { const arm = 3; const vox = new Set(); const dirs = [[1,0,0],[-1,0,0],[0,1,0],[0,-1,0],[0,0,1],[0,0,-1]]; vox.add([0,0,0].join(",")); const basis = [[0,1,0],[0,0,1],[1,0,0]]; for (const d of dirs) { for (let i=1;i<=arm;i++) vox.add([i*d[0],i*d[1],i*d[2]].join(",")); const end = [arm*d[0],arm*d[1],arm*d[2]]; const bar = basis.find(b => Math.abs(dot3(b,d)) < 0.1); vox.add([end[0]+bar[0], end[1]+bar[1], end[2]+bar[2]].join(",")); vox.add([end[0]-bar[0], end[1]-bar[1], end[2]-bar[2]].join(",")); } return generatePolycubeData([...vox].map(s => s.split(",").map(Number))); })())] }, "1_semicross": { name:"1-Semicross (Tripod)", category:["Polycubes"], build: () => [make_tile("1-Semi", gen_n_semicross_data(1))] }, "2_semicross": { name:"2-Semicross (Corner)", category:["Polycubes"], build: () => [make_tile("2-Semi", gen_n_semicross_data(2))] }, "buckled_ring": { name:"Buckled Ring", category:["Polycubes"], build: () => [make_tile("BuckledRing", gen_buckled_ring_data())] }, "large_buckled_ring": { name:"Large Buckled Ring", category:["Polycubes"], build: () => [make_tile("LargeRing", gen_large_buckled_ring_data())] }, "double_ring": { name:"Double Buckled Ring", category:["Polycubes"], build: () => [make_tile("DoubleRing", gen_double_ring_data())] }, "tuning_fork": { name:"Tuning Fork (Reinhardt)", category:["Polycubes"], build: () => [make_tile("Fork", gen_tuning_fork())] }, "twisted_h": { name:"Letter H (Twisted)", category:["Polycubes"], build: () => [make_tile("TwistedH", gen_twisted_h_data())] }, "cube": { name:"Cube", category:["Fedorov Solids","Polycubes"], build: () => [make_tile("Cube", gen_cube_data())] }, "letter_o": { name: "Letter O", category: ["Polycubes"], build: () => [make_tile("LetterO", gen_letter_o_data())], forbidden_rules: [ ["inner_single", "outer_side"] ] }, "1_cross_plus": { name:"1-Cross + 1", category:["Polycubes"], build: () => [make_tile("1CrossPlus", gen_1cross_plus_data())] }, "hex_prism": { name:"Hexagonal Prism", category:["Fedorov Solids"], build: () => [make_tile("HexPrism", gen_hex_prism())] }, "rhombic": { name:"Rhombic Dodecahedron", category:["Fedorov Solids"], build: () => [make_tile("RhombicDod", gen_rhombic_robust())] }, "elongated_dod": { name:"Elongated Dodecahedron", category:["Fedorov Solids"], build: () => [make_tile("ElongatedDod", gen_elongated_dodecahedron())] }, "trunc_oct": { name:"Truncated Octahedron", category:["Fedorov Solids"], build: () => [make_tile("TruncOct", gen_trunc_oct_robust())] }, "twist": { name:"Twist (Tetracube)", category:["Polycubes"], build: () => [make_tile("Twist", gen_s_tetracube())] }, "knuckle": { name:"Knuckle (Pentacube)", category:["Polycubes"], build: () => [make_tile("Knuckle", gen_knuckle_pentacube())] }, "tet_oct": { name:"Tetrahedron + Octahedron", category:["Platonic Solids"], build: () => [ make_tile("Tetrahedron", gen_tetrahedron_data()), make_tile("Octahedron", gen_octahedron_data()) ] }, "tetragonal_disphenoid": { name:"Tetragonal Disphenoid (B₃ alcove)", category:["Space Fillers"], build: () => [make_tile("Disphenoid", gen_tetragonal_disphenoid_data())] }, "diamond_lattice": { name:"Double FCC Lattice (Diamond)", category:["Platonic Solids"], build: () => [ make_tile("Tetrahedron", gen_tetrahedron_data()), make_tile("Octahedron", gen_octahedron_data()), make_tile("CornerTetra", gen_corner_tetra_data()) ], forbidden_rules: [ ["TET_FACE", "OCTA_FACE_A"], ["OCTA_FACE_B", "CORNER_CENTER"], ["CORNER_OUTER", "CORNER_CENTER"], ["CORNER_SIDE_L","CORNER_SIDE_R"] ], default_viz: { opacities:[0.9,0.1,0.1], internal:true } }, "perovskite": { name:"Perovskite (Cuboctahedron + Octa)", category:["Platonic Solids"], build: () => [ make_tile("Cuboctahedron", gen_cuboctahedron_data()), make_tile("Octahedron", gen_octahedron_data()) ], matching_rules: [], default_viz: { opacities:[0.5,0.9], internal:true } }, "orthoscheme": { name:"Orthoscheme (B̃₃ alcove)", category:["Space Fillers"], build: () => [make_tile("Orthoscheme", gen_orthoscheme_robust())], forbidden_rules: [], default_viz: { opacities:[0.6], internal:true } }, "elongated_sq_bipyramid": { name:"Elongated Bipyramid (J15)", category:["Space Fillers"], build: () => [make_tile("Johnson15", gen_elongated_square_bipyramid())] }, "gyrobifastigium": { name:"Gyrobifastigium (J26)", category:["Space Fillers"], build: () => [make_tile("Johnson26", gen_gyrobifastigium_data())] }, "laves_c15": { name:"Laves C15 (Truncated Tetra + Tetra))", category:["Platonic Solids"], build: () => [ make_tile("TruncTetra", gen_trunc_tetra_friauf()), make_tile("Tetra", gen_tetrahedron_data()) ], default_viz: { opacities:[0.4,1.0], internal:true } }, "escher_compound": { name:"Escher Solid (Core + Spikes)", category:["Space Fillers"], build: () => [ (() => { const d = gen_rhombic_robust(); d.f_data = d.f_data.map(f => ({ ...f, type:"RHOMBIC_CORE_FACE" })); return make_tile("RhombicCore", d); })(), make_tile("PyramidSpike", gen_rhombic_pyramid()) ], forbidden_rules: [ ["RHOMBIC_CORE_FACE","RHOMBIC_CORE_FACE"], ["RHOMBIC_SPIKE_BASE","RHOMBIC_SPIKE_BASE"] ], default_viz: { opacities:[1.0,0.5], internal:true } }, "fcc_pure": { name: "FCC (Pure Rhombic Dodecahedron)", category: ["Sphere Packings"], build: () => { const { rd } = gen_barlow_polyhedra(); return [make_tile("Rhombic_Dodecahedron_(FCC)", rd)]; }, default_viz: { opacities: [0.9], internal: true } }, "hcp_pure": { name: "HCP (Pure Trapezo-Rhombic Dodecahedron)", category: ["Sphere Packings"], build: () => { const { trd } = gen_barlow_polyhedra(); return [make_tile("Trapezo_Rhombic_Dodecahedron_(HCP)", trd)]; }, default_viz: { opacities: [0.9], internal: true } }, "barlow_fcc": { name: "Barlow Packing (Root: FCC)", category: ["Sphere Packings"], build: () => { const { rd, trd } = gen_barlow_polyhedra(); return [ make_tile("Rhombic_Dodecahedron_(FCC)", rd), make_tile("Trapezo_Rhombic_Dodecahedron_(HCP)", trd) ]; }, default_viz: { opacities: [0.8, 0.8], internal: true } }, "barlow_hcp": { name: "Barlow Packing (Root: HCP)", category: ["Sphere Packings"], build: () => { const { rd, trd } = gen_barlow_polyhedra(); return [ make_tile("Trapezo_Rhombic_Dodecahedron_(HCP)", trd), make_tile("Rhombic_Dodecahedron_(FCC)", rd) ]; }, default_viz: { opacities: [0.8, 0.8], internal: true } } }; const metadata = {}; for (const [k,v] of Object.entries(TILING_REGISTRY)) { const tiles = v.build(); metadata[k] = { name: v.name, category: v.category || [], is_chiral: !!tiles[0]?.is_chiral, default_viz: v.default_viz || {} }; } const categories = new Map(); for (const [k,meta] of Object.entries(metadata)) { for (const c of (meta.category || ["Other"])) { if (!categories.has(c)) categories.set(c, []); categories.get(c).push({ id: k, name: meta.name }); } } const options = [...categories.entries()] .sort((a,b)=>a[0].localeCompare(b[0])) .map(([group, tiles]) => ({ group, tiles: tiles.sort((a,b)=>a.name.localeCompare(b.name)) })); const addMirrorsIfChiral = (tiles) => { const out = tiles.slice(); for (const t of tiles) { if (t.is_chiral) { const m = t.get_mirror_copy(); if (m) out.push(m); } } return out; }; const getForbiddenPairs = (mode_key) => { const entry = TILING_REGISTRY[mode_key]; if (!entry || !entry.forbidden_rules || !entry.forbidden_rules.length) return new Set(); const forb = new Set(); for (const [a,b] of entry.forbidden_rules) { forb.add(`${a}@@${b}`); forb.add(`${b}@@${a}`); } return forb; }; return { SCALE, COLOR_PALETTE, TILING_REGISTRY, metadata, options, addMirrorsIfChiral, getForbiddenPairs }; })();