2e:null 2f:["$","title",null,{"children":"3D Lattice Tiler | Yao Liu | Observable"}] 34:T6677,viewof app = { const root = document.createElement("div"); root.style.cssText = ` width:100%; font-family: ui-sans-serif, system-ui, -apple-system, Segoe UI, Roboto, Helvetica, Arial; `; root.innerHTML = `

CONTROLS

Select Tiles

Max Tiles Layers

Max Tiles

Include mirror tiles (if chiral) Exhaustive Search

VIEW

Show Internal Faces Show Edges

TILES

`; const viewport = root.querySelector("#viewport"); const treePanel = root.querySelector("#treePanel"); const previewContainer = root.querySelector("#previewContainer"); const sleep = (ms) => new Promise(res => setTimeout(res, ms)); const deepClone = (x) => (typeof structuredClone === "function") ? structuredClone(x) : JSON.parse(JSON.stringify(x)); const prettyNameMap = new Map([ ["J15", "Johnson solid J15"], ["Gyro", "Gyro polyhedron"], ["FriaufPoly", "Friauf polyhedron"] ]); const prettyName = (s) => prettyNameMap.get(s) ?? s; // --- Three.js (assumes THREE + OrbitControls already imported in notebook) --- const scene = new THREE.Scene(); scene.background = new THREE.Color(0xf0f0f0); const camera = new THREE.PerspectiveCamera(50, 1, 0.1, 2000); camera.position.set(20, 20, 20); const renderer = new THREE.WebGLRenderer({ antialias: true }); viewport.appendChild(renderer.domElement); renderer.domElement.addEventListener("wheel", (e) => e.preventDefault(), { passive: false }); const controls = new OrbitControls(camera, renderer.domElement); controls.enableDamping = true; controls.minDistance = 0.5; controls.maxDistance = 1e6; scene.add(new THREE.AmbientLight(0xffffff, 0.65)); const dirLight = new THREE.DirectionalLight(0xffffff, 0.7); dirLight.position.set(10, 20, 10); scene.add(dirLight); const groupFaces = new THREE.Group(); const groupEdges = new THREE.Group(); scene.add(groupFaces); scene.add(groupEdges); function resize() { const w = viewport.clientWidth; const h = viewport.clientHeight; camera.aspect = w / h; camera.updateProjectionMatrix(); renderer.setSize(w, h, false); } new ResizeObserver(resize).observe(viewport); resize(); function clearGroup(g) { while (g.children.length) g.remove(g.children[0]); } // --- UI handles --- const selMode = root.querySelector("#selMode"); const statusEl = root.querySelector("#status"); const btnRun = root.querySelector("#btnRun"); const chkInternal = root.querySelector("#chkInternal"); const chkEdges = root.querySelector("#chkEdges"); const chkMirrors = root.querySelector("#chkMirrors"); const labMirrors = root.querySelector("#labMirrors"); const chkExhaustive = root.querySelector("#chkExhaustive"); const inpMax = root.querySelector("#inpMax"); const inpLayer = root.querySelector("#inpLayer"); const divCount = root.querySelector("#divCount"); const divLayer = root.querySelector("#divLayer"); const radios = [...root.querySelectorAll('input[name="criterion"]')]; const palette = tileSpecs.COLOR_PALETTE; function criterion() { return radios.find(r => r.checked).value; } function updateCriterionUI() { const c = criterion(); divCount.style.display = c === "count" ? "block" : "none"; divLayer.style.display = c === "layer" ? "block" : "none"; } radios.forEach(r => r.addEventListener("change", updateCriterionUI)); updateCriterionUI(); function setStatus(s) { statusEl.textContent = s; } // --- Simple Custom Tree Implementation (No D3) --- const treeMap = new Map(); // id -> node object const pendingSnapshots = new Map(); const expandedNodes = new Set(); // Track which nodes are expanded const manuallyExpanded = new Set(); // Track manually expanded nodes (won't auto-collapse) // Create a tree node element function createTreeNode(nodeId, depth = 0, isLastInGroup = false) { const node = treeMap.get(nodeId); if (!node) return null; const container = document.createElement("div"); container.style.cssText = ` position: relative; min-height: 20px; line-height: 20px; margin-left: ${depth * 18}px; padding-left: 20px; `; // Add toggle if node has children if (node.children && node.children.length > 0) { const toggle = document.createElement("span"); const isExpanded = expandedNodes.has(nodeId); const nodeColor = node.color_id != null && palette[node.color_id] ? palette[node.color_id] : "#666"; toggle.style.cssText = ` position: absolute; left: 0; top: 5px; width: 12px; height: 12px; cursor: pointer; display: flex; align-items: center; justify-content: center; font-size: ${isExpanded ? '14px' : '12px'}; color: ${nodeColor}; user-select: none; font-family: Arial, sans-serif; `; toggle.textContent = isExpanded ? "▼" : "▶"; toggle.onclick = (e) => { e.stopPropagation(); if (expandedNodes.has(nodeId)) { expandedNodes.delete(nodeId); manuallyExpanded.delete(nodeId); } else { expandedNodes.add(nodeId); manuallyExpanded.add(nodeId); } renderTree(); }; container.appendChild(toggle); } // Add node content const content = document.createElement("div"); content.className = "node-content"; content.style.cssText = ` display: inline-flex; align-items: center; padding: 2px 6px; border-radius: 8px; border: 1px solid transparent; cursor: ${node.snapshot ? 'pointer' : 'default'}; ${node.status === 'working' ? 'background:#e3f2fd; color:#1976d2;' : node.status === 'success' ? 'color:#2e7d32; font-weight:900;' : node.status === 'fail' ? 'color:#c62828; text-decoration:line-through; opacity:0.75;' : 'color:#aaa;'} ${node.is_forced ? 'font-style: italic; color: #555;' : ''} `; const text = document.createElement("span"); const prefix = depth === 1 ? '[1] ' : ''; const displayText = node.statusText ? `${node.label} ${node.statusText}` : node.label; text.textContent = `${prefix}${displayText}`; content.appendChild(text); // Click handler for showing snapshot if (node.snapshot) { content.onclick = (e) => { e.stopPropagation(); updateScene(node.snapshot); // Highlight selected node treePanel.querySelectorAll('.node-content').forEach(el => { el.style.border = "1px solid transparent"; }); content.style.border = "1px solid #333"; }; } container.appendChild(content); return container; } // Render the entire tree function renderTree() { treePanel.innerHTML = ""; function renderNode(nodeId, depth = 0, isLast = false) { const node = treeMap.get(nodeId); if (!node) return; const element = createTreeNode(nodeId, depth, isLast); if (element) { treePanel.appendChild(element); } // Render children if expanded and not failed (unless manually expanded) if (node.children && node.children.length > 0) { const shouldShowChildren = expandedNodes.has(nodeId) && (node.status !== 'fail' || manuallyExpanded.has(nodeId)); if (shouldShowChildren) { node.children.forEach((childId, index) => { const isLastChild = index === node.children.length - 1; renderNode(childId, depth + 1, isLastChild); }); } } } // Start with root-level nodes (nodes with no parent) const rootNodes = Array.from(treeMap.values()).filter(n => !n.parentId); rootNodes.forEach((node, index) => { const isLast = index === rootNodes.length - 1; renderNode(node.id, 1, isLast); }); // Auto-scroll to working nodes for (const node of treeMap.values()) { if (node.status === 'working') { // Find the node element setTimeout(() => { // We need to find the element by traversing the DOM // Since we don't have a direct reference, we'll scroll the treePanel to show working nodes const workingNodes = treePanel.querySelectorAll('.node-content'); for (const el of workingNodes) { if (el.textContent.includes(node.label)) { el.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); break; } } }, 50); } } } // Add a node to the tree function addNodeToTree(id, label, parentId = null, is_forced = false) { // Check if node already exists if (treeMap.has(id)) { const existingNode = treeMap.get(id); // Update the label if provided if (label?.trim()) { existingNode.label = label.trim(); } existingNode.is_forced = !!is_forced; renderTree(); return existingNode; } // Create new node const node = { id, label: label?.trim() || '', parentId, is_forced: !!is_forced, children: [], snapshot: null, status: 'pending', statusText: '', color_id: null }; treeMap.set(id, node); // Add to parent's children if (parentId) { const parent = treeMap.get(parentId); if (parent && !parent.children.includes(id)) { parent.children.push(id); } } // Auto-expand first level nodes if (parentId === null && !expandedNodes.has(id)) { expandedNodes.add(id); } renderTree(); return node; } // Update a node's status function updateNodeStatus(id, status, text = '', color_id = null) { const node = treeMap.get(id); if (node) { const prevStatus = node.status; node.status = status; // Update status text if provided if (text?.trim()) { node.statusText = text; } if (color_id != null) { node.color_id = color_id; } // Auto-collapse failed nodes (unless manually expanded) if (status === 'fail' && prevStatus !== 'fail' && !manuallyExpanded.has(id)) { expandedNodes.delete(id); } // Auto-expand ancestors of working nodes if (status === 'working' && node.parentId) { let currentId = node.parentId; while (currentId) { if (!expandedNodes.has(currentId)) { expandedNodes.add(currentId); } const parent = treeMap.get(currentId); currentId = parent?.parentId; } } renderTree(); } } // Clear the entire tree function clearTreeData() { treeMap.clear(); pendingSnapshots.clear(); expandedNodes.clear(); manuallyExpanded.clear(); treePanel.innerHTML = ""; } // --- Scene --- let lastSnapshot = null; let prototileInfo = null; let currentOpacities = {}; let rootCentered = false; function centroidOfSnapshotVertices(snapshot, scale) { const seen = new Set(); let sx = 0, sy = 0, sz = 0, n = 0; for (const face of snapshot.faces ?? []) { for (const p of (face.v ?? [])) { const x = p[0] / scale, y = p[1] / scale, z = p[2] / scale; const key = `${x},${y},${z}`; if (seen.has(key)) continue; seen.add(key); sx += x; sy += y; sz += z; n++; } } if (!n) return null; return [sx / n, sy / n, sz / n]; } function centerOnRootOnce(snapshot) { if (rootCentered) return; const scale = prototileInfo?.scale ?? 2; const c = centroidOfSnapshotVertices(snapshot, scale); if (!c) return; const camOffset = camera.position.clone().sub(controls.target); controls.target.set(c[0], c[1], c[2]); camera.position.copy(new THREE.Vector3(c[0], c[1], c[2]).add(camOffset)); controls.update(); rootCentered = true; } function updateScene(snapshot) { lastSnapshot = snapshot; clearGroup(groupFaces); clearGroup(groupEdges); const showInternal = chkInternal.checked; const showEdges = chkEdges.checked; const scale = prototileInfo?.scale ?? 2; for (const face of snapshot.faces ?? []) { if (face.internal && !showInternal) continue; const tIdx = face.type_idx ?? 0; const alpha = (currentOpacities[tIdx] ?? 0.9); if (alpha < 0.01) continue; const v = face.v; const tris = []; const lines = []; for (let i = 1; i < v.length - 1; i++) { const v0 = v[0], v1 = v[i], v2 = v[i + 1]; tris.push( v0[0] / scale, v0[1] / scale, v0[2] / scale, v1[0] / scale, v1[1] / scale, v1[2] / scale, v2[0] / scale, v2[1] / scale, v2[2] / scale ); } const geo = new THREE.BufferGeometry(); geo.setAttribute("position", new THREE.Float32BufferAttribute(tris, 3)); geo.computeVertexNormals(); const mat = new THREE.MeshPhongMaterial({ color: new THREE.Color(face.color), transparent: true, opacity: alpha, side: THREE.DoubleSide, flatShading: true, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 1, depthWrite: alpha > 0.5 }); groupFaces.add(new THREE.Mesh(geo, mat)); if (showEdges) { for (let i = 0; i < v.length; i++) { const a = v[i], b = v[(i + 1) % v.length]; lines.push( a[0] / scale, a[1] / scale, a[2] / scale, b[0] / scale, b[1] / scale, b[2] / scale ); } const lg = new THREE.BufferGeometry(); lg.setAttribute("position", new THREE.Float32BufferAttribute(lines, 3)); const lm = new THREE.LineBasicMaterial({ color: 0x000000, transparent: true, opacity: alpha }); groupEdges.add(new THREE.LineSegments(lg, lm)); } } } function initPreviews(info) { previewContainer.innerHTML = ""; prototileInfo = info; const defOps = info.default_opacities ?? []; info.tiles.forEach((t, i) => { if (currentOpacities[i] == null) currentOpacities[i] = (defOps[i] ?? 0.9); }); const nameW = 110; const sliderW = 80; info.tiles.forEach((tile, idx) => { const row = document.createElement("div"); row.style.cssText = "display:flex; align-items:center; justify-content:space-between; gap:8px; border:1px solid #ddd; border-radius:10px; padding:8px; background:#fff; box-sizing:border-box;"; const name = document.createElement("div"); name.textContent = prettyName(tile.name); name.title = prettyName(tile.name); name.style.cssText = `width:${nameW}px; max-width:${nameW}px; font-size:12px; font-weight:800; color:#333; overflow:hidden; text-overflow:ellipsis; white-space:nowrap;`; const slider = document.createElement("input"); slider.type = "range"; slider.min = "0"; slider.max = "1"; slider.step = "0.05"; slider.value = currentOpacities[idx]; slider.style.cssText = `width:${sliderW}px; flex:0 0 auto;`; slider.addEventListener("input", (e) => { currentOpacities[idx] = +e.target.value; if (lastSnapshot) updateScene(lastSnapshot); }); row.appendChild(name); row.appendChild(slider); previewContainer.appendChild(row); }); const c = info.global_center ?? [0, 0, 0]; controls.target.set(c[0], c[1], c[2]); const r = info.global_radius ?? 5; const dist = r * 6 + 10; camera.position.set(c[0] + dist, c[1] + dist * 0.7, c[2] + dist); controls.update(); } function setModeOptions() { selMode.innerHTML = ""; for (const group of tileSpecs.options) { const og = document.createElement("optgroup"); og.label = group.group; for (const t of group.tiles) { const opt = document.createElement("option"); opt.value = t.id; opt.textContent = prettyName(t.name); og.appendChild(opt); } selMode.appendChild(og); } } function updateInternalDefault() { const mode = selMode.value; const meta = tileSpecs.metadata[mode]; chkInternal.checked = !!(meta?.default_viz?.internal); } function updateMirrorCheckboxEnabled() { const mode = selMode.value; const meta = tileSpecs.metadata?.[mode] ?? null; const isChiral = !!meta?.is_chiral; chkMirrors.disabled = !isChiral; labMirrors.style.opacity = isChiral ? "1" : "0.45"; labMirrors.style.cursor = isChiral ? "pointer" : "not-allowed"; if (!isChiral) chkMirrors.checked = false; } // --- run/pause/continue state (true pause: stop consuming iterator) --- let stopToken = { stop: false }; let running = false; // actively consuming stream let paused = false; // stream exists but not consuming let isFinished = false; // last stream ended with finished let runSeq = 0; // cancels old consumers let streamIter = null; // active async generator iterator let pausedConfigKey = null; function configKey() { return JSON.stringify({ mode_key: selMode.value, criterion: criterion(), target_val: criterion() === "count" ? +inpMax.value : +inpLayer.value, exhaustive: chkExhaustive.checked, include_mirrors: chkMirrors.checked }); } function canBrowseTree() { return !running; } function setRunButton() { if (running) { btnRun.textContent = "▌▌ PAUSE"; return; } if (paused && pausedConfigKey === configKey()) btnRun.textContent = "▶︎ CONTINUE"; else btnRun.textContent = "▶︎ RUN"; } // --- Tree Message Handlers --- function onBranchSet({ parent, branches }) { if (!branches || !Array.isArray(branches)) return; branches.forEach(branch => { if (branch && branch.id) { addNodeToTree(branch.id, branch.text || "", parent, branch.is_forced); } }); } function onNodeStatus({ id, status, text, color_id }) { if (!id) return; updateNodeStatus(id, status, text || "", color_id); } function handleMessage(msg) { if (msg.type === "prototile_info") return initPreviews(msg); if (msg.type === "branch_set") return onBranchSet(msg); if (msg.type === "node_status") return onNodeStatus(msg); if (msg.type === "full_update") { centerOnRootOnce(msg); updateScene(msg); const frozen = deepClone(msg); if (msg.node_id != null) { const n = treeMap.get(msg.node_id); if (n) { n.snapshot = frozen; renderTree(); } else { pendingSnapshots.set(msg.node_id, frozen); } } return; } if (msg.type === "finished") { isFinished = true; setStatus(`Finished: ${msg.tile_count} tiles`); running = false; paused = false; streamIter = null; setRunButton(); return; } } async function consumeStream(mySeq) { while (streamIter && mySeq === runSeq && running && !paused) { const { value: msg, done } = await streamIter.next(); if (mySeq !== runSeq) break; if (done) break; handleMessage(msg); if (msg?.type === "full_update") { await new Promise(requestAnimationFrame); await sleep(100); } if (msg?.type === "finished") break; } if (mySeq !== runSeq) return; setRunButton(); if (!isFinished && paused) setStatus("Paused"); } function invalidatePausedRunIfNeeded() { if (!paused) { setRunButton(); return; } if (pausedConfigKey !== configKey()) { runSeq++; streamIter = null; paused = false; setStatus("Ready"); } setRunButton(); } function startNewRun() { runSeq++; streamIter = null; paused = false; stopToken = { stop: false }; isFinished = false; rootCentered = false; clearTreeData(); clearGroup(groupFaces); clearGroup(groupEdges); const cfg = JSON.parse(configKey()); pausedConfigKey = configKey(); running = true; paused = false; setRunButton(); setStatus("Running…"); streamIter = createTilingStream(cfg, tileSpecs, stopToken); const mySeq = runSeq; consumeStream(mySeq); } function continueRun() { if (!streamIter) return startNewRun(); paused = false; running = true; setRunButton(); setStatus("Running…"); const mySeq = runSeq; consumeStream(mySeq); } function pauseRun() { paused = true; running = false; setRunButton(); setStatus("Paused"); } // --- view toggles --- chkInternal.addEventListener("change", () => { if (lastSnapshot) updateScene(lastSnapshot); }); chkEdges.addEventListener("change", () => { if (lastSnapshot) updateScene(lastSnapshot); }); // --- criterion UI + invalidation --- radios.forEach(r => r.addEventListener("change", () => { updateCriterionUI(); invalidatePausedRunIfNeeded(); })); inpMax.addEventListener("input", invalidatePausedRunIfNeeded); inpLayer.addEventListener("input", invalidatePausedRunIfNeeded); chkExhaustive.addEventListener("change", invalidatePausedRunIfNeeded); chkMirrors.addEventListener("change", invalidatePausedRunIfNeeded); // --- mode options + defaults --- setModeOptions(); selMode.addEventListener("change", () => { updateInternalDefault(); updateMirrorCheckboxEnabled(); currentOpacities = {}; invalidatePausedRunIfNeeded(); }); updateInternalDefault(); updateMirrorCheckboxEnabled(); // --- RUN / PAUSE / CONTINUE button --- btnRun.addEventListener("click", () => { if (running) return pauseRun(); if (paused && pausedConfigKey === configKey() && streamIter) return continueRun(); startNewRun(); }); setRunButton(); setStatus("Ready"); // Animation loop (function animate() { requestAnimationFrame(animate); controls.update(); renderer.render(scene, camera); })(); // Start initial run queueMicrotask(startNewRun); return root; }35:T697f,// CELL 2 (tiler) — Added Branching Factor & MinGen Stats to labels createTilingStream = (() => { const __protoAdjCache = new Map(); return async function* createTilingStream(config, tileSpecs, stopToken) { const SCALE = tileSpecs.SCALE; const MAX_SOLID_ANGLE = 48; const COLOR_PALETTE = tileSpecs.COLOR_PALETTE; const tick = () => new Promise(requestAnimationFrame); const keyFace = (verts) => { const s = [...verts].map(v => v.join(",")).sort(); return s.join("|"); }; const faceSignature = (verts) => { const n = verts.length; const edges = []; for (let i = 0; i < n; i++) { const a = verts[i], b = verts[(i + 1) % n]; edges.push([b[0] - a[0], b[1] - a[1], b[2] - a[2]]); } const lengths = edges.map(e => e[0] * e[0] + e[1] * e[1] + e[2] * e[2]); const dots = edges.map((e, i) => { const f = edges[(i + 1) % n]; return e[0] * f[0] + e[1] * f[1] + e[2] * f[2]; }); const combined = lengths.map((L, i) => [L, dots[i]]); const rotate = (arr, k) => arr.slice(k).concat(arr.slice(0, k)); let best = combined; for (let k = 1; k < n; k++) { const r = rotate(combined, k); let better = false; for (let i = 0; i < n; i++) { if (r[i][0] !== best[i][0]) { better = r[i][0] < best[i][0]; break; } if (r[i][1] !== best[i][1]) { better = r[i][1] < best[i][1]; break; } } if (better) best = r; } return best.map(p => `${p[0]},${p[1]}`).join("|"); }; const faceSignatureUndirected = (verts) => { const a = faceSignature(verts); const b = faceSignature([...verts].slice().reverse()); return (a < b) ? a : b; }; const isCyclicPermutation = (a, b) => { if (a.length !== b.length) return false; const n = a.length; const a0 = a[0].join(","); let start = -1; for (let i = 0; i < n; i++) if (b[i].join(",") === a0) { start = i; break; } if (start < 0) return false; for (let i = 0; i < n; i++) { const ai = a[i], bi = b[(start + i) % n]; if (ai[0] !== bi[0] || ai[1] !== bi[1] || ai[2] !== bi[2]) return false; } return true; }; const add3 = (a, b) => [a[0] + b[0], a[1] + b[1], a[2] + b[2]]; const isForbidden = (rules, a, b) => rules ? rules.has(`${a}@@${b}`) : false; // --- Build Prototiles First (to ensure correct order and cache key) --- const { mode_key } = config; const includeMirrors = !!config.include_mirrors; const modeDef = tileSpecs.TILING_REGISTRY[mode_key]; if (!modeDef) throw new Error(`Unknown mode_key: ${mode_key}`); const baseTiles = modeDef.build(); const prototiles = (() => { const out = []; for (const t of baseTiles) { out.push(t); if (includeMirrors && t.is_chiral) { const m = t.get_mirror_copy?.(); if (m) { if (t.name.startsWith("reflected ")) { m.name = t.name.substring(10); } else { m.name = `reflected ${t.name}`; } m.__is_mirror = true; out.push(m); } } } return out; })(); const tileSignature = prototiles.map(t => t.name).join("||"); const cacheKey = `${SCALE}::${mode_key}::${includeMirrors ? 1 : 0}::${tileSignature}`; let cached = __protoAdjCache.get(cacheKey); if (!cached) { console.time("LUT building"); const forbiddenRules0 = (() => { const rules = modeDef.forbidden_rules ?? null; if (!rules || !rules.length) return null; const S = new Set(); for (const [a, b] of rules) { S.add(`${a}@@${b}`); S.add(`${b}@@${a}`); } return S; })(); const adjacency0 = new Map(); const orientFaceSignatures = new Map(); for (let p_idx = 0; p_idx < prototiles.length; p_idx++) { const p = prototiles[p_idx]; for (const orient of p.unique_orientations) { const faceSigs = []; for (let f_idx = 0; f_idx < orient.faces.length; f_idx++) { const faceIdx = orient.faces[f_idx]; const fVerts = faceIdx.map(i => orient.verts[i]); const sig = faceSignatureUndirected(fVerts); faceSigs.push(sig); if (!adjacency0.has(sig)) adjacency0.set(sig, []); adjacency0.get(sig).push({ p_idx, orient, f_indices: faceIdx, face_type: orient.face_types[f_idx] }); } orientFaceSignatures.set(orient, faceSigs); } } const viablePlacements0 = new Map(); for (let src_p = 0; src_p < prototiles.length; src_p++) { const srcProto = prototiles[src_p]; for (const srcOrient of srcProto.unique_orientations) { for (let src_fi = 0; src_fi < srcOrient.faces.length; src_fi++) { const srcFaceIdx = srcOrient.faces[src_fi]; const srcVerts = srcFaceIdx.map(i => srcOrient.verts[i]); const srcSig = faceSignatureUndirected(srcVerts); const srcFaceType = srcOrient.face_types[src_fi]; const pot = adjacency0.get(srcSig) ?? []; const filtered = forbiddenRules0 ? pot.filter(e => !forbiddenRules0.has(`${srcFaceType}@@${e.face_type}`)) : pot; const srcFaceSigs = orientFaceSignatures.get(srcOrient); for (const cand of filtered) { const base = cand.orient.vertsForFace(cand.f_indices); const faceLoops = [base, [...base].slice().reverse()]; const n = base.length; for (const candFaceVerts of faceLoops) { for (let r = 0; r < n; r++) { const cv0 = candFaceVerts[r]; const srcV0 = srcVerts[0]; const translation = [srcV0[0] - cv0[0], srcV0[1] - cv0[1], srcV0[2] - cv0[2]]; let okGeom = true; for (let k = 0; k < n; k++) { const v = candFaceVerts[(r + k) % n]; const g = [v[0] + translation[0], v[1] + translation[1], v[2] + translation[2]]; const t = srcVerts[k]; if (g[0] !== t[0] || g[1] !== t[1] || g[2] !== t[2]) { okGeom = false; break; } } if (!okGeom) continue; const candFaceSigs = orientFaceSignatures.get(cand.orient); let isViable = true; for (let f_idx = 0; f_idx < cand.orient.faces.length; f_idx++) { if (f_idx === cand.f_indices) continue; const sig = candFaceSigs[f_idx]; const potentialMatches = adjacency0.get(sig); if (!potentialMatches || potentialMatches.length === 0) { isViable = false; break; } const candFaceType = cand.orient.face_types[f_idx]; let hasValidMatch = false; for (const match of potentialMatches) { if (forbiddenRules0 && forbiddenRules0.has(`${candFaceType}@@${match.face_type}`)) continue; hasValidMatch = true; break; } if (!hasValidMatch) { isViable = false; break; } } const transHash = translation.join(","); const viabilityKey = `${src_p}::${src_fi}::${cand.p_idx}::${transHash}`; viablePlacements0.set(viabilityKey, isViable); } } } } } } cached = { adjacency: adjacency0, viablePlacements: viablePlacements0, orientFaceSignatures: orientFaceSignatures, forbiddenRules: forbiddenRules0 }; __protoAdjCache.set(cacheKey, cached); console.timeEnd("LUT building"); } const { adjacency, viablePlacements, orientFaceSignatures, forbiddenRules } = cached; const isPolycubeSystem = (modeDef.category ?? []).includes("Polycubes"); const protoInfo = prototiles.map(p => { return { name: p.name, verts: p.verts, faces: p.faces, lattice_points: isPolycubeSystem ? [] : p.occupancy_points.map(o => o.pos), is_chiral: !!p.is_chiral, is_mirror: !!p.__is_mirror }; }); let global_center = [0, 0, 0], global_radius = 5; const allUnscaled = []; protoInfo.forEach(p => p.verts.forEach(v => allUnscaled.push([v[0]/SCALE, v[1]/SCALE, v[2]/SCALE]))); if (allUnscaled.length) { const mins = [Infinity, Infinity, Infinity], maxs = [-Infinity, -Infinity, -Infinity]; for (const v of allUnscaled) { for (let i = 0; i < 3; i++) { mins[i] = Math.min(mins[i], v[i]); maxs[i] = Math.max(maxs[i], v[i]); } } global_center = [(mins[0] + maxs[0]) / 2, (mins[1] + maxs[1]) / 2, (mins[2] + maxs[2]) / 2]; const dx = maxs[0] - global_center[0], dy = maxs[1] - global_center[1], dz = maxs[2] - global_center[2]; global_radius = Math.sqrt(dx * dx + dy * dy + dz * dz) || 2; } yield { type: "palette", colors: COLOR_PALETTE }; yield { type: "prototile_info", tiles: protoInfo, scale: SCALE, global_center, global_radius, default_opacities: modeDef.default_viz?.opacities ?? [], default_internal: !!modeDef.default_viz?.internal }; const state = { placements: [], frontier: new Map(), lattice: new Map(), viz_faces: new Map() }; let faceCounter = 0; let nodeCounter = 0; const nowId = () => (++nodeCounter); const branchSet = (parent, branches) => ({ type: "branch_set", parent, branches }); const nodeStatus = (id, status, append_text = "", extra = {}) => ({ type: "node_status", id, status, text: append_text, ...extra }); const snapshot = (node_id = null) => { const faces = []; for (const stack of state.viz_faces.values()) for (const f of stack) faces.push(f); return { type: "full_update", tile_count: state.placements.length, faces, node_id }; }; const latticeGet = (pos) => state.lattice.get(pos.join(",")) ?? 0; const latticeAdd = (pos, w) => { const k = pos.join(","); state.lattice.set(k, (state.lattice.get(k) ?? 0) + w); if (state.lattice.get(k) <= 0) state.lattice.delete(k); }; const isMoveValid = (move) => { const { orient, translation } = move; for (const pt of orient.occupancy) { const g = add3(pt.pos, translation); if (latticeGet(g) + pt.weight > MAX_SOLID_ANGLE) return { ok: false }; } const gVerts = orient.verts.map(v => add3(v, translation)); for (let f_idx = 0; f_idx < orient.faces.length; f_idx++) { const fIdx = orient.faces[f_idx]; const poly = fIdx.map(i => gVerts[i]); const k = keyFace(poly); const existing = state.frontier.get(k); if (existing) { const rev = [...existing.ordered_verts].slice().reverse(); if (!isCyclicPermutation(poly, rev)) return { ok: false }; if (isForbidden(forbiddenRules, existing.face_type, orient.face_types[f_idx])) return { ok: false }; } } const occData = orient.occupancy.map(pt => ({ pos: add3(pt.pos, translation), weight: pt.weight })); return { ok: true, occData }; }; const isMoveViable = (move, frontierFaceKey, srcFaceType) => { const validCheck = isMoveValid(move); if (!validCheck.ok) return false; const existing = state.frontier.get(frontierFaceKey); if (existing) { const transHash = move.translation.join(","); const viabilityKey = `${existing.type}::${existing.face_idx}::${move.prototile_idx}::${transHash}`; if (viablePlacements.has(viabilityKey)) return viablePlacements.get(viabilityKey); } const gVerts = move.orient.verts.map(v => add3(v, move.translation)); const candFaceSigs = orientFaceSignatures.get(move.orient); for (let f_idx = 0; f_idx < move.orient.faces.length; f_idx++) { const fIdx = move.orient.faces[f_idx]; const poly = fIdx.map(i => gVerts[i]); const faceKey = keyFace(poly); if (faceKey === frontierFaceKey) continue; const existing = state.frontier.get(faceKey); if (existing) continue; const sig = candFaceSigs[f_idx]; const potentialMatches = adjacency.get(sig); if (!potentialMatches || potentialMatches.length === 0) return false; const candFaceType = move.orient.face_types[f_idx]; let hasValidMatch = false; for (const match of potentialMatches) { if (isForbidden(forbiddenRules, candFaceType, match.face_type)) continue; hasValidMatch = true; break; } if (!hasValidMatch) return false; } return true; }; const getCandidatesForFace = (faceKeyStr) => { const existing = state.frontier.get(faceKeyStr); const target = existing.ordered_verts; const needed = [...target].slice().reverse(); const sig = faceSignatureUndirected(needed); let pot = adjacency.get(sig) ?? []; if (!pot.length) return []; const v0t = needed[0]; const tv = [needed[1][0] - v0t[0], needed[1][1] - v0t[1], needed[1][2] - v0t[2]]; const dedup = new Map(); for (const pm of pot) { if (isForbidden(forbiddenRules, existing.face_type, pm.face_type)) continue; const base = pm.orient.vertsForFace(pm.f_indices); const faceLoops = [base, [...base].slice().reverse()]; for (const candFaceVerts of faceLoops) { const n = candFaceVerts.length; for (let r = 0; r < n; r++) { const cv0 = candFaceVerts[r]; const cv1 = candFaceVerts[(r + 1) % n]; const dv = [cv1[0] - cv0[0], cv1[1] - cv0[1], cv1[2] - cv0[2]]; if (dv[0] !== tv[0] || dv[1] !== tv[1] || dv[2] !== tv[2]) continue; const translation = [v0t[0] - cv0[0], v0t[1] - cv0[1], v0t[2] - cv0[2]]; let okGeom = true; for (let k = 0; k < n; k++) { const v = candFaceVerts[(r + k) % n]; const g = [v[0] + translation[0], v[1] + translation[1], v[2] + translation[2]]; const t = needed[k]; if (g[0] !== t[0] || g[1] !== t[1] || g[2] !== t[2]) { okGeom = false; break; } } if (!okGeom) continue; const mv = { prototile_idx: pm.p_idx, translation, orient: pm.orient }; const gVerts = mv.orient.verts.map(v => add3(v, mv.translation)); let forbiddenDetected = false; for (let f_idx = 0; f_idx < mv.orient.faces.length; f_idx++) { const fIdx = mv.orient.faces[f_idx]; const poly = fIdx.map(i => gVerts[i]); const k = keyFace(poly); const existingFace = state.frontier.get(k); if (existingFace && isForbidden(forbiddenRules, existingFace.face_type, mv.orient.face_types[f_idx])) { forbiddenDetected = true; break; } } if (forbiddenDetected) continue; if (!isMoveViable(mv, faceKeyStr, existing.face_type)) continue; const chk = isMoveValid(mv); if (!chk.ok) continue; const occKey = chk.occData.map(o => o.pos.join(",")).sort().join("|"); const dKey = `${pm.p_idx}::${occKey}`; if (!dedup.has(dKey)) dedup.set(dKey, { ...mv, occupancy_data: chk.occData, dedup_key: dKey }); } } } return [...dedup.values()]; }; const applyMove = (move) => { state.placements.push(move); for (const o of move.occupancy_data) latticeAdd(o.pos, o.weight); const gVerts = move.orient.verts.map(v => add3(v, move.translation)); const neighborColors = new Set(); const coveredGens = []; for (const fIdx of move.orient.faces) { const poly = fIdx.map(i => gVerts[i]); const k = keyFace(poly); if (state.frontier.has(k)) { neighborColors.add(state.frontier.get(k).color_id); coveredGens.push(state.frontier.get(k).gen); } } const newGen = coveredGens.length ? (Math.min(...coveredGens) + 1) : 0; const available = COLOR_PALETTE.map((_, i) => i).filter(i => !neighborColors.has(i)); move.color_id = available.length ? available[Math.floor(Math.random() * available.length)] : 0; const added = [], removed = [], modified_gens = []; for (let f_idx = 0; f_idx < move.orient.faces.length; f_idx++) { const fIdx = move.orient.faces[f_idx]; const poly = fIdx.map(i => gVerts[i]); const k = keyFace(poly); const face_type = move.orient.face_types[f_idx]; if (state.frontier.has(k)) { removed.push([k, state.frontier.get(k)]); state.frontier.delete(k); if (!state.viz_faces.has(k)) state.viz_faces.set(k, []); state.viz_faces.get(k).push({ v: poly, color: COLOR_PALETTE[move.color_id], internal: true, type_idx: move.prototile_idx }); for (const vf of state.viz_faces.get(k)) vf.internal = true; } else { faceCounter += 1; state.frontier.set(k, { type: move.prototile_idx, face_idx: f_idx, ordered_verts: poly, color_id: move.color_id, id: faceCounter, gen: newGen, face_type }); added.push(k); const viz = { v: poly, color: COLOR_PALETTE[move.color_id], internal: false, type_idx: move.prototile_idx }; if (!state.viz_faces.has(k)) state.viz_faces.set(k, []); state.viz_faces.get(k).push(viz); } } if (added.length) { const activeVerts = new Set(); for (const k of added) for (const v of state.frontier.get(k).ordered_verts) activeVerts.add(v.join(",")); const vertToKeys = new Map(); for (const [k, entry] of state.frontier.entries()) { for (const v of entry.ordered_verts) { const kk = v.join(","); if (activeVerts.has(kk)) { if (!vertToKeys.has(kk)) vertToKeys.set(kk, []); vertToKeys.get(kk).push(k); } } } const q = [...added]; while (q.length) { const curr = q.shift(); const ce = state.frontier.get(curr); if (!ce) continue; for (const v of ce.ordered_verts) { for (const nk of (vertToKeys.get(v.join(",")) ?? [])) { if (nk === curr) continue; const ne = state.frontier.get(nk); if (ne && ne.gen > ce.gen + 1) { modified_gens.push([nk, ne.gen]); ne.gen = ce.gen + 1; q.push(nk); } } } } } return { added, removed, modified_gens }; }; const undoMove = (move, rb) => { for (const [k, oldGen] of (rb.modified_gens ?? [])) { const e = state.frontier.get(k); if(e) e.gen = oldGen; } for (const [k, val] of rb.removed) { state.frontier.set(k, val); const stack = state.viz_faces.get(k); if (stack) { stack.pop(); if (stack.length === 1) stack[0].internal = false; if (stack.length === 0) state.viz_faces.delete(k); } } for (const k of rb.added) { state.frontier.delete(k); const stack = state.viz_faces.get(k); if (stack) { stack.pop(); if (stack.length === 0) state.viz_faces.delete(k); } } for (const o of move.occupancy_data) latticeAdd(o.pos, -o.weight); state.placements.pop(); }; const p0 = prototiles[0]; const startOrient = p0.unique_orientations[0]; const startTrans = [-startOrient.verts[0][0], -startOrient.verts[0][1], -startOrient.verts[0][2]]; const startOcc = startOrient.occupancy.map(pt => ({ pos: add3(pt.pos, startTrans), weight: pt.weight })); const calculateFrontierStats = () => { let minGen = Infinity, minGenCount = 0; for (const v of state.frontier.values()) { if (v.gen < minGen) { minGen = v.gen; minGenCount = 1; } else if (v.gen === minGen) minGenCount++; } return { min_gen: minGen === Infinity ? 0 : minGen, count: minGenCount, total_faces: state.frontier.size }; }; const startMove = { prototile_idx: 0, translation: startTrans, occupancy_data: startOcc, orient: startOrient, color_id: 0 }; state.placements.push(startMove); for (const o of startMove.occupancy_data) latticeAdd(o.pos, o.weight); const gVerts0 = startOrient.verts.map(v => add3(v, startTrans)); for (let f_idx = 0; f_idx < startOrient.faces.length; f_idx++) { const fIdx = startOrient.faces[f_idx]; const poly = fIdx.map(i => gVerts0[i]); const k = keyFace(poly); faceCounter += 1; state.frontier.set(k, { type: 0, face_idx: f_idx, ordered_verts: poly, color_id: 0, id: faceCounter, gen: 0, face_type: startOrient.face_types[f_idx] }); state.viz_faces.set(k, [{ v: poly, color: COLOR_PALETTE[0], internal: false, type_idx: 0 }]); } const rootId = nowId(); const rootStats = calculateFrontierStats(); yield branchSet(null, [{ id: rootId, text: `${p0.name} (root) | ${rootStats.count} faces @ gen ${rootStats.min_gen}` }]); yield nodeStatus(rootId, "working", "", { color_id: 0, frontier_stats: rootStats }); yield snapshot(rootId); await tick(); const exhaustive = !!config.exhaustive; const criterion = config.criterion ?? "count"; const targetVal = Math.max(1, +config.target_val || 50); const safetyMax = 2000; const moveCoverage = (m) => { const gVerts = m.orient.verts.map(v => add3(v, m.translation)); let c = 0; for (const fIdx of m.orient.faces) if (state.frontier.has(keyFace(fIdx.map(i => gVerts[i])))) c++; return c; }; async function* search(parentId) { if (stopToken.stop) return false; const forcedBatch = []; const doReturn = async function* (retval) { if (retval && !exhaustive) return true; while (forcedBatch.length) { const [mv, rb] = forcedBatch.pop(); undoMove(mv, rb); } return retval; }; while (true) { if (stopToken.stop) return false; if (state.frontier.size === 0) { yield nodeStatus(parentId, "success"); return yield* doReturn(true); } const faces = [...state.frontier.keys()]; let forcedCount = 0; const preForcedStats = calculateFrontierStats(); for (const f of faces) { if (!state.frontier.has(f)) continue; const cands = getCandidatesForFace(f); if (cands.length === 0) { yield nodeStatus(parentId, "fail"); return yield* doReturn(false); } if (cands.length === 1) { const mv = cands[0]; const gVerts = mv.orient.verts.map(v => add3(v, mv.translation)); const coveredGens = []; for (const fIdx of mv.orient.faces) { const k = keyFace(fIdx.map(i => gVerts[i])); if (state.frontier.get(k)) coveredGens.push(state.frontier.get(k).gen); } const newGen = coveredGens.length ? (Math.min(...coveredGens) + 1) : 0; if (newGen <= preForcedStats.min_gen + 2) { const rb = applyMove(mv); forcedBatch.push([mv, rb]); forcedCount += 1; } } } if (forcedCount > 0) { const postForcedStats = calculateFrontierStats(); const forcedNodeId = nowId(); yield branchSet(parentId, [{ id: forcedNodeId, text: `+ ${forcedCount} forced | ${postForcedStats.count} faces @ gen ${postForcedStats.min_gen}`, is_forced: true, frontier_stats: postForcedStats }]); yield nodeStatus(forcedNodeId, "success"); yield snapshot(forcedNodeId); await tick(); } let ok = false; if (criterion === "count" && state.placements.length >= targetVal) ok = true; else if (criterion === "layer" && calculateFrontierStats().min_gen >= targetVal) ok = true; if (state.placements.length >= safetyMax) ok = true; if (ok) { yield nodeStatus(parentId, "success"); return yield* doReturn(true); } if (forcedCount === 0) break; } const currentStats = calculateFrontierStats(); const minGenFaces = []; for (const [k, v] of state.frontier.entries()) if (v.gen === currentStats.min_gen) minGenFaces.push(k); let bestFace = null; if (minGenFaces.length) { let bestCoverage = -1; for (const f of minGenFaces) { const moves = getCandidatesForFace(f); if (!moves.length) continue; for (const m of moves) { const c = moveCoverage(m); if (c > bestCoverage) { bestCoverage = c; bestFace = f; } } } if (!bestFace) for (const f of minGenFaces) if (getCandidatesForFace(f).length) { bestFace = f; break; } } if (!bestFace) { yield nodeStatus(parentId, "fail", "Dead End"); return yield* doReturn(false); } const bestMoves = getCandidatesForFace(bestFace).sort((a, b) => moveCoverage(b) - moveCoverage(a)); const payload = bestMoves.map(() => { const id = nowId(); return { id, text: "" }; }); for (let i = 0; i < bestMoves.length; i++) bestMoves[i].node_id = payload[i].id; yield branchSet(parentId, payload); let anySuccess = false; for (let i = 0; i < bestMoves.length; i++) { const mv = bestMoves[i]; const rb = applyMove(mv); const postMoveStats = calculateFrontierStats(); yield nodeStatus(mv.node_id, "working", `[${state.placements.length}] ${prototiles[mv.prototile_idx].name} (${i+1}/${bestMoves.length}) • ${postMoveStats.count} @ gen ${postMoveStats.min_gen}`, { color_id: mv.color_id, frontier_stats: postMoveStats }); yield snapshot(mv.node_id); await tick(); const child = yield* search(mv.node_id); if (child) { anySuccess = true; yield nodeStatus(mv.node_id, "success"); if (!exhaustive) return yield* doReturn(true); } else { yield nodeStatus(mv.node_id, "fail"); } undoMove(mv, rb); } if (anySuccess && exhaustive) { yield nodeStatus(parentId, "success"); return yield* doReturn(true); } yield nodeStatus(parentId, "fail"); return yield* doReturn(false); } const success = yield* search(rootId); yield nodeStatus(rootId, success ? "success" : "fail"); yield snapshot(null); await tick(); yield { type: "finished", tile_count: state.placements.length }; }; })();36:Taab4,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}@@${a}`); } return forb; }; return { SCALE, COLOR_PALETTE, TILING_REGISTRY, metadata, options, addMirrorsIfChiral, getForbiddenPairs }; })();37:[] 32:{"id":"dbb0bf006629a056","slug":"3d-lattice-tiler","title":"3D Lattice Tiler","thumbnail":"3b649b1409a5d298096f5f9454724abd7779c6b18d37a93d6929240dd79ec34a","access_level":"public","create_time":"$D2025-12-17T05:27:35.639Z","update_time":"$D2026-02-08T08:49:35.103Z","view_time":null,"first_public_time":"$D2025-12-17T06:39:48.836Z","has_unpublished_edits":null,"fork":false,"stars":4,"starred":false,"owner":{"type":"team","id":"490427fcc4ec2c1d","login":"liuyao12","name":"Yao Liu","avatar_url":"https://avatars-next.observableusercontent.com/895964f8b86922c183ea757cd86944e8e9d463ef5ba08171fab539d4dc087c54","tier":"starter_2024"},"version":394,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"ae908de8dd38723a","login":"liuyao12","name":"Yao Liu","avatar_url":"https://avatars-next.observableusercontent.com/895964f8b86922c183ea757cd86944e8e9d463ef5ba08171fab539d4dc087c54","tier":null}],"members":[{"type":"team","id":"490427fcc4ec2c1d","login":"liuyao12","name":"Yao Liu","avatar_url":"https://avatars-next.observableusercontent.com/895964f8b86922c183ea757cd86944e8e9d463ef5ba08171fab539d4dc087c54","tier":"starter_2024","role":"editor"},{"type":"individual","id":"ae908de8dd38723a","login":"liuyao12","name":"Yao Liu","avatar_url":"https://avatars-next.observableusercontent.com/895964f8b86922c183ea757cd86944e8e9d463ef5ba08171fab539d4dc087c54","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"3D Lattice Tiler","cells":[{"id":0,"value":"# 3D Lattice Tiler\n\n* a simple face-to-face tiler for *lattice* polyhedra (i.e., all the *vertices* lie on the ${tex`\\mathbb Z^3`} lattice, and only allowing rotations that are *symmetries* of the lattice). \n\n* Tilings of Euclidean 3-space are also known as [honeycombs](https://en.wikipedia.org/wiki/Honeycomb_(geometry%29).\n\n* The code is generated by multiple LLMs on top of one another (no effort spent on finding the best one though). Feel free to add your own tile.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"## Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10,"value":"THREE = require(\"three@0.150.1\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"OrbitControls = (await import(\n \"three@0.150.1/examples/jsm/controls/OrbitControls.js\"\n)).OrbitControls","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1","titling":"auto"}} 33:"$32:body"