websperiments/standalone/goldberg-sphere/placer_relax.mjs

// Shared-vertex spring relaxation.
//
// Builds an indexed mesh (union-find over per-face vertex slots) so
// topologically identical vertices are the same array entry — sharing is
// exact, not glued. Two spring types per iteration:
//   1. Edge-length: each edge pulls toward a depth-scaled target length.
//   2. Radial: each vertex pulls toward its face's depth-scaled circumradius.
//
// curvature=0 → flat (uniform size); >0 → outer tiles shrink (sphere-like);
// <0 → outer tiles grow (hyperbolic-like). depth_scale(d) = (1-curvature)^d.
//
// Displacement is clamped per iteration to spread unavoidable curvature
// (from pentagon defects) evenly rather than concentrating it in a few faces.
//
// Returns Map<face_index, { vertices_2d, centroid_2d, depth }>

import {
	regular_polygon_2d,
	centroid_2d,
	similarity_transform_2d,
	apply_transform_2d,
} from './geometry.mjs';

const RELAX_ITERS   = 30;
const ALPHA_EDGE    = 0.5;
const ALPHA_RADIAL  = 0.4;
const MAX_MOVE_FRAC = 0.12;

export function place_relax(poly, neighborhood, root_face_index, cx, cy, face_size, curvature = 0) {
	const placed_set = new Set(neighborhood.map(e => e.face.index));

	// --- Union-find over per-face vertex slots ---
	const face_base = new Map();
	let uf_size = 0;
	for (const entry of neighborhood) {
		face_base.set(entry.face.index, uf_size);
		uf_size += entry.face.size;
	}
	const uf_parent = Array.from({ length: uf_size }, (_, i) => i);
	const uf_find = (i) => {
		while (uf_parent[i] !== i) { uf_parent[i] = uf_parent[uf_parent[i]]; i = uf_parent[i]; }
		return i;
	};
	const uf_union = (i, j) => { uf_parent[uf_find(i)] = uf_find(j); };

	const adj_seen = new Set();
	for (const entry of neighborhood) {
		const fi_a   = entry.face.index;
		const face_a = entry.face;
		const na     = face_a.size;
		const base_a = face_base.get(fi_a);
		for (let ea = 0; ea < na; ea++) {
			const fi_b = face_a.edge_neighbors[ea];
			if (fi_b === null || fi_b === undefined || !placed_set.has(fi_b)) { continue; }
			const pair_key = fi_a < fi_b ? `${fi_a}:${fi_b}` : `${fi_b}:${fi_a}`;
			if (adj_seen.has(pair_key)) { continue; }
			adj_seen.add(pair_key);

			const face_b = poly.faces[fi_b];
			const nb     = face_b.size;
			const base_b = face_base.get(fi_b);
			let eb = -1;
			for (let j = 0; j < nb; j++) {
				if (face_b.edge_neighbors[j] === fi_a) { eb = j; break; }
			}
			if (eb === -1) { continue; }

			// Opposite winding: A's slot ea ≡ B's slot (eb+1)%nb, A's (ea+1)%na ≡ B's eb.
			uf_union(base_a + ea,             base_b + (eb + 1) % nb);
			uf_union(base_a + (ea + 1) % na,  base_b + eb);
		}
	}

	// Assign compact position IDs to canonical slots.
	const canon_to_pid = new Map();
	let pid_count = 0;
	const face_pids = new Map();
	for (const entry of neighborhood) {
		const fi   = entry.face.index;
		const n    = entry.face.size;
		const base = face_base.get(fi);
		const pids = [];
		for (let i = 0; i < n; i++) {
			const canon = uf_find(base + i);
			if (!canon_to_pid.has(canon)) { canon_to_pid.set(canon, pid_count++); }
			pids.push(canon_to_pid.get(canon));
		}
		face_pids.set(fi, pids);
	}

	// --- Initial positions via BFS unfolding (no depth shrink) ---
	const positions  = Array.from({ length: pid_count }, () => [0, 0]);
	const placed_pid = new Uint8Array(pid_count);

	for (const entry of neighborhood) {
		const fi   = entry.face.index;
		const face = entry.face;
		const n    = face.size;
		const pids = face_pids.get(fi);

		if (entry.parent_index === null) {
			const pts = regular_polygon_2d(n, face_size).map(([x, y]) => [x + cx, y + cy]);
			for (let i = 0; i < n; i++) { positions[pids[i]] = pts[i]; placed_pid[pids[i]] = 1; }
		} else {
			const parent_fi   = entry.parent_index;
			const parent_face = poly.faces[parent_fi];
			const parent_pids = face_pids.get(parent_fi);
			const ea          = entry.parent_edge_index;

			let eb = -1;
			for (let j = 0; j < n; j++) {
				if (face.edge_neighbors[j] === parent_fi) { eb = j; break; }
			}
			if (eb === -1) { continue; }

			const local_pts = regular_polygon_2d(n, 1);
			const pa        = positions[parent_pids[ea]];
			const pb        = positions[parent_pids[(ea + 1) % parent_face.size]];
			const transform = similarity_transform_2d(local_pts[eb], local_pts[(eb + 1) % n], pb, pa);

			for (let i = 0; i < n; i++) {
				if (!placed_pid[pids[i]]) {
					positions[pids[i]] = apply_transform_2d(transform, local_pts[i]);
					placed_pid[pids[i]] = 1;
				}
			}
		}
	}

	// --- Collect unique edges ---
	const edge_seen = new Set();
	const edges = [];
	for (const [, pids] of face_pids) {
		const n = pids.length;
		for (let i = 0; i < n; i++) {
			const u = pids[i], v = pids[(i + 1) % n];
			const ek = u < v ? `${u}:${v}` : `${v}:${u}`;
			if (!edge_seen.has(ek)) { edge_seen.add(ek); edges.push([u, v]); }
		}
	}

	// --- Target length from root face ---
	const root_pids = face_pids.get(root_face_index);
	let target_len = face_size;
	if (root_pids) {
		const n = root_pids.length;
		let sum = 0;
		for (let i = 0; i < n; i++) {
			const a = positions[root_pids[i]], b = positions[root_pids[(i + 1) % n]];
			sum += Math.sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2);
		}
		target_len = sum / n;
	}

	// Pin root face positions.
	const pinned = new Set(root_pids ?? []);

	// depth_scale(d) = (1 - curvature)^d
	const depth_scale = (d) => Math.pow(1 - curvature, d);

	// Per-vertex average depth (for interpolating target length across edges).
	const pid_depth_sum   = new Float64Array(pid_count);
	const pid_depth_count = new Uint32Array(pid_count);
	for (const entry of neighborhood) {
		for (const pid of face_pids.get(entry.face.index)) {
			pid_depth_sum[pid]   += entry.depth;
			pid_depth_count[pid] += 1;
		}
	}
	const pid_depth = Array.from({ length: pid_count },
		(_, i) => pid_depth_count[i] > 0 ? pid_depth_sum[i] / pid_depth_count[i] : 0);

	const max_move = target_len * MAX_MOVE_FRAC;

	// --- Spring relaxation ---
	for (let iter = 0; iter < RELAX_ITERS; iter++) {
		const deltas = Array.from({ length: pid_count }, () => [0, 0]);

		// Spring 1: edge-length (depth-scaled target).
		for (const [u, v] of edges) {
			const pu = positions[u], pv = positions[v];
			const dx = pv[0] - pu[0], dy = pv[1] - pu[1];
			const len = Math.sqrt(dx * dx + dy * dy);
			if (len < 1e-6) { continue; }
			const t_len = target_len * depth_scale((pid_depth[u] + pid_depth[v]) / 2);
			const err   = (len - t_len) / len;
			const fx = dx * err * 0.5 * ALPHA_EDGE;
			const fy = dy * err * 0.5 * ALPHA_EDGE;
			if (!pinned.has(u)) { deltas[u][0] += fx; deltas[u][1] += fy; }
			if (!pinned.has(v)) { deltas[v][0] -= fx; deltas[v][1] -= fy; }
		}

		// Spring 2: radial (vertex-to-centroid → depth-scaled circumradius).
		for (const entry of neighborhood) {
			const fi   = entry.face.index;
			const pids = face_pids.get(fi);
			const n    = pids.length;
			const t_r  = target_len * depth_scale(entry.depth);

			let fcx = 0, fcy = 0;
			for (const pid of pids) { fcx += positions[pid][0]; fcy += positions[pid][1]; }
			fcx /= n; fcy /= n;

			for (const pid of pids) {
				if (pinned.has(pid)) { continue; }
				const vx = positions[pid][0] - fcx;
				const vy = positions[pid][1] - fcy;
				const dist = Math.sqrt(vx * vx + vy * vy);
				if (dist < 1e-6) { continue; }
				const err = (dist - t_r) / dist;
				deltas[pid][0] -= vx * err * ALPHA_RADIAL;
				deltas[pid][1] -= vy * err * ALPHA_RADIAL;
			}
		}

		// Apply with displacement clamp.
		for (let i = 0; i < pid_count; i++) {
			if (pinned.has(i)) { continue; }
			const dx = deltas[i][0], dy = deltas[i][1];
			const d  = Math.sqrt(dx * dx + dy * dy);
			const sc = d > max_move ? max_move / d : 1;
			positions[i][0] += dx * sc;
			positions[i][1] += dy * sc;
		}
	}

	// --- Build placements map ---
	const placements = new Map();
	for (const entry of neighborhood) {
		const fi  = entry.face.index;
		const pts = face_pids.get(fi).map(pid => positions[pid]);
		placements.set(fi, { vertices_2d: pts, centroid_2d: centroid_2d(pts), depth: entry.depth });
	}

	return placements;
}