websperiments/standalone/goldberg-sphere/placer_unfold.mjs

// Placement via unfolding: each neighbor face is placed adjacent to its BFS
// parent by a similarity transform, then shrunk toward its centroid by
// DEPTH_SHRINK^depth so depth rings visually separate.
//
// 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 DEPTH_SHRINK = 0.82;

export function place_unfold(poly, neighborhood, root_face_index, cx, cy, face_size) {
	const placements = new Map();

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

		if (entry.parent_index === null) {
			// Root face: regular polygon centred on canvas.
			const pts = regular_polygon_2d(n, face_size).map(([x, y]) => [x + cx, y + cy]);
			placements.set(fi, { vertices_2d: pts, centroid_2d: [cx, cy], depth: 0 });
		} else {
			const parent_pl   = placements.get(entry.parent_index);
			if (!parent_pl) { continue; }

			const parent_face = poly.faces[entry.parent_index];
			const pei = entry.parent_edge_index;
			const pa  = parent_pl.vertices_2d[pei];
			const pb  = parent_pl.vertices_2d[(pei + 1) % parent_face.size];

			// Find which edge of this face leads back to the parent.
			let nei = -1;
			for (let j = 0; j < face.edge_neighbors.length; j++) {
				if (face.edge_neighbors[j] === entry.parent_index) { nei = j; break; }
			}
			if (nei === -1) {
				console.warn(`place_unfold: face ${fi} has no reverse edge to parent ${entry.parent_index}`);
				continue;
			}

			// Winding is opposite: parent (a→b) ≡ neighbor (b→a).
			const local_pts = regular_polygon_2d(n, 1);
			const local_a   = local_pts[nei];
			const local_b   = local_pts[(nei + 1) % n];
			const transform = similarity_transform_2d(local_a, local_b, pb, pa);

			let vertices_2d = local_pts.map(pt => apply_transform_2d(transform, pt));
			const c = centroid_2d(vertices_2d);

			// Shrink toward centroid after transform (before would be cancelled by scaling).
			const shrink = Math.pow(DEPTH_SHRINK, entry.depth);
			vertices_2d = vertices_2d.map(([x, y]) => [
				c[0] + (x - c[0]) * shrink,
				c[1] + (y - c[1]) * shrink,
			]);

			placements.set(fi, { vertices_2d, centroid_2d: c, depth: entry.depth });
		}
	}

	return placements;
}