feat(tile): render tiles with the mesh generator

Replace the per-shape tile geometries with @tts/mesh extrusion, honoring
the tile type and stretch aspect ratio. Add extrudeShapeParts so the
caps carry the texture while the walls are solid white, matching TTS
tinting. Fix bottom-face UVs to mirror horizontally and make wall UVs
inherit the front mapping independent of z.

packages/mesh/src/extrude.test.ts

@@ -1,6 +1,6 @@
 import { describe, expect, it } from 'vitest';
-import { extrudeShape, mergeFaces } from './extrude.js';
-import { rectShape, hexShape, circleShape, roundedRectShape } from './shapes.js';
+import { extrudeShape, extrudeShapeParts, mergeFaces } from './extrude.js';
+import { rectShape, hexShape, circleShape, roundedRectShape, scaleShape } from './shapes.js';
 import { capFaces } from './tessellate.js';
 import { wallFaces } from './walls.js';
 import type { FaceGeometry } from './types.js';
@@ -44,6 +44,36 @@ describe('extrudeShape', () => {
     expect(geo.uvs[1]).toBeCloseTo(0, 5);
     expect(geo.uvs[4]).toBeCloseTo(2, 5);
   });
+
+  it('produces non-square geometry when scaled by an aspect ratio', () => {
+    const geo = extrudeShape(scaleShape(rectShape(2, 2), 2, 1), { height: 0.5 });
+    let minX = Infinity;
+    let maxX = -Infinity;
+    let minY = Infinity;
+    let maxY = -Infinity;
+    for (let i = 0; i < geo.positions.length; i += 3) {
+      minX = Math.min(minX, geo.positions[i]!);
+      maxX = Math.max(maxX, geo.positions[i]!);
+      minY = Math.min(minY, geo.positions[i + 1]!);
+      maxY = Math.max(maxY, geo.positions[i + 1]!);
+    }
+    expect(maxX - minX).toBeCloseTo(4, 5); // 2 * aspect 2
+    expect(maxY - minY).toBeCloseTo(2, 5);
+  });
+});
+
+describe('extrudeShapeParts', () => {
+  it('returns caps and walls as separate geometries', () => {
+    const { caps, walls } = extrudeShapeParts(rectShape(2, 2), { height: 1 });
+    // Caps: 2 faces * 4 outline points = 8 vertices.
+    expect(caps.positions.length / 3).toBe(8);
+    // Walls: 4 outline points * 2 vertices = 8 vertices.
+    expect(walls.positions.length / 3).toBe(8);
+    // Combined, they match `extrudeShape`.
+    const combined = extrudeShape(rectShape(2, 2), { height: 1 });
+    expect(caps.positions.length + walls.positions.length).toBe(combined.positions.length);
+    expect(caps.indices.length + walls.indices.length).toBe(combined.indices.length);
+  });
 });
 
 describe('mergeFaces', () => {