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/tessellate.test.ts

@@ -72,6 +72,22 @@ describe('capFaces', () => {
     expect(uvs[5]).toBeCloseTo(1, 5);
   });
 
+  it('bottom face UVs are a left/right flip of the top face', () => {
+    const face = capFaces(rectShape(2, 2), 1);
+    const outlineCount = 4;
+    // Top face: outline point i maps to ((x-minX)/spanX, (y-minY)/spanY).
+    // Bottom face mirrors U (1 - u) but keeps V, so the texture reads
+    // correctly from underneath.
+    for (let i = 0; i < outlineCount; i++) {
+      const topU = face.uvs[i * 2]!;
+      const topV = face.uvs[i * 2 + 1]!;
+      const bottomU = face.uvs[(outlineCount + i) * 2]!;
+      const bottomV = face.uvs[(outlineCount + i) * 2 + 1]!;
+      expect(bottomU).toBeCloseTo(1 - topU, 5);
+      expect(bottomV).toBeCloseTo(topV, 5);
+    }
+  });
+
   it('top face triangles are CCW (positive area)', () => {
     const face = capFaces(rectShape(2, 2), 1);
     const topIndices = face.indices.slice(0, 6);