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/walls.test.ts

@@ -27,12 +27,17 @@ describe('wallFaces', () => {
     expect(wall.positions[5]).toBe(3);
   });
 
-  it('maps u across the perimeter and v up the height', () => {
+  it('uses planar UVs from the top face mapping, independent of z', () => {
     const wall = wallFaces(rectShape(2, 2), 2);
-    // u starts at 0 for the first outline point.
+    // First outline point is (-1,-1) -> planar UV (0, 0).
     expect(wall.uvs[0]).toBeCloseTo(0, 5);
-    // v goes 0 -> 1 from bottom to top.
     expect(wall.uvs[1]).toBeCloseTo(0, 5);
-    expect(wall.uvs[3]).toBeCloseTo(1, 5);
+    // The bottom and top vertices of the same outline point share a UV,
+    // so the texture is constant down the wall regardless of z.
+    expect(wall.uvs[2]).toBeCloseTo(wall.uvs[0]!, 5);
+    expect(wall.uvs[3]).toBeCloseTo(wall.uvs[1]!, 5);
+    // Third outline point is (1, 1) -> planar UV (1, 1).
+    expect(wall.uvs[8]).toBeCloseTo(1, 5);
+    expect(wall.uvs[9]).toBeCloseTo(1, 5);
   });
 });