fix(web): correct transform rotation and lay-flat sign

Conjugate the rotation by the Z-reflection (negate rotX/rotY, keep rotZ) and use -90 degrees about X to lay extruded meshes flat so faces point up.

apps/web/src/components/viewers/transform.ts

@@ -7,8 +7,10 @@ import type { TTSObject } from '@tts/shared';
  *
  * TTS is left-handed with Y up and +Z toward the player; three.js is
  * right-handed with Y up. Converting by reflecting the Z axis (negating Z in
- * position and every rotation angle) maps a TTS placement onto the three.js
- * scene while preserving the physical layout.
+ * position) maps a TTS placement onto the three.js scene while preserving the
+ * physical layout. The rotation is conjugated by the reflection: `R_three =
+ * M·R_tts·M` with `M = diag(1,1,-1)`, which negates `rotX`/`rotY` but leaves
+ * `rotZ` unchanged.
  *
  * Our viewer meshes are authored for inspection (standing up, extruded along
  * Z, sized in arbitrary units), so each class also gets a base-size correction
@@ -43,11 +45,12 @@ const CORRECTION: Record<string, number> = {
 
 /**
  * Rotation that lays an extruded mesh flat. The tile/token/card meshes extrude
- * along +Z with their face in the XY plane (standing up); rotating +90° about
- * X puts the face up (+Y), matching how objects lie on a TTS table. Custom
- * models are authored standing up already, so they need no correction.
+ * along +Z with their face in the XY plane (standing up); rotating −90° about
+ * X maps the +Z face normal to +Y, so the face points up like an object lying
+ * on a TTS table. Custom models are authored standing up already, so they need
+ * no correction.
  */
-const LAY_FLAT: [number, number, number] = [Math.PI / 2, 0, 0];
+const LAY_FLAT: [number, number, number] = [-Math.PI / 2, 0, 0];
 
 const FLAT_CLASSES = new Set([
   'Card',
@@ -78,7 +81,8 @@ export function objectPlacement(object: TTSObject): ObjectPlacement | null {
   const corr = CORRECTION[object.Name] ?? 1;
   return {
     position: [t.posX, t.posY, -t.posZ],
-    rotation: [-rad(t.rotX), -rad(t.rotY), -rad(t.rotZ)],
+    // Reflection conjugates the rotation: Rx/Ry negate, Rz keeps its sign.
+    rotation: [-rad(t.rotX), -rad(t.rotY), rad(t.rotZ)],
     scale: [t.scaleX * corr, t.scaleY * corr, t.scaleZ * corr],
     layFlat: FLAT_CLASSES.has(object.Name) ? LAY_FLAT : [0, 0, 0],
   };