feat(tabletop): add tilt and zStart/zEnd stacking options

Replace the per-part lift with a local Y-axis tilt that fans the stack,
and add zStart/zEnd to ramp the stack's height across the curve so it
arches in 3D. Update the poker deck and docs accordingly.

docs/bgm-format.md

@@ -359,6 +359,9 @@ layout:
       limit: 5
       align: center
       steps: 4
+      tilt: 0.1
+      zStart: 0
+      zEnd: 30
 ```
 
 - `curve` — an SVG path string to spread the content along, relative to the
@@ -368,6 +371,13 @@ layout:
 - `align` — `start`, `end`, or `center` of the curve.
 - `steps` — the maximum number of parts per curve length unit. Defaults to
   `1`. See the positioning process below.
+- `tilt` — rotation in radians per shown part about the card's local Y (long)
+  axis. Each part tilts `tilt` more than the previous, fanning the stack so
+  its edges stay visible. It applies even without a `curve`, so a bare `tilt`
+  fans a straight pile.
+- `zStart` / `zEnd` — the height (surface-normal) in mm at the start and end
+  of the `curve`. The stack ramps linearly between them across its span,
+  lifting it in 3D. Requires a `curve`.
 
 #### positioning process
 
@@ -377,6 +387,10 @@ layout:
    `step length × (# of parts − 1)` on the curve.
 3. **Place each part.** Part `#0` is at the start, the last part at the end,
    each `step length` apart.
+4. **Lift each part.** The part's height is `zStart + (zEnd − zStart) × u`,
+   where `u` is its normalized position along the `curve`.
+5. **Tilt each part.** Each part is rotated `tilt × # of parts before it`
+   about its local Y (long) axis.
 
 ### Edge cases
 

docs/bgm-tabletop-plan.md

@@ -118,10 +118,12 @@ interface GameState {
 
 ### 7. Stacking (`stacking.ts`) ✅
 
-- `useStacking(route.stacking, index, stackSize)` → `{ offset, rotation }`.
+- `useStacking(route.stacking, index, stackSize)` → `{ x, y, rotation, z, tilt }`.
 - Implements the format's positioning process (`bgm-format.md` §4): step
   length from curve length / `max(steps, count-1)`, alignment (`start`/`end`/
   `center`), and `limit` (`0` all, `n` first n, `-n` last n).
+- `z` ramps linearly from `zStart` to `zEnd` across the curve's span; `tilt`
+  fans each shown part about its local Y (long) axis.
 - Curve length from an SVG path string (small helper; no new dep).
 
 ### 8. Public API (`index.ts`) ✅
@@ -148,7 +150,8 @@ consumers share them (see Open decisions).
 
 - `state.ts` — derived render state: enabled surfaces, route matching,
   candidate selection, stacking index/stackSize.
-- `stacking.ts` — positioning process: step length, alignment, limit.
+- `stacking.ts` — positioning process: step length, alignment, limit, z ramp,
+  tilt.
 - `setup.ts` — seeding + bare-type expansion.
 - `mount.ts` — mount tree resolution (table/hud/child, children refs).
 - `partView.tsx` — geometry from a part def (size/fillet/crop), sprite UVs.

docs/bgm-tabletop.md

@@ -40,7 +40,7 @@ the render map is per enabled surface: a piece may appear on more than one enabl
 
 ## 4. stacking
 
-the format's stacking strategy (curve / limit / align / steps, see `bgm-format.md` §4) is implemented as a hook, e.g. `useStacking(route.stacking, index, stackSize)`, returning the offset/rotation to apply to a piece. `PartPlacement` consumes it.
+the format's stacking strategy (`curve` / `limit` / `align` / `steps` / `tilt` / `zStart` / `zEnd`, see `bgm-format.md` §4) is implemented as a hook, e.g. `useStacking(route.stacking, index, stackSize)`, returning the offset/rotation to apply to a piece: `{ x, y, rotation, z, tilt }`. `x`/`y`/`rotation` come from the `curve`; `z` is the surface-normal height ramped from `zStart` to `zEnd`; `tilt` is the per-part fan about the card's local Y (long) axis. `PartPlacement` consumes it.
 
 ## 5. usage
 

games/poker/poker.md

@@ -106,6 +106,9 @@ layout:
       curve: M 0 0 C 20 -20 40 -20 60 0
       limit: 0
       align: center
+      tilt: 0.015
+      zStart: 0
+      zEnd: 10
   - route: /community/:slot
     candidates:
       $variants: ./community.csv

packages/bgm/src/schemas.ts

@@ -17,6 +17,9 @@ const stacking = z.object({
   limit: z.number().optional(),
   align: z.enum(['start', 'end', 'center']).optional(),
   steps: z.number().optional(),
+  tilt: z.number().optional(),
+  zStart: z.number().optional(),
+  zEnd: z.number().optional(),
 });
 
 const route = z.object({

packages/bgm/src/types.ts

@@ -107,6 +107,20 @@ export interface Stacking {
   align?: 'start' | 'end' | 'center';
   /** Maximum parts per curve length unit; defaults to `1`. */
   steps?: number;
+  /**
+   * Rotation in radians per shown part about the card's local Y (long) axis.
+   * Each part tilts `tilt` more than the previous, fanning the stack so its
+   * edges stay visible. Works with or without a `curve`.
+   */
+  tilt?: number;
+  /**
+   * Height (surface-normal) in mm at the start of the `curve`. The stack
+   * ramps linearly to `zEnd` across its span, lifting it in 3D. Requires a
+   * `curve`.
+   */
+  zStart?: number;
+  /** Height (surface-normal) in mm at the end of the `curve`. */
+  zEnd?: number;
 }
 
 /** How a surface is mounted. `kind` selects the mount type. */

packages/tabletop/src/placement.tsx

@@ -17,20 +17,22 @@ export function PartPlacement({ pkg, placement }: { pkg: Package; placement: Pla
   const part = pkg.parts.get(piece.split(':').slice(1).join(':'));
   if (!part) return null;
 
-  const { x, y, rotation } = useStacking(route.stacking, index, stackSize);
+  const { x, y, rotation, z, tilt } = useStacking(route.stacking, index, stackSize);
 
   // Route anchors and stacking offsets are in mm; convert to world units so
-  // parts land on the (world-scaled) surface.
+  // parts land on the (world-scaled) surface. `z` raises the part along the
+  // surface normal (world +Y); `tilt` fans it about its local Y (long) axis.
   const anchorX = ((candidate?.x ?? route.x ?? 0) + x) * MM_TO_WORLD;
   const anchorY = ((candidate?.y ?? route.y ?? 0) + y) * MM_TO_WORLD;
+  const anchorZ = z * MM_TO_WORLD;
   const anchorRotation = (candidate?.rotation ?? route.rotation ?? 0) + rotation;
 
   return (
-    <group position={[anchorX, 0, anchorY]} rotation={[0, anchorRotation, 0]}>
+    <group position={[anchorX, anchorZ, anchorY]} rotation={[0, anchorRotation, 0]}>
       {/* The part mesh extrudes along +Z; lay it flat so its face points up. */}
-      <group rotation={[-Math.PI / 2, 0, 0]}>
+      <group rotation={[-Math.PI / 2, 0, tilt]}>
         <PartView part={part} baseUrl={part.baseUrl} />
       </group>
     </group>
   );
-}
+}

packages/tabletop/src/stacking.test.ts

@@ -85,4 +85,35 @@ describe('stackingOffset', () => {
     const offset = stackingOffset({ curve: 'M 0 0 L 100 0', steps: 4 }, 1, 3);
     expect(offset.x).toBeCloseTo(25);
   });
+
+  it('tilts each part without a curve', () => {
+    const offset = stackingOffset({ tilt: 0.1 }, 2, 3);
+    expect(offset).toEqual({ x: 0, y: 0, rotation: 0, z: 0, tilt: 0.2 });
+  });
+
+  it('tilts parts along the curve', () => {
+    const offset = stackingOffset({ curve: 'M 0 0 L 100 0', tilt: 0.1 }, 1, 3);
+    expect(offset.x).toBeCloseTo(50);
+    expect(offset.tilt).toBeCloseTo(0.1);
+  });
+
+  it('tilts only the shown parts', () => {
+    // limit 2 shows indices 0,1; index 2 is dropped.
+    expect(stackingOffset({ tilt: 0.1, limit: 2 }, 2, 4)).toBe(NO_OFFSET);
+    expect(stackingOffset({ tilt: 0.1, limit: 2 }, 1, 4).tilt).toBeCloseTo(0.1);
+  });
+
+  it('ramps z from zStart to zEnd across the curve', () => {
+    // 3 parts on a 100-long curve: u = 0, 0.5, 1. z ramps 0 -> 40.
+    const first = stackingOffset({ curve: 'M 0 0 L 100 0', zStart: 0, zEnd: 40 }, 0, 3);
+    const mid = stackingOffset({ curve: 'M 0 0 L 100 0', zStart: 0, zEnd: 40 }, 1, 3);
+    const last = stackingOffset({ curve: 'M 0 0 L 100 0', zStart: 0, zEnd: 40 }, 2, 3);
+    expect(first.z).toBeCloseTo(0);
+    expect(mid.z).toBeCloseTo(20);
+    expect(last.z).toBeCloseTo(40);
+  });
+
+  it('returns no offset without a curve, tilt, or z ramp', () => {
+    expect(stackingOffset({ limit: 5 }, 0, 3)).toBe(NO_OFFSET);
+  });
 });

packages/tabletop/src/stacking.ts

@@ -16,48 +16,77 @@ export interface StackOffset {
   y: number;
   /** Rotation in radians. */
   rotation: number;
+  /** Vertical (surface-normal) offset from the anchor, in mm. */
+  z: number;
+  /** Rotation in radians about the card's local Y (long) axis. */
+  tilt: number;
 }
 
 /** The identity offset: no stacking applied. */
-export const NO_OFFSET: StackOffset = { x: 0, y: 0, rotation: 0 };
+export const NO_OFFSET: StackOffset = { x: 0, y: 0, rotation: 0, z: 0, tilt: 0 };
 
 /**
  * Compute the offset/rotation for the piece at `index` of a `stackSize`-piece
  * stack, given the route's stacking strategy. Returns `NO_OFFSET` when there's
- * no curve or the stack is empty.
+ * no curve, no tilt, and no z profile, or the stack is empty.
  */
 export function stackingOffset(
   stacking: Stacking | undefined,
   index: number,
   stackSize: number,
 ): StackOffset {
-  if (!stacking?.curve || stackSize <= 0) return NO_OFFSET;
+  if (stackSize <= 0) return NO_OFFSET;
 
   // `limit` selects which pieces are shown; the offset is computed over the
   // shown span. `0` (or absent) shows all.
-  const shown = applyLimit(stacking.limit, stackSize);
+  const shown = applyLimit(stacking?.limit, stackSize);
   const shownIndex = shown.indexOf(index);
   if (shownIndex < 0) return NO_OFFSET;
 
-  const curve = parsePath(stacking.curve);
-  const length = curve.length;
-  if (length <= 0) return NO_OFFSET;
+  // `tilt` fans each shown part about its local Y (long) axis, so the stack's
+  // edges stay visible. It applies even without a curve.
+  const tilt = (stacking?.tilt ?? 0) * shownIndex;
 
-  // Step length: curve length / max(steps, # parts − 1). A single part sits
-  // at the start of the curve.
-  const steps = stacking.steps ?? 1;
-  const span = Math.max(steps, shown.length - 1);
-  const step = length / span;
+  // The horizontal position along the curve (or a straight pile when there's
+  // no curve), plus the normalized progress used to ramp the z height.
+  let x = 0;
+  let y = 0;
+  let rotation = 0;
+  let u = shown.length > 1 ? shownIndex / (shown.length - 1) : 0;
 
-  // Alignment: how far the whole span is inset from the curve's start.
-  const spanLength = step * (shown.length - 1);
-  let start = 0;
-  if (stacking.align === 'end') start = length - spanLength;
-  else if (stacking.align === 'center') start = (length - spanLength) / 2;
+  if (stacking?.curve) {
+    const curve = parsePath(stacking.curve);
+    const length = curve.length;
+    if (length > 0) {
+      // Step length: curve length / max(steps, # parts − 1). A single part
+      // sits at the start of the curve.
+      const steps = stacking.steps ?? 1;
+      const span = Math.max(steps, shown.length - 1);
+      const step = length / span;
 
-  const distance = start + shownIndex * step;
-  const { x, y, angle } = pointAt(curve, distance);
-  return { x, y, rotation: angle };
+      // Alignment: how far the whole span is inset from the curve's start.
+      const spanLength = step * (shown.length - 1);
+      let start = 0;
+      if (stacking.align === 'end') start = length - spanLength;
+      else if (stacking.align === 'center') start = (length - spanLength) / 2;
+
+      const distance = start + shownIndex * step;
+      const point = pointAt(curve, distance);
+      x = point.x;
+      y = point.y;
+      rotation = point.angle;
+      u = distance / length;
+    }
+  }
+
+  // The z height ramps linearly from `zStart` to `zEnd` across the curve's
+  // span, lifting the stack in 3D.
+  const zStart = stacking?.zStart ?? 0;
+  const zEnd = stacking?.zEnd ?? 0;
+  const z = zStart + (zEnd - zStart) * u;
+
+  if (x === 0 && y === 0 && rotation === 0 && z === 0 && tilt === 0) return NO_OFFSET;
+  return { x, y, rotation, z, tilt };
 }
 
 /** The stacking hook: memoized `stackingOffset` for a piece. */