Half the warp pairings were secretly mirrors

Eric walked a five-player board's corner warp and the world stretched.
The lane rule — carry the along-the-edge offset through unchanged —
is only correct for half the side pairings: for the rest (N to N,
E to N, and their kin, the ones five-player boards deal), the proper
rotation lands the entry axis head-to-head against the exit axis, and
preserving the raw lane smuggled a REFLECTION into the traversal —
rays crossing over at the mouth, parallax inverted, the far room
swimming. warpLaneMirrored computes the pairing's sign from the
rotation itself; castRay mirrors the lane where required, and
warpMotion anchors the far mouth at its opposite corner to stay the
same pure rotation — so sprites and projectile legs agree with the
rays again. The workshop grows ?players=2..6 to stand on any table
size (the mirror-class mouths live on the five-player boards).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

packages/web/src/fpv/raycast.ts

@@ -39,6 +39,25 @@ export interface Hit {
 export const SIDE_ANGLE: Record<Side, number> = { E: 0, S: Math.PI / 2, W: Math.PI, N: -Math.PI / 2 };
 export const OPPOSITE: Record<Side, Side> = { E: "W", W: "E", N: "S", S: "N" };
 
+/** Unit vector along an edge's lane axis (the direction `along` grows). */
+const LANE_AXIS: Record<Side, [number, number]> = {
+  E: [0, 1], W: [0, 1], N: [1, 0], S: [1, 0],
+};
+
+/** Does this warp pair MIRROR the lane? A traversal is a proper rigid
+ * rotation; for half the side pairings the rotated entry axis points
+ * AGAINST the exit edge's axis, and preserving the raw lane there would
+ * smuggle in a reflection — rays crossing over at the mouth, parallax
+ * inverted, the far room stretching as the eye moves. */
+export function warpLaneMirrored(from: Side, to: Side): boolean {
+  const d = SIDE_ANGLE[OPPOSITE[to]] - SIDE_ANGLE[from];
+  const [x, y] = LANE_AXIS[from];
+  const rx = x * Math.cos(d) - y * Math.sin(d);
+  const ry = x * Math.sin(d) + y * Math.cos(d);
+  const [ex2, ey] = LANE_AXIS[to];
+  return rx * ex2 + ry * ey < 0;
+}
+
 /** Is this edge passable to the EYE (rays), and if not, what is it?
  * Doors always report as doors; how far each stands open — fully for an
  * open or held door, mid-swing during an animation — is castRay's call. */
@@ -180,11 +199,12 @@ export function castRay(
         );
         if (!warp) return { dist: baseDist + dist, kind: "rim", u: texU, axis, worldU: along, warped, ghost, doorway };
         // Step through: re-enter at the paired mouth, heading inward, the
-        // offset along the edge preserved (a wraparound keeps its lane).
+        // lane carried by the same proper rotation the heading turns by —
+        // mirrored for the pairings whose axes land head-to-head.
         const exitHeading = SIDE_ANGLE[OPPOSITE[warp.to.side]];
         angle = angle + (exitHeading - SIDE_ANGLE[warp.from.side]);
         const c = warp.to.cell;
-        const lane = texU;
+        const lane = warpLaneMirrored(warp.from.side, warp.to.side) ? 1 - texU : texU;
         if (warp.to.side === "E") { ox = c.x + 1 - 1e-4; oy = c.y + lane; }
         else if (warp.to.side === "W") { ox = c.x + 1e-4; oy = c.y + lane; }
         else if (warp.to.side === "S") { ox = c.x + lane; oy = c.y + 1 - 1e-4; }
@@ -280,7 +300,15 @@ export function warpMotion(w: GameView["board"]["warps"][number]): {
 } {
   const delta = SIDE_ANGLE[OPPOSITE[w.to.side]] - SIDE_ANGLE[w.from.side];
   const a1 = mouthAnchor(w.from);
-  const a2 = mouthAnchor(w.to);
+  // Mirrored pairings anchor the far mouth at its OTHER corner — the
+  // lane runs backwards there, and this keeps the motion a pure
+  // rotation matching castRay's traversal.
+  const a2 = { ...mouthAnchor(w.to) };
+  if (warpLaneMirrored(w.from.side, w.to.side)) {
+    const [lx, ly] = LANE_AXIS[w.to.side];
+    a2.x += lx;
+    a2.y += ly;
+  }
   const c = Math.cos(delta), s = Math.sin(delta);
   return {
     toVirtual(p) {