Add main menu, 3v3 with goalies, and dead-puck faceoffs.

Players pick 1-on-1 shootout or 3-on-3 scrimmage; 3v3 gets nets,
goalies, scoring, OOB whistles to the nearest faceoff circle, and
one-way board re-entry for skaters who leave the ice.

shared/rink.js

@@ -32,6 +32,65 @@ export const MARKINGS = Object.freeze({
   zoneDotX: 20.2,
 });
 
+/**
+ * All nine faceoff dots: centre, four neutral-zone, four end-zone.
+ * Order is stable so tests and HUD labels can index if they want.
+ */
+export const FACEOFF_DOTS = Object.freeze([
+  Object.freeze({ id: 'centre', x: 0, z: 0 }),
+  Object.freeze({ id: 'nz-pp', x: MARKINGS.faceoffDotX, z: MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'nz-pm', x: MARKINGS.faceoffDotX, z: -MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'nz-mp', x: -MARKINGS.faceoffDotX, z: MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'nz-mm', x: -MARKINGS.faceoffDotX, z: -MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'ez-pp', x: MARKINGS.zoneDotX, z: MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'ez-pm', x: MARKINGS.zoneDotX, z: -MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'ez-mp', x: -MARKINGS.zoneDotX, z: MARKINGS.faceoffDotZ }),
+  Object.freeze({ id: 'ez-mm', x: -MARKINGS.zoneDotX, z: -MARKINGS.faceoffDotZ }),
+]);
+
+/** Nearest faceoff dot to a world point — where a whistle drops the next draw. */
+export function nearestFaceoffDot(x, z) {
+  let best = FACEOFF_DOTS[0];
+  let bestD = Infinity;
+  for (const d of FACEOFF_DOTS) {
+    const dd = (d.x - x) * (d.x - x) + (d.z - z) * (d.z - z);
+    if (dd < bestD) {
+      bestD = dd;
+      best = d;
+    }
+  }
+  return best;
+}
+
+/**
+ * Is the puck still in play?
+ *
+ * Horizontal: must be on the ice surface (small inset so "on the boards" is
+ * still playable, but over the glass / past the outline is dead).
+ * Vertical: above the glass, under the slab, or impossibly high is unplayable.
+ */
+export function puckPlayable(x, y, z, radius = 0.0381) {
+  if (!Number.isFinite(x) || !Number.isFinite(y) || !Number.isFinite(z)) {
+    return { ok: false, reason: 'nan' };
+  }
+  // Far outside the barn entirely (escaped continuous collision).
+  if (Math.abs(x) > RINK.halfX + 4 || Math.abs(z) > RINK.halfZ + 4) {
+    return { ok: false, reason: 'escaped' };
+  }
+  // Under the ice or stuck in the slab.
+  if (y < -0.15) return { ok: false, reason: 'under' };
+  // Over the glass. Boards are ~1.07 m; glass is visual only above that.
+  if (y > RINK.boardHeight + RINK.glassHeight * 0.55) {
+    return { ok: false, reason: 'over' };
+  }
+  // Centre past the board line — the puck has left the playing surface.
+  // Tiny slack so a rattle against the boards does not whistle every contact.
+  if (rinkPenetration(x, z, 0).dist > radius * 0.75) {
+    return { ok: false, reason: 'out' };
+  }
+  return { ok: true, reason: '' };
+}
+
 /**
  * Centre of the corner arc nearest (x, z), and the sign of the quadrant.
  * Points outside the straight sections belong to exactly one corner.