room settings button: centroid pull breaks the plateau tie

The inscribed-circle criterion is FLAT along the long axis of any elongated
room — every midline point fits the same circle — and a plain argmax took
the first plateau sample: left of centre on the owner's kitchen-living
room, above centre in the sauna. The score now subtracts a soft pull
toward the area centroid (shoelace-weighted): on the plateau the nearest-
to-centroid point wins, while real clearance differences still dominate,
so the point never wanders into a thinner limb of an L.

Verified on a replica of the owner's floor: kitchen slab centre within a
few units, sauna dead-centre both axes. Units: wide and tall rectangles
centre on both axes; the L keeps to its slab near the centroid x.

src/logic.ts

@@ -250,6 +250,24 @@ export function poleOfInaccessibility(poly: number[][], steps = 24): number[] {
   const ys = poly.map((p) => p[1]);
   const minX = Math.min(...xs), maxX = Math.max(...xs);
   const minY = Math.min(...ys), maxY = Math.max(...ys);
+  const span = Math.max(maxX - minX, maxY - minY) || 1;
+  // Area centroid (shoelace-weighted). Clearance alone has a PLATEAU on any
+  // elongated room — every point of the long midline fits the same circle —
+  // and a plain argmax took the first plateau point: left of centre on the
+  // owner's kitchen, above centre in the sauna. A soft pull toward the
+  // centroid breaks the tie along the plateau without ever dragging the
+  // point into a thinner limb (clearance differences dominate the score).
+  let a2 = 0, cx = 0, cy = 0;
+  for (let i = 0; i < poly.length; i++) {
+    const p = poly[i], q = poly[(i + 1) % poly.length];
+    const cross = p[0] * q[1] - q[0] * p[1];
+    a2 += cross;
+    cx += (p[0] + q[0]) * cross;
+    cy += (p[1] + q[1]) * cross;
+  }
+  const centroid = Math.abs(a2) > 1e-9
+    ? [cx / (3 * a2), cy / (3 * a2)]
+    : [(minX + maxX) / 2, (minY + maxY) / 2];
   const clearance = (x: number, y: number): number => {
     if (!pointInPolygon([x, y], poly)) return -Infinity;
     let d = Infinity;
@@ -259,14 +277,19 @@ export function poleOfInaccessibility(poly: number[][], steps = 24): number[] {
     }
     return d;
   };
+  const score = (x: number, y: number): number => {
+    const d = clearance(x, y);
+    if (d === -Infinity) return d;
+    return d - 0.08 * Math.hypot(x - centroid[0], y - centroid[1]) - 0.0001 * span;
+  };
   let best: number[] | null = null;
-  let bestD = -Infinity;
+  let bestS = -Infinity;
   for (let i = 1; i < steps; i++) {
     for (let j = 1; j < steps; j++) {
       const x = minX + ((maxX - minX) * i) / steps;
       const y = minY + ((maxY - minY) * j) / steps;
-      const d = clearance(x, y);
+      const sc = score(x, y);
-      if (d > bestD) { bestD = d; best = [x, y]; }
+      if (sc > bestS) { bestS = sc; best = [x, y]; }
     }
   }
   if (best) {
@@ -275,8 +298,8 @@ export function poleOfInaccessibility(poly: number[][], steps = 24): number[] {
     for (let i = -4; i <= 4; i++) {
       for (let j = -4; j <= 4; j++) {
         const x = bx + (cw * i) / 4, y = by + (ch * j) / 4;
-        const d = clearance(x, y);
+        const sc = score(x, y);
-        if (d > bestD) { bestD = d; best = [x, y]; }
+        if (sc > bestS) { bestS = sc; best = [x, y]; }
       }
     }
   }

test/logic.test.mjs

@@ -917,12 +917,22 @@ test('poleOfInaccessibility: the VISUAL centre, not just any interior point', ()
   const p = poleOfInaccessibility(sq);
   assert.ok(Math.abs(p[0] - 5) < 0.6 && Math.abs(p[1] - 5) < 0.6);
 
+  // an ELONGATED rectangle: clearance is a plateau along the midline, and a
+  // plain argmax used to take its first point — left of centre on the
+  // owner's kitchen, above centre in the sauna. The centroid pull centres it.
+  const wide = [[0, 0], [30, 0], [30, 10], [0, 10]];
+  const w = poleOfInaccessibility(wide);
+  assert.ok(Math.abs(w[0] - 15) < 1.2 && Math.abs(w[1] - 5) < 1.2, 'centred both axes: ' + w);
+  const tall = [[0, 0], [8, 0], [8, 28], [0, 28]];
+  const tl = poleOfInaccessibility(tall);
+  assert.ok(Math.abs(tl[0] - 4) < 1 && Math.abs(tl[1] - 14) < 1.2, 'sauna case, centred vertically: ' + tl);
+
   // the owner's kitchen-living room shape: a THICK top slab with a narrower
-  // column hanging off the right side. The button belongs in the middle of
+  // column hanging off the right side. The button belongs near the middle of
-  // the slab — the widest open space — not near the seam or down the column.
+  // the slab — pulled toward the area centroid, never down the thin column.
   const L = [[0, 0], [20, 0], [20, 16], [16, 16], [16, 8], [0, 8]];
   const q = poleOfInaccessibility(L);
   assert.ok(pointInPolygon(q, L), 'inside, always');
   assert.ok(q[1] < 8, 'in the thick slab (y < 8), not down the column: ' + q);
-  assert.ok(q[0] > 2 && q[0] < 16, 'horizontally inside the slab body: ' + q);
+  assert.ok(Math.abs(q[0] - 11.3) < 2.5, 'near the centroid x within the slab: ' + q);
 });