perf: cache the detected piece so margin changes only re-trace it

Margin slider steps drop from ~800 ms to under 70 ms in the browser.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/detect.test.ts

@@ -1,5 +1,5 @@
 import { beforeAll, describe, expect, it } from 'vitest';
-import { detect, detectPrepared, disposePrepared, otsuThreshold, prepareImage, preparedThreshold } from '../src/lib/detect';
+import { detect, detectPrepared, disposePrepared, otsuThreshold, prepareImage, preparedThreshold, segmentPiece, traceMask } from '../src/lib/detect';
 import { bounds } from '../src/lib/geometry';
 import { loadOpenCV, type CV } from '../src/lib/opencv-loader';
 import type { DetectParams } from '../src/lib/types';
@@ -149,4 +149,27 @@ describe('detect', () => {
     const b = bounds(detect(cv, plywood, params({ threshold: 140 }))!.outer);
     near(b.minX, 150); near(b.maxX, 449); near(b.minY, 100); near(b.maxY, 299);
   });
+
+  it('segments once and applies different margins to the same piece mask', () => {
+    const prepared = prepareImage(cv, plateScene);
+    const piece = segmentPiece(cv, prepared, { threshold: 128, seed: null, minHolePx: 0 })!;
+    try {
+      for (const marginPx of [0, -5, 3]) {
+        const direct = detectPrepared(cv, prepared, params({ marginPx }))!;
+        expect(bounds(traceMask(cv, piece, marginPx)!.outer)).toEqual(bounds(direct.outer));
+      }
+    } finally {
+      piece.delete();
+      disposePrepared(prepared);
+    }
+  });
+
+  it('segmentPiece returns null when nothing is found', () => {
+    const prepared = prepareImage(cv, grayImage(100, 100, () => 30));
+    try {
+      expect(segmentPiece(cv, prepared, { threshold: 128, seed: null, minHolePx: 0 })).toBeNull();
+    } finally {
+      disposePrepared(prepared);
+    }
+  });
 });