fix(capture): rotate length-axis rectangle and scale from mask span

Length axis keeps the approved mask, replaces Flip 180 with a ± angle
slider, and sets scale from wood span along the approved direction rather
than bbox.longSidePx. Widths still sample every 6 in perpendicular to that
axis.

frontend/src/geometry/rect.test.ts

@@ -0,0 +1,51 @@
+import { test } from 'node:test';
+import assert from 'node:assert/strict';
+import { minAreaRect, orientedRect, maskSpanAlong } from './rect.ts';
+import { measure } from '../measure/measure.ts';
+
+// 100×20 horizontal slab
+const W = 100, H = 20;
+const bitset = new Uint8Array(W * H);
+for (let x = 0; x < W; x++) for (let y = 0; y < H; y++) bitset[y * W + x] = 1;
+
+test('maskSpanAlong of a 100×20 slab: X ≈ 99–100, Y ≈ 19–20', () => {
+  const sx = maskSpanAlong(bitset, W, H, 1, 0);
+  const sy = maskSpanAlong(bitset, W, H, 0, 1);
+  assert.ok(sx >= 99 && sx <= 100, `spanX ${sx}`);
+  assert.ok(sy >= 19 && sy <= 20, `spanY ${sy}`);
+});
+
+test('orientedRect changes angleDeg and preserves longSidePx', () => {
+  const prev = minAreaRect(bitset, W, H);
+  assert.ok(prev, 'minAreaRect returned a box');
+  const rotated = orientedRect(prev, 45);
+  assert.ok(Math.abs(rotated.angleDeg - 45) < 1e-9);
+  assert.equal(rotated.longSidePx, prev.longSidePx);
+  // The long side (angleDeg 0 → +x) must be preserved by the rotation.
+  const longOf = (c) => Math.hypot(c[3][0] - c[0][0], c[3][1] - c[0][1]);
+  assert.ok(Math.abs(longOf(rotated.corners) - longOf(prev.corners)) < 1e-9);
+  assert.ok(Math.abs(longOf(prev.corners) - prev.longSidePx) < 1e-9);
+  // angle normalization to [0, 180)
+  assert.ok(orientedRect(prev, 190).angleDeg >= 0 && orientedRect(prev, 190).angleDeg < 180);
+});
+
+test('measure scale uses mask span along the axis, not longSidePx', () => {
+  // Thin slab (20 long, 100 wide): minAreaRect's long side (angleDeg 90) is
+  // the 100-px dimension along +y. Rotate the axis to angleDeg 0 (+x), which
+  // crosses only the 20-px slab width — span 19, not longSidePx 99.
+  const TW = 20, TH = 100;
+  const thin = new Uint8Array(TW * TH).fill(1);
+  const thinBox = minAreaRect(thin, TW, TH);
+  assert.ok(thinBox && thinBox.longSidePx >= 99, `longSide ${thinBox?.longSidePx}`);
+  const rotated = orientedRect(thinBox, 0);
+  const lengthEighths = 24; // 3 in
+  const m = measure(thin, TW, TH, rotated, lengthEighths, 8, TW * TH);
+  // Scale = span along the axis / length. Span ≈ 19 → scale ≈ 6.3 px/in,
+  // far from the old longSidePx/3 ≈ 33.
+  const ex = rotated.corners[0][0] - rotated.corners[3][0];
+  const ey = rotated.corners[0][1] - rotated.corners[3][1];
+  const elen = Math.hypot(ex, ey);
+  const span = maskSpanAlong(thin, TW, TH, ex / elen, ey / elen);
+  assert.ok(Math.abs(m.scale - span / (lengthEighths / 8)) < 1e-9);
+  assert.ok(m.scale < 10, `scale ${m.scale} should be span-based, not ${thinBox.longSidePx / 3}`);
+});

frontend/src/geometry/rect.ts

@@ -92,3 +92,39 @@ export function minAreaRect(bitset: Uint8Array, w: number, h: number): BBox | nu
   const angleDeg = ((Math.atan2(lv, lu) * 180) / Math.PI + 180) % 180;
   return { corners, longSidePx: halfL * 2, angleDeg };
 }
+
+// Rotate the long side to a new angle, keeping center and half-extents.
+// Corners are rebuilt in minAreaRect order so corners[3] → corners[0] stays the
+// long side (the axis arrow direction).
+export function orientedRect(prev: BBox, angleDeg: number): BBox {
+  const a = ((angleDeg % 180) + 180) % 180;
+  const halfL = prev.longSidePx / 2;
+  const halfS = Math.hypot(prev.corners[0][0] - prev.corners[1][0], prev.corners[0][1] - prev.corners[1][1]) / 2;
+  // corners[i] is a corner point: average of all four = center
+  const cx = (prev.corners[0][0] + prev.corners[1][0] + prev.corners[2][0] + prev.corners[3][0]) / 4;
+  const cy = (prev.corners[0][1] + prev.corners[1][1] + prev.corners[2][1] + prev.corners[3][1]) / 4;
+  const r = (a * Math.PI) / 180;
+  const lu = Math.cos(r), lv = Math.sin(r);
+  const su = -lv, sv = lu;
+  const corners: [number, number][] = [];
+  for (const [aSign, bSign] of [[1, 1], [1, -1], [-1, -1], [-1, 1]] as const) {
+    corners.push([cx + aSign * halfL * lu + bSign * halfS * su, cy + aSign * halfL * lv + bSign * halfS * sv]);
+  }
+  return { corners, longSidePx: prev.longSidePx, angleDeg: a };
+}
+
+// Project every slab pixel onto the unit vector (ux, uy); return max − min
+// extent in px. 0 when the mask is empty.
+export function maskSpanAlong(bitset: Uint8Array, w: number, h: number, ux: number, uy: number): number {
+  let min = Infinity, max = -Infinity;
+  for (let y = 0; y < h; y++) {
+    const row = y * w;
+    for (let x = 0; x < w; x++) {
+      if (!bitset[row + x]) continue;
+      const p = x * ux + y * uy;
+      if (p < min) min = p;
+      if (p > max) max = p;
+    }
+  }
+  return max < min ? 0 : max - min;
+}