Function inverse

src/utils/cameraUndistortion.ts:94–127

(p: Vec2, i: CameraIntrinsics)

  },

  inverse(p: Vec2, i: CameraIntrinsics): UndistortResult {
    let x = p.x;
    let y = p.y;
    for (let iter = 0; iter < 20; iter++) {
      const r2 = x * x + y * y;
      const R = _prFactor(r2, i);
      const Rp = _prDeriv(r2, i);

      const dx = x * R + 2 * i.p1 * x * y + i.p2 * (r2 + 2 * x * x);
      const dy = y * R + i.p1 * (r2 + 2 * y * y) + 2 * i.p2 * x * y;

      // Jacobian of (u + delta(u)) w.r.t. u.
      // Tangential Jacobian terms vanish exactly when p1=p2=0.
      const j11 = 1 + R + 2 * x * x * Rp + 2 * i.p1 * y + 6 * i.p2 * x;
      const j12 = 2 * x * y * Rp + 2 * i.p1 * x + 2 * i.p2 * y;
      const j21 = 2 * x * y * Rp + 2 * i.p1 * x + 2 * i.p2 * y;
      const j22 = 1 + R + 2 * y * y * Rp + 6 * i.p1 * y + 2 * i.p2 * x;

      const gx = x + dx - p.x;
      const gy = y + dy - p.y;
      const det = j11 * j22 - j12 * j21;
      if (Math.abs(det) < 1e-15) break;
      const stepX = (j22 * gx - j12 * gy) / det;
      const stepY = (j11 * gy - j21 * gx) / det;
      x -= stepX;
      y -= stepY;
      if (stepX * stepX + stepY * stepY < 1e-20) break;
    }
    // Reject non-physical roots: if re-distorting the Newton result doesn't land
    // back near the input, the ray has no valid pre-image (folded barrel map).
    const check = perspectiveRadialStrategy.forward({ x, y }, i);
    const valid = Math.hypot(check.x - p.x, check.y - p.y) < PERSPECTIVE_INVERSE_RESIDUAL_TOL;
    return { x, y, valid };
  },
};

// ── 'fov' strategy ────────────────────────────────────────────────────────────