Function decomposeRelativeTransform

packages/backend/src/common/color.ts:84–133

(
  t1: [number, number, number],
  t2: [number, number, number],
)

// from https://math.stackexchange.com/a/2888105
export const decomposeRelativeTransform = (
  t1: [number, number, number],
  t2: [number, number, number],
): {
  translation: [number, number];
  rotation: number;
  scale: [number, number];
  skew: [number, number];
} => {
  const a: number = t1[0];
  const b: number = t1[1];
  const c: number = t1[2];
  const d: number = t2[0];
  const e: number = t2[1];
  const f: number = t2[2];

  const delta = a * d - b * c;

  const result: {
    translation: [number, number];
    rotation: number;
    scale: [number, number];
    skew: [number, number];
  } = {
    translation: [e, f],
    rotation: 0,
    scale: [0, 0],
    skew: [0, 0],
  };

  // Apply the QR-like decomposition.
  if (a !== 0 || b !== 0) {
    const r = Math.sqrt(a * a + b * b);
    result.rotation = b > 0 ? Math.acos(a / r) : -Math.acos(a / r);
    result.scale = [r, delta / r];
    result.skew = [Math.atan((a * c + b * d) / (r * r)), 0];
  }
  // these are not currently being used.
  // else if (c != 0 || d != 0) {
  //   const s = Math.sqrt(c * c + d * d);
  //   result.rotation =
  //     Math.PI / 2 - (d > 0 ? Math.acos(-c / s) : -Math.acos(c / s));
  //   result.scale = [delta / s, s];
  //   result.skew = [0, Math.atan((a * c + b * d) / (s * s))];
  // } else {
  //   // a = b = c = d = 0
  // }

  return result;
};

// ---- Common color check helpers ----