extract rotation, scale values from 2d transformation matrix

Question

how can i extract rotation, scale and translation values from 2d transformation matrix? i mean a have a 2d transformation

matrix = [1, 0, 0, 1, 0, 0]

matri         


        

Answer 1

The term for this is matrix decomposition. Here is a solution that includes skew as described by Frédéric Wang.

function decompose_2d_matrix(mat) {
  var a = mat[0];
  var b = mat[1];
  var c = mat[2];
  var d = mat[3];
  var e = mat[4];
  var f = mat[5];

  var delta = a * d - b * c;

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

  // Apply the QR-like decomposition.
  if (a != 0 || b != 0) {
    var 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];
  } else if (c != 0 || d != 0) {
    var 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;
}