@thi.ng/matrices/invert.js

Matrix & quaternion operations for 2D/3D geometry processing

import { dotC4, dotC6 } from "@thi.ng/vectors/dotc";
import { magSq4 } from "@thi.ng/vectors/magsq";
import { setC, setC4, setC6 } from "@thi.ng/vectors/setc";
import { vop } from "@thi.ng/vectors/vop";
import { det44FromCoeffs, detCoeffs44 } from "./determinant.js";
const invert = vop(1);
const invert22 = invert.add(4, (out, m) => {
  const [m00, m01, m10, m11] = m;
  let det = dotC4(m00, m11, -m01, m10);
  if (det === 0) return;
  det = 1 / det;
  return setC4(out || m, m11 * det, -m01 * det, -m10 * det, m00 * det);
});
const invert23 = invert.add(6, (out, m) => {
  const [m00, m01, m10, m11, m20, m21] = m;
  let det = dotC4(m00, m11, -m01, m10);
  if (det === 0) return;
  det = 1 / det;
  return setC6(
    out || m,
    m11 * det,
    -m01 * det,
    -m10 * det,
    m00 * det,
    dotC4(m10, m21, -m11, m20) * det,
    dotC4(m01, m20, -m00, m21) * det
  );
});
const invert33 = invert.add(9, (out, m) => {
  const [m00, m01, m02, m10, m11, m12, m20, m21, m22] = m;
  const d01 = dotC4(m22, m11, -m12, m21);
  const d11 = dotC4(m12, m20, -m22, m10);
  const d21 = dotC4(m21, m10, -m11, m20);
  let det = dotC6(m00, d01, m01, d11, m02, d21);
  if (det === 0) return;
  det = 1 / det;
  return setC(
    out || m,
    d01 * det,
    dotC4(-m22, m01, m02, m21) * det,
    dotC4(m12, m01, -m02, m11) * det,
    d11 * det,
    dotC4(m22, m00, -m02, m20) * det,
    dotC4(-m12, m00, m02, m10) * det,
    d21 * det,
    dotC4(-m21, m00, m01, m20) * det,
    dotC4(m11, m00, -m01, m10) * det
  );
});
const invert44 = invert.add(16, (out, m) => {
  const coeffs = detCoeffs44(m);
  let det = det44FromCoeffs(coeffs);
  if (det === 0) return;
  det = 1 / det;
  const [
    m00,
    m01,
    m02,
    m03,
    m10,
    m11,
    m12,
    m13,
    m20,
    m21,
    m22,
    m23,
    m30,
    m31,
    m32,
    m33
  ] = m;
  const [d00, d01, d02, d03, d04, d05, d06, d07, d08, d09, d10, d11] = coeffs;
  return setC(
    out || m,
    dotC6(m11, d11, -m12, d10, m13, d09) * det,
    dotC6(-m01, d11, m02, d10, -m03, d09) * det,
    dotC6(m31, d05, -m32, d04, m33, d03) * det,
    dotC6(-m21, d05, m22, d04, -m23, d03) * det,
    dotC6(-m10, d11, m12, d08, -m13, d07) * det,
    dotC6(m00, d11, -m02, d08, m03, d07) * det,
    dotC6(-m30, d05, m32, d02, -m33, d01) * det,
    dotC6(m20, d05, -m22, d02, m23, d01) * det,
    dotC6(m10, d10, -m11, d08, m13, d06) * det,
    dotC6(-m00, d10, m01, d08, -m03, d06) * det,
    dotC6(m30, d04, -m31, d02, m33, d00) * det,
    dotC6(-m20, d04, m21, d02, -m23, d00) * det,
    dotC6(-m10, d09, m11, d07, -m12, d06) * det,
    dotC6(m00, d09, -m01, d07, m02, d06) * det,
    dotC6(-m30, d03, m31, d01, -m32, d00) * det,
    dotC6(m20, d03, -m21, d01, m22, d00) * det
  );
});
const invertQ = (out, a) => {
  let d = magSq4(a);
  d = d > 0 ? -1 / d : 0;
  return setC4(out || a, a[0] * d, a[1] * d, a[2] * d, -a[3] * d);
};
export {
  invert,
  invert22,
  invert23,
  invert33,
  invert44,
  invertQ
};