d3-geo-polygon/src/polyhedral/matrix.js

Clipping and geometric operations for spherical polygons.

import {atan2, cos, sin, sqrt} from "../math.js";

// Note: 6-element arrays are used to denote the 3x3 affine transform matrix:
// [a, b, c,
//  d, e, f,
//  0, 0, 1] - this redundant row is left out.

// Transform matrix for [a0, a1] -> [b0, b1].
export default function(a, b) {
  const u = subtract(a[1], a[0]);
  const v = subtract(b[1], b[0]);
  const phi = angle(u, v);
  const s = length(u) / length(v);

  return multiply([
    1, 0, a[0][0],
    0, 1, a[0][1]
  ], multiply([
    s, 0, 0,
    0, s, 0
  ], multiply([
    cos(phi), sin(phi), 0,
    -sin(phi), cos(phi), 0
  ], [
    1, 0, -b[0][0],
    0, 1, -b[0][1]
  ])));
}

// Inverts a transform matrix.
export function inverse(m) {
  const k = 1 / (m[0] * m[4] - m[1] * m[3]);
  return [
    k * m[4], -k * m[1], k * (m[1] * m[5] - m[2] * m[4]),
    -k * m[3], k * m[0], k * (m[2] * m[3] - m[0] * m[5])
  ];
}

// Multiplies two 3x2 matrices.
export function multiply(a, b) {
  return [
    a[0] * b[0] + a[1] * b[3],
    a[0] * b[1] + a[1] * b[4],
    a[0] * b[2] + a[1] * b[5] + a[2],
    a[3] * b[0] + a[4] * b[3],
    a[3] * b[1] + a[4] * b[4],
    a[3] * b[2] + a[4] * b[5] + a[5]
  ];
}

// Subtracts 2D vectors.
function subtract(a, b) {
  return [a[0] - b[0], a[1] - b[1]];
}

// Magnitude of a 2D vector.
function length(v) {
  return sqrt(v[0] * v[0] + v[1] * v[1]);
}

// Angle between two 2D vectors.
function angle(a, b) {
  return atan2(a[0] * b[1] - a[1] * b[0], a[0] * b[0] + a[1] * b[1]);
}