transformation-matrix/src/fromTriangles.js

2d transformation matrix functions written in ES6 syntax. Tree shaking ready!

import { inverse } from './inverse'
import { transform } from './transform'
import { smoothMatrix } from './smoothMatrix'

/**
 * Returns a matrix that transforms a triangle t1 into another triangle t2, or throws an exception if it is impossible.
 * @param t1 {Point[]} Array of points containing the three points for the first triangle
 * @param t2 {Point[]} Array of points containing the three points for the second triangle
 * @returns {Matrix} Matrix which transforms t1 to t2
 * @throws Exception if the matrix becomes not invertible
 */
export function fromTriangles (t1, t2) {
  // point p = first point of the triangle
  const px1 = t1[0].x != null ? t1[0].x : t1[0][0]
  const py1 = t1[0].y != null ? t1[0].y : t1[0][1]
  const px2 = t2[0].x != null ? t2[0].x : t2[0][0]
  const py2 = t2[0].y != null ? t2[0].y : t2[0][1]

  // point q = second point of the triangle
  const qx1 = t1[1].x != null ? t1[1].x : t1[1][0]
  const qy1 = t1[1].y != null ? t1[1].y : t1[1][1]
  const qx2 = t2[1].x != null ? t2[1].x : t2[1][0]
  const qy2 = t2[1].y != null ? t2[1].y : t2[1][1]

  // point r = third point of the triangle
  const rx1 = t1[2].x != null ? t1[2].x : t1[2][0]
  const ry1 = t1[2].y != null ? t1[2].y : t1[2][1]
  const rx2 = t2[2].x != null ? t2[2].x : t2[2][0]
  const ry2 = t2[2].y != null ? t2[2].y : t2[2][1]

  const r1 = {
    a: px1 - rx1,
    b: py1 - ry1,
    c: qx1 - rx1,
    d: qy1 - ry1,
    e: rx1,
    f: ry1
  }
  const r2 = {
    a: px2 - rx2,
    b: py2 - ry2,
    c: qx2 - rx2,
    d: qy2 - ry2,
    e: rx2,
    f: ry2
  }

  const inverseR1 = inverse(r1)
  const affineMatrix = transform([r2, inverseR1])

  // round the matrix elements to smooth the finite inversion
  return smoothMatrix(affineMatrix)
}