mathjs/lib/esm/function/geometry/intersect.js

import { isBigNumber } from '../../utils/is.js';
import { factory } from '../../utils/factory.js';
var name = 'intersect';
var dependencies = ['typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar'];
export var createIntersect = /* #__PURE__ */factory(name, dependencies, (_ref) => {
  var {
    typed,
    config,
    abs,
    add,
    addScalar,
    matrix,
    multiply,
    multiplyScalar,
    divideScalar,
    subtract,
    smaller,
    equalScalar
  } = _ref;

  /**
   * Calculates the point of intersection of two lines in two or three dimensions
   * and of a line and a plane in three dimensions. The inputs are in the form of
   * arrays or 1 dimensional matrices. The line intersection functions return null
   * if the lines do not meet.
   *
   * Note: Fill the plane coefficients as `x + y + z = c` and not as `x + y + z + c = 0`.
   *
   * Syntax:
   *
   *    math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2)
   *    math.intersect(endPoint1, endPoint2, planeCoefficients)
   *
   * Examples:
   *
   *    math.intersect([0, 0], [10, 10], [10, 0], [0, 10])              // Returns [5, 5]
   *    math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0])  // Returns [5, 5, 0]
   *    math.intersect([1, 0, 1],  [4, -2, 2], [1, 1, 1, 6])            // Returns [7, -4, 3]
   *
   * @param  {Array | Matrix} w   Co-ordinates of first end-point of first line
   * @param  {Array | Matrix} x   Co-ordinates of second end-point of first line
   * @param  {Array | Matrix} y   Co-ordinates of first end-point of second line
   *                              OR Co-efficients of the plane's equation
   * @param  {Array | Matrix} z   Co-ordinates of second end-point of second line
   *                              OR null if the calculation is for line and plane
   * @return {Array}              Returns the point of intersection of lines/lines-planes
   */
  return typed('intersect', {
    'Array, Array, Array': function ArrayArrayArray(x, y, plane) {
      if (!_3d(x)) {
        throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument');
      }

      if (!_3d(y)) {
        throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument');
      }

      if (!_4d(plane)) {
        throw new TypeError('Array with 4 numbers expected as third argument');
      }

      return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3]);
    },
    'Array, Array, Array, Array': function ArrayArrayArrayArray(w, x, y, z) {
      if (w.length === 2) {
        if (!_2d(w)) {
          throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument');
        }

        if (!_2d(x)) {
          throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument');
        }

        if (!_2d(y)) {
          throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument');
        }

        if (!_2d(z)) {
          throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument');
        }

        return _intersect2d(w, x, y, z);
      } else if (w.length === 3) {
        if (!_3d(w)) {
          throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument');
        }

        if (!_3d(x)) {
          throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument');
        }

        if (!_3d(y)) {
          throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument');
        }

        if (!_3d(z)) {
          throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument');
        }

        return _intersect3d(w[0], w[1], w[2], x[0], x[1], x[2], y[0], y[1], y[2], z[0], z[1], z[2]);
      } else {
        throw new TypeError('Arrays with two or thee dimensional points expected');
      }
    },
    'Matrix, Matrix, Matrix': function MatrixMatrixMatrix(x, y, plane) {
      return matrix(this(x.valueOf(), y.valueOf(), plane.valueOf()));
    },
    'Matrix, Matrix, Matrix, Matrix': function MatrixMatrixMatrixMatrix(w, x, y, z) {
      // TODO: output matrix type should match input matrix type
      return matrix(this(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()));
    }
  });

  function _isNumeric(a) {
    // intersect supports numbers and bignumbers
    return typeof a === 'number' || isBigNumber(a);
  }

  function _2d(x) {
    return x.length === 2 && _isNumeric(x[0]) && _isNumeric(x[1]);
  }

  function _3d(x) {
    return x.length === 3 && _isNumeric(x[0]) && _isNumeric(x[1]) && _isNumeric(x[2]);
  }

  function _4d(x) {
    return x.length === 4 && _isNumeric(x[0]) && _isNumeric(x[1]) && _isNumeric(x[2]) && _isNumeric(x[3]);
  }

  function _intersect2d(p1a, p1b, p2a, p2b) {
    var o1 = p1a;
    var o2 = p2a;
    var d1 = subtract(o1, p1b);
    var d2 = subtract(o2, p2b);
    var det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1]));

    if (smaller(abs(det), config.epsilon)) {
      return null;
    }

    var d20o11 = multiplyScalar(d2[0], o1[1]);
    var d21o10 = multiplyScalar(d2[1], o1[0]);
    var d20o21 = multiplyScalar(d2[0], o2[1]);
    var d21o20 = multiplyScalar(d2[1], o2[0]);
    var t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det);
    return add(multiply(d1, t), o1);
  }

  function _intersect3dHelper(a, b, c, d, e, f, g, h, i, j, k, l) {
    // (a - b)*(c - d) + (e - f)*(g - h) + (i - j)*(k - l)
    var add1 = multiplyScalar(subtract(a, b), subtract(c, d));
    var add2 = multiplyScalar(subtract(e, f), subtract(g, h));
    var add3 = multiplyScalar(subtract(i, j), subtract(k, l));
    return addScalar(addScalar(add1, add2), add3);
  }

  function _intersect3d(x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) {
    var d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3);

    var d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1);

    var d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1);

    var d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3);

    var d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1);

    var ta = divideScalar(subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)), subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)));
    var tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343);
    var pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1)));
    var pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1)));
    var paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1)));
    var pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3)));
    var pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3)));
    var pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3)));

    if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) {
      return [pax, pay, paz];
    } else {
      return null;
    }
  }

  function _intersectLinePlane(x1, y1, z1, x2, y2, z2, x, y, z, c) {
    var x1x = multiplyScalar(x1, x);
    var x2x = multiplyScalar(x2, x);
    var y1y = multiplyScalar(y1, y);
    var y2y = multiplyScalar(y2, y);
    var z1z = multiplyScalar(z1, z);
    var z2z = multiplyScalar(z2, z);
    var t = divideScalar(subtract(subtract(subtract(c, x1x), y1y), z1z), subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z));
    var px = addScalar(x1, multiplyScalar(t, subtract(x2, x1)));
    var py = addScalar(y1, multiplyScalar(t, subtract(y2, y1)));
    var pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1)));
    return [px, py, pz]; // TODO: Add cases when line is parallel to the plane:
    //       (a) no intersection,
    //       (b) line contained in plane
  }
});