feat:node-modules

node_modules/mathjs/lib/cjs/function/geometry/intersect.js

@@ -0,0 +1,206 @@
+"use strict";
+
+Object.defineProperty(exports, "__esModule", {
+  value: true
+});
+exports.createIntersect = void 0;
+var _factory = require("../../utils/factory.js");
+const name = 'intersect';
+const dependencies = ['typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar', 'flatten', 'isZero', 'isNumeric'];
+const createIntersect = exports.createIntersect = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
+  let {
+    typed,
+    config,
+    abs,
+    add,
+    addScalar,
+    matrix,
+    multiply,
+    multiplyScalar,
+    divideScalar,
+    subtract,
+    smaller,
+    equalScalar,
+    flatten,
+    isZero,
+    isNumeric
+  } = _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 undefined 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': _AAA,
+    'Array, Array, Array, Array': _AAAA,
+    'Matrix, Matrix, Matrix': function (x, y, plane) {
+      const arr = _AAA(x.valueOf(), y.valueOf(), plane.valueOf());
+      return arr === null ? null : matrix(arr);
+    },
+    'Matrix, Matrix, Matrix, Matrix': function (w, x, y, z) {
+      // TODO: output matrix type should match input matrix type
+      const arr = _AAAA(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf());
+      return arr === null ? null : matrix(arr);
+    }
+  });
+  function _AAA(x, y, plane) {
+    x = _coerceArr(x);
+    y = _coerceArr(y);
+    plane = _coerceArr(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]);
+  }
+  function _AAAA(w, x, y, z) {
+    w = _coerceArr(w);
+    x = _coerceArr(x);
+    y = _coerceArr(y);
+    z = _coerceArr(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');
+    }
+  }
+
+  /** Coerce row and column 2-dim arrays to 1-dim array */
+  function _coerceArr(arr) {
+    // row matrix
+    if (arr.length === 1) return arr[0];
+
+    // column matrix
+    if (arr.length > 1 && Array.isArray(arr[0])) {
+      if (arr.every(el => Array.isArray(el) && el.length === 1)) return flatten(arr);
+    }
+    return arr;
+  }
+  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) {
+    const o1 = p1a;
+    const o2 = p2a;
+    const d1 = subtract(o1, p1b);
+    const d2 = subtract(o2, p2b);
+    const det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1]));
+    if (isZero(det)) return null;
+    if (smaller(abs(det), config.relTol)) {
+      return null;
+    }
+    const d20o11 = multiplyScalar(d2[0], o1[1]);
+    const d21o10 = multiplyScalar(d2[1], o1[0]);
+    const d20o21 = multiplyScalar(d2[0], o2[1]);
+    const d21o20 = multiplyScalar(d2[1], o2[0]);
+    const 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)
+    const add1 = multiplyScalar(subtract(a, b), subtract(c, d));
+    const add2 = multiplyScalar(subtract(e, f), subtract(g, h));
+    const 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) {
+    const d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3);
+    const d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1);
+    const d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1);
+    const d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3);
+    const d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1);
+    const numerator = subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343));
+    const denominator = subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321));
+    if (isZero(denominator)) return null;
+    const ta = divideScalar(numerator, denominator);
+    const tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343);
+    const pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1)));
+    const pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1)));
+    const paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1)));
+    const pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3)));
+    const pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3)));
+    const 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) {
+    const x1x = multiplyScalar(x1, x);
+    const x2x = multiplyScalar(x2, x);
+    const y1y = multiplyScalar(y1, y);
+    const y2y = multiplyScalar(y2, y);
+    const z1z = multiplyScalar(z1, z);
+    const z2z = multiplyScalar(z2, z);
+    const numerator = subtract(subtract(subtract(c, x1x), y1y), z1z);
+    const denominator = subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z);
+    const t = divideScalar(numerator, denominator);
+    const px = addScalar(x1, multiplyScalar(t, subtract(x2, x1)));
+    const py = addScalar(y1, multiplyScalar(t, subtract(y2, y1)));
+    const 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
+  }
+});