242 lines
8.8 KiB
JavaScript
242 lines
8.8 KiB
JavaScript
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"use strict";
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Object.defineProperty(exports, "__esModule", {
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value: true
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});
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exports.createIntersect = void 0;
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var _factory = require("../../utils/factory.js");
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var name = 'intersect';
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var dependencies = ['typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar', 'flatten', 'isZero', 'isNumeric'];
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var createIntersect = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
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var typed = _ref.typed,
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config = _ref.config,
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abs = _ref.abs,
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add = _ref.add,
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addScalar = _ref.addScalar,
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matrix = _ref.matrix,
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multiply = _ref.multiply,
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multiplyScalar = _ref.multiplyScalar,
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divideScalar = _ref.divideScalar,
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subtract = _ref.subtract,
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smaller = _ref.smaller,
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equalScalar = _ref.equalScalar,
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flatten = _ref.flatten,
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isZero = _ref.isZero,
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isNumeric = _ref.isNumeric;
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/**
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* Calculates the point of intersection of two lines in two or three dimensions
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* and of a line and a plane in three dimensions. The inputs are in the form of
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* arrays or 1 dimensional matrices. The line intersection functions return null
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* if the lines do not meet.
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*
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* Note: Fill the plane coefficients as `x + y + z = c` and not as `x + y + z + c = 0`.
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*
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* Syntax:
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*
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* math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2)
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* math.intersect(endPoint1, endPoint2, planeCoefficients)
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*
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* Examples:
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*
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* math.intersect([0, 0], [10, 10], [10, 0], [0, 10]) // Returns [5, 5]
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* math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0]) // Returns [5, 5, 0]
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* math.intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6]) // Returns [7, -4, 3]
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*
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* @param {Array | Matrix} w Co-ordinates of first end-point of first line
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* @param {Array | Matrix} x Co-ordinates of second end-point of first line
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* @param {Array | Matrix} y Co-ordinates of first end-point of second line
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* OR Co-efficients of the plane's equation
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* @param {Array | Matrix} z Co-ordinates of second end-point of second line
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* OR undefined if the calculation is for line and plane
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* @return {Array} Returns the point of intersection of lines/lines-planes
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*/
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return typed('intersect', {
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'Array, Array, Array': _AAA,
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'Array, Array, Array, Array': _AAAA,
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'Matrix, Matrix, Matrix': function MatrixMatrixMatrix(x, y, plane) {
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var arr = _AAA(x.valueOf(), y.valueOf(), plane.valueOf());
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return arr === null ? null : matrix(arr);
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},
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'Matrix, Matrix, Matrix, Matrix': function MatrixMatrixMatrixMatrix(w, x, y, z) {
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// TODO: output matrix type should match input matrix type
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var arr = _AAAA(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf());
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return arr === null ? null : matrix(arr);
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}
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});
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function _AAA(x, y, plane) {
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x = _coerceArr(x);
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y = _coerceArr(y);
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plane = _coerceArr(plane);
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if (!_3d(x)) {
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throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument');
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}
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if (!_3d(y)) {
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throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument');
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}
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if (!_4d(plane)) {
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throw new TypeError('Array with 4 numbers expected as third argument');
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}
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return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3]);
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}
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function _AAAA(w, x, y, z) {
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w = _coerceArr(w);
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x = _coerceArr(x);
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y = _coerceArr(y);
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z = _coerceArr(z);
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if (w.length === 2) {
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if (!_2d(w)) {
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throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument');
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}
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if (!_2d(x)) {
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throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument');
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}
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if (!_2d(y)) {
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throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument');
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}
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if (!_2d(z)) {
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throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument');
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}
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return _intersect2d(w, x, y, z);
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} else if (w.length === 3) {
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if (!_3d(w)) {
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throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument');
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}
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if (!_3d(x)) {
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throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument');
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}
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if (!_3d(y)) {
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throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument');
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}
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if (!_3d(z)) {
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throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument');
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}
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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]);
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} else {
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throw new TypeError('Arrays with two or thee dimensional points expected');
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}
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}
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/** Coerce row and column 2-dim arrays to 1-dim array */
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function _coerceArr(arr) {
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// row matrix
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if (arr.length === 1) return arr[0]; // column matrix
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if (arr.length > 1 && Array.isArray(arr[0])) {
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if (arr.every(function (el) {
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return Array.isArray(el) && el.length === 1;
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})) return flatten(arr);
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}
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return arr;
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}
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function _2d(x) {
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return x.length === 2 && isNumeric(x[0]) && isNumeric(x[1]);
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}
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function _3d(x) {
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return x.length === 3 && isNumeric(x[0]) && isNumeric(x[1]) && isNumeric(x[2]);
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}
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function _4d(x) {
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return x.length === 4 && isNumeric(x[0]) && isNumeric(x[1]) && isNumeric(x[2]) && isNumeric(x[3]);
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}
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function _intersect2d(p1a, p1b, p2a, p2b) {
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var o1 = p1a;
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var o2 = p2a;
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var d1 = subtract(o1, p1b);
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var d2 = subtract(o2, p2b);
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var det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1]));
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if (isZero(det)) return null;
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if (smaller(abs(det), config.epsilon)) {
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return null;
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}
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var d20o11 = multiplyScalar(d2[0], o1[1]);
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var d21o10 = multiplyScalar(d2[1], o1[0]);
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var d20o21 = multiplyScalar(d2[0], o2[1]);
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var d21o20 = multiplyScalar(d2[1], o2[0]);
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var t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det);
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return add(multiply(d1, t), o1);
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}
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function _intersect3dHelper(a, b, c, d, e, f, g, h, i, j, k, l) {
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// (a - b)*(c - d) + (e - f)*(g - h) + (i - j)*(k - l)
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var add1 = multiplyScalar(subtract(a, b), subtract(c, d));
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var add2 = multiplyScalar(subtract(e, f), subtract(g, h));
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var add3 = multiplyScalar(subtract(i, j), subtract(k, l));
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return addScalar(addScalar(add1, add2), add3);
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}
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function _intersect3d(x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) {
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var d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3);
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var d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1);
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var d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1);
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var d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3);
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var d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1);
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var numerator = subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343));
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var denominator = subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321));
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if (isZero(denominator)) return null;
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var ta = divideScalar(numerator, denominator);
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var tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343);
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var pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1)));
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var pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1)));
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var paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1)));
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var pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3)));
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var pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3)));
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var pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3)));
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if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) {
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return [pax, pay, paz];
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} else {
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return null;
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}
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}
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function _intersectLinePlane(x1, y1, z1, x2, y2, z2, x, y, z, c) {
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var x1x = multiplyScalar(x1, x);
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var x2x = multiplyScalar(x2, x);
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var y1y = multiplyScalar(y1, y);
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var y2y = multiplyScalar(y2, y);
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var z1z = multiplyScalar(z1, z);
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var z2z = multiplyScalar(z2, z);
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var numerator = subtract(subtract(subtract(c, x1x), y1y), z1z);
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var denominator = subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z);
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var t = divideScalar(numerator, denominator);
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var px = addScalar(x1, multiplyScalar(t, subtract(x2, x1)));
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var py = addScalar(y1, multiplyScalar(t, subtract(y2, y1)));
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var pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1)));
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return [px, py, pz]; // TODO: Add cases when line is parallel to the plane:
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// (a) no intersection,
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// (b) line contained in plane
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}
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});
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exports.createIntersect = createIntersect;
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