"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
}
});