mathjs
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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif
171 lines (151 loc) • 7.96 kB
JavaScript
'use strict'
function factory (type, config, load, typed) {
const abs = load(require('../arithmetic/abs'))
const add = load(require('../arithmetic/add'))
const addScalar = load(require('../arithmetic/addScalar'))
const matrix = load(require('../../type/matrix/function/matrix'))
const multiply = load(require('../arithmetic/multiply'))
const multiplyScalar = load(require('../arithmetic/multiplyScalar'))
const divideScalar = load(require('../arithmetic/divideScalar'))
const subtract = load(require('../arithmetic/subtract'))
const smaller = load(require('../relational/smaller'))
const equalScalar = load(require('../relational/equalScalar'))
/**
* 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
*/
const intersect = typed('intersect', {
'Array, Array, Array': function (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 (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 (x, y, plane) {
return matrix(intersect(x.valueOf(), y.valueOf(), plane.valueOf()))
},
'Matrix, Matrix, Matrix, Matrix': function (w, x, y, z) {
// TODO: output matrix type should match input matrix type
return matrix(intersect(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()))
}
})
function _isNumber (a) {
// intersect supports numbers and bignumbers
return (typeof a === 'number' || type.isBigNumber(a))
}
function _2d (x) {
return x.length === 2 && _isNumber(x[0]) && _isNumber(x[1])
}
function _3d (x) {
return x.length === 3 && _isNumber(x[0]) && _isNumber(x[1]) && _isNumber(x[2])
}
function _4d (x) {
return x.length === 4 && _isNumber(x[0]) && _isNumber(x[1]) && _isNumber(x[2]) && _isNumber(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 (smaller(abs(det), config.epsilon)) {
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 ta = divideScalar(
subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)),
subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)))
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 t = divideScalar(
subtract(subtract(subtract(c, x1x), y1y), z1z),
subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z))
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
}
return intersect
}
exports.name = 'intersect'
exports.factory = factory