intersect.js (8576B)
1 import { factory } from '../../utils/factory.js'; 2 var name = 'intersect'; 3 var dependencies = ['typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar', 'flatten', 'isZero', 'isNumeric']; 4 export var createIntersect = /* #__PURE__ */factory(name, dependencies, _ref => { 5 var { 6 typed, 7 config, 8 abs, 9 add, 10 addScalar, 11 matrix, 12 multiply, 13 multiplyScalar, 14 divideScalar, 15 subtract, 16 smaller, 17 equalScalar, 18 flatten, 19 isZero, 20 isNumeric 21 } = _ref; 22 23 /** 24 * Calculates the point of intersection of two lines in two or three dimensions 25 * and of a line and a plane in three dimensions. The inputs are in the form of 26 * arrays or 1 dimensional matrices. The line intersection functions return null 27 * if the lines do not meet. 28 * 29 * Note: Fill the plane coefficients as `x + y + z = c` and not as `x + y + z + c = 0`. 30 * 31 * Syntax: 32 * 33 * math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2) 34 * math.intersect(endPoint1, endPoint2, planeCoefficients) 35 * 36 * Examples: 37 * 38 * math.intersect([0, 0], [10, 10], [10, 0], [0, 10]) // Returns [5, 5] 39 * math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0]) // Returns [5, 5, 0] 40 * math.intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6]) // Returns [7, -4, 3] 41 * 42 * @param {Array | Matrix} w Co-ordinates of first end-point of first line 43 * @param {Array | Matrix} x Co-ordinates of second end-point of first line 44 * @param {Array | Matrix} y Co-ordinates of first end-point of second line 45 * OR Co-efficients of the plane's equation 46 * @param {Array | Matrix} z Co-ordinates of second end-point of second line 47 * OR undefined if the calculation is for line and plane 48 * @return {Array} Returns the point of intersection of lines/lines-planes 49 */ 50 return typed('intersect', { 51 'Array, Array, Array': _AAA, 52 'Array, Array, Array, Array': _AAAA, 53 'Matrix, Matrix, Matrix': function MatrixMatrixMatrix(x, y, plane) { 54 var arr = _AAA(x.valueOf(), y.valueOf(), plane.valueOf()); 55 56 return arr === null ? null : matrix(arr); 57 }, 58 'Matrix, Matrix, Matrix, Matrix': function MatrixMatrixMatrixMatrix(w, x, y, z) { 59 // TODO: output matrix type should match input matrix type 60 var arr = _AAAA(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()); 61 62 return arr === null ? null : matrix(arr); 63 } 64 }); 65 66 function _AAA(x, y, plane) { 67 x = _coerceArr(x); 68 y = _coerceArr(y); 69 plane = _coerceArr(plane); 70 71 if (!_3d(x)) { 72 throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument'); 73 } 74 75 if (!_3d(y)) { 76 throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument'); 77 } 78 79 if (!_4d(plane)) { 80 throw new TypeError('Array with 4 numbers expected as third argument'); 81 } 82 83 return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3]); 84 } 85 86 function _AAAA(w, x, y, z) { 87 w = _coerceArr(w); 88 x = _coerceArr(x); 89 y = _coerceArr(y); 90 z = _coerceArr(z); 91 92 if (w.length === 2) { 93 if (!_2d(w)) { 94 throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument'); 95 } 96 97 if (!_2d(x)) { 98 throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument'); 99 } 100 101 if (!_2d(y)) { 102 throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument'); 103 } 104 105 if (!_2d(z)) { 106 throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument'); 107 } 108 109 return _intersect2d(w, x, y, z); 110 } else if (w.length === 3) { 111 if (!_3d(w)) { 112 throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument'); 113 } 114 115 if (!_3d(x)) { 116 throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument'); 117 } 118 119 if (!_3d(y)) { 120 throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument'); 121 } 122 123 if (!_3d(z)) { 124 throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument'); 125 } 126 127 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]); 128 } else { 129 throw new TypeError('Arrays with two or thee dimensional points expected'); 130 } 131 } 132 /** Coerce row and column 2-dim arrays to 1-dim array */ 133 134 135 function _coerceArr(arr) { 136 // row matrix 137 if (arr.length === 1) return arr[0]; // column matrix 138 139 if (arr.length > 1 && Array.isArray(arr[0])) { 140 if (arr.every(el => Array.isArray(el) && el.length === 1)) return flatten(arr); 141 } 142 143 return arr; 144 } 145 146 function _2d(x) { 147 return x.length === 2 && isNumeric(x[0]) && isNumeric(x[1]); 148 } 149 150 function _3d(x) { 151 return x.length === 3 && isNumeric(x[0]) && isNumeric(x[1]) && isNumeric(x[2]); 152 } 153 154 function _4d(x) { 155 return x.length === 4 && isNumeric(x[0]) && isNumeric(x[1]) && isNumeric(x[2]) && isNumeric(x[3]); 156 } 157 158 function _intersect2d(p1a, p1b, p2a, p2b) { 159 var o1 = p1a; 160 var o2 = p2a; 161 var d1 = subtract(o1, p1b); 162 var d2 = subtract(o2, p2b); 163 var det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1])); 164 if (isZero(det)) return null; 165 166 if (smaller(abs(det), config.epsilon)) { 167 return null; 168 } 169 170 var d20o11 = multiplyScalar(d2[0], o1[1]); 171 var d21o10 = multiplyScalar(d2[1], o1[0]); 172 var d20o21 = multiplyScalar(d2[0], o2[1]); 173 var d21o20 = multiplyScalar(d2[1], o2[0]); 174 var t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det); 175 return add(multiply(d1, t), o1); 176 } 177 178 function _intersect3dHelper(a, b, c, d, e, f, g, h, i, j, k, l) { 179 // (a - b)*(c - d) + (e - f)*(g - h) + (i - j)*(k - l) 180 var add1 = multiplyScalar(subtract(a, b), subtract(c, d)); 181 var add2 = multiplyScalar(subtract(e, f), subtract(g, h)); 182 var add3 = multiplyScalar(subtract(i, j), subtract(k, l)); 183 return addScalar(addScalar(add1, add2), add3); 184 } 185 186 function _intersect3d(x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) { 187 var d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3); 188 189 var d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1); 190 191 var d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1); 192 193 var d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3); 194 195 var d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1); 196 197 var numerator = subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)); 198 var denominator = subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)); 199 if (isZero(denominator)) return null; 200 var ta = divideScalar(numerator, denominator); 201 var tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343); 202 var pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1))); 203 var pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1))); 204 var paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1))); 205 var pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3))); 206 var pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3))); 207 var pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3))); 208 209 if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) { 210 return [pax, pay, paz]; 211 } else { 212 return null; 213 } 214 } 215 216 function _intersectLinePlane(x1, y1, z1, x2, y2, z2, x, y, z, c) { 217 var x1x = multiplyScalar(x1, x); 218 var x2x = multiplyScalar(x2, x); 219 var y1y = multiplyScalar(y1, y); 220 var y2y = multiplyScalar(y2, y); 221 var z1z = multiplyScalar(z1, z); 222 var z2z = multiplyScalar(z2, z); 223 var numerator = subtract(subtract(subtract(c, x1x), y1y), z1z); 224 var denominator = subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z); 225 var t = divideScalar(numerator, denominator); 226 var px = addScalar(x1, multiplyScalar(t, subtract(x2, x1))); 227 var py = addScalar(y1, multiplyScalar(t, subtract(y2, y1))); 228 var pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1))); 229 return [px, py, pz]; // TODO: Add cases when line is parallel to the plane: 230 // (a) no intersection, 231 // (b) line contained in plane 232 } 233 });