intersect.js (9029B)
1 "use strict"; 2 3 Object.defineProperty(exports, "__esModule", { 4 value: true 5 }); 6 exports.createIntersect = void 0; 7 8 var _factory = require("../../utils/factory.js"); 9 10 var name = 'intersect'; 11 var dependencies = ['typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar', 'flatten', 'isZero', 'isNumeric']; 12 var createIntersect = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) { 13 var typed = _ref.typed, 14 config = _ref.config, 15 abs = _ref.abs, 16 add = _ref.add, 17 addScalar = _ref.addScalar, 18 matrix = _ref.matrix, 19 multiply = _ref.multiply, 20 multiplyScalar = _ref.multiplyScalar, 21 divideScalar = _ref.divideScalar, 22 subtract = _ref.subtract, 23 smaller = _ref.smaller, 24 equalScalar = _ref.equalScalar, 25 flatten = _ref.flatten, 26 isZero = _ref.isZero, 27 isNumeric = _ref.isNumeric; 28 29 /** 30 * Calculates the point of intersection of two lines in two or three dimensions 31 * and of a line and a plane in three dimensions. The inputs are in the form of 32 * arrays or 1 dimensional matrices. The line intersection functions return null 33 * if the lines do not meet. 34 * 35 * Note: Fill the plane coefficients as `x + y + z = c` and not as `x + y + z + c = 0`. 36 * 37 * Syntax: 38 * 39 * math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2) 40 * math.intersect(endPoint1, endPoint2, planeCoefficients) 41 * 42 * Examples: 43 * 44 * math.intersect([0, 0], [10, 10], [10, 0], [0, 10]) // Returns [5, 5] 45 * math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0]) // Returns [5, 5, 0] 46 * math.intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6]) // Returns [7, -4, 3] 47 * 48 * @param {Array | Matrix} w Co-ordinates of first end-point of first line 49 * @param {Array | Matrix} x Co-ordinates of second end-point of first line 50 * @param {Array | Matrix} y Co-ordinates of first end-point of second line 51 * OR Co-efficients of the plane's equation 52 * @param {Array | Matrix} z Co-ordinates of second end-point of second line 53 * OR undefined if the calculation is for line and plane 54 * @return {Array} Returns the point of intersection of lines/lines-planes 55 */ 56 return typed('intersect', { 57 'Array, Array, Array': _AAA, 58 'Array, Array, Array, Array': _AAAA, 59 'Matrix, Matrix, Matrix': function MatrixMatrixMatrix(x, y, plane) { 60 var arr = _AAA(x.valueOf(), y.valueOf(), plane.valueOf()); 61 62 return arr === null ? null : matrix(arr); 63 }, 64 'Matrix, Matrix, Matrix, Matrix': function MatrixMatrixMatrixMatrix(w, x, y, z) { 65 // TODO: output matrix type should match input matrix type 66 var arr = _AAAA(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()); 67 68 return arr === null ? null : matrix(arr); 69 } 70 }); 71 72 function _AAA(x, y, plane) { 73 x = _coerceArr(x); 74 y = _coerceArr(y); 75 plane = _coerceArr(plane); 76 77 if (!_3d(x)) { 78 throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument'); 79 } 80 81 if (!_3d(y)) { 82 throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument'); 83 } 84 85 if (!_4d(plane)) { 86 throw new TypeError('Array with 4 numbers expected as third argument'); 87 } 88 89 return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3]); 90 } 91 92 function _AAAA(w, x, y, z) { 93 w = _coerceArr(w); 94 x = _coerceArr(x); 95 y = _coerceArr(y); 96 z = _coerceArr(z); 97 98 if (w.length === 2) { 99 if (!_2d(w)) { 100 throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument'); 101 } 102 103 if (!_2d(x)) { 104 throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument'); 105 } 106 107 if (!_2d(y)) { 108 throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument'); 109 } 110 111 if (!_2d(z)) { 112 throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument'); 113 } 114 115 return _intersect2d(w, x, y, z); 116 } else if (w.length === 3) { 117 if (!_3d(w)) { 118 throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument'); 119 } 120 121 if (!_3d(x)) { 122 throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument'); 123 } 124 125 if (!_3d(y)) { 126 throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument'); 127 } 128 129 if (!_3d(z)) { 130 throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument'); 131 } 132 133 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]); 134 } else { 135 throw new TypeError('Arrays with two or thee dimensional points expected'); 136 } 137 } 138 /** Coerce row and column 2-dim arrays to 1-dim array */ 139 140 141 function _coerceArr(arr) { 142 // row matrix 143 if (arr.length === 1) return arr[0]; // column matrix 144 145 if (arr.length > 1 && Array.isArray(arr[0])) { 146 if (arr.every(function (el) { 147 return Array.isArray(el) && el.length === 1; 148 })) return flatten(arr); 149 } 150 151 return arr; 152 } 153 154 function _2d(x) { 155 return x.length === 2 && isNumeric(x[0]) && isNumeric(x[1]); 156 } 157 158 function _3d(x) { 159 return x.length === 3 && isNumeric(x[0]) && isNumeric(x[1]) && isNumeric(x[2]); 160 } 161 162 function _4d(x) { 163 return x.length === 4 && isNumeric(x[0]) && isNumeric(x[1]) && isNumeric(x[2]) && isNumeric(x[3]); 164 } 165 166 function _intersect2d(p1a, p1b, p2a, p2b) { 167 var o1 = p1a; 168 var o2 = p2a; 169 var d1 = subtract(o1, p1b); 170 var d2 = subtract(o2, p2b); 171 var det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1])); 172 if (isZero(det)) return null; 173 174 if (smaller(abs(det), config.epsilon)) { 175 return null; 176 } 177 178 var d20o11 = multiplyScalar(d2[0], o1[1]); 179 var d21o10 = multiplyScalar(d2[1], o1[0]); 180 var d20o21 = multiplyScalar(d2[0], o2[1]); 181 var d21o20 = multiplyScalar(d2[1], o2[0]); 182 var t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det); 183 return add(multiply(d1, t), o1); 184 } 185 186 function _intersect3dHelper(a, b, c, d, e, f, g, h, i, j, k, l) { 187 // (a - b)*(c - d) + (e - f)*(g - h) + (i - j)*(k - l) 188 var add1 = multiplyScalar(subtract(a, b), subtract(c, d)); 189 var add2 = multiplyScalar(subtract(e, f), subtract(g, h)); 190 var add3 = multiplyScalar(subtract(i, j), subtract(k, l)); 191 return addScalar(addScalar(add1, add2), add3); 192 } 193 194 function _intersect3d(x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) { 195 var d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3); 196 197 var d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1); 198 199 var d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1); 200 201 var d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3); 202 203 var d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1); 204 205 var numerator = subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)); 206 var denominator = subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)); 207 if (isZero(denominator)) return null; 208 var ta = divideScalar(numerator, denominator); 209 var tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343); 210 var pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1))); 211 var pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1))); 212 var paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1))); 213 var pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3))); 214 var pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3))); 215 var pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3))); 216 217 if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) { 218 return [pax, pay, paz]; 219 } else { 220 return null; 221 } 222 } 223 224 function _intersectLinePlane(x1, y1, z1, x2, y2, z2, x, y, z, c) { 225 var x1x = multiplyScalar(x1, x); 226 var x2x = multiplyScalar(x2, x); 227 var y1y = multiplyScalar(y1, y); 228 var y2y = multiplyScalar(y2, y); 229 var z1z = multiplyScalar(z1, z); 230 var z2z = multiplyScalar(z2, z); 231 var numerator = subtract(subtract(subtract(c, x1x), y1y), z1z); 232 var denominator = subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z); 233 var t = divideScalar(numerator, denominator); 234 var px = addScalar(x1, multiplyScalar(t, subtract(x2, x1))); 235 var py = addScalar(y1, multiplyScalar(t, subtract(y2, y1))); 236 var pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1))); 237 return [px, py, pz]; // TODO: Add cases when line is parallel to the plane: 238 // (a) no intersection, 239 // (b) line contained in plane 240 } 241 }); 242 exports.createIntersect = createIntersect;