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