1 | 'use strict';
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2 |
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3 | function factory(type, config, load, typed) {
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4 | var abs = load(require('../arithmetic/abs'));
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5 | var add = load(require('../arithmetic/add'));
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6 | var addScalar = load(require('../arithmetic/addScalar'));
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7 | var matrix = load(require('../../type/matrix/function/matrix'));
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8 | var multiply = load(require('../arithmetic/multiply'));
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9 | var multiplyScalar = load(require('../arithmetic/multiplyScalar'));
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10 | var divideScalar = load(require('../arithmetic/divideScalar'));
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11 | var subtract = load(require('../arithmetic/subtract'));
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12 | var smaller = load(require('../relational/smaller'));
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13 | var equalScalar = load(require('../relational/equalScalar'));
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14 |
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40 |
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41 |
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42 | var intersect = typed('intersect', {
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43 | 'Array, Array, Array': function ArrayArrayArray(x, y, plane) {
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44 | if (!_3d(x)) {
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45 | throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument');
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46 | }
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47 | if (!_3d(y)) {
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48 | throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument');
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49 | }
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50 | if (!_4d(plane)) {
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51 | throw new TypeError('Array with 4 numbers expected as third argument');
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52 | }
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53 |
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54 | return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3]);
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55 | },
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56 |
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57 | 'Array, Array, Array, Array': function ArrayArrayArrayArray(w, x, y, z) {
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58 | if (w.length === 2) {
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59 | if (!_2d(w)) {
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60 | throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument');
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61 | }
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62 | if (!_2d(x)) {
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63 | throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument');
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64 | }
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65 | if (!_2d(y)) {
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66 | throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument');
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67 | }
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68 | if (!_2d(z)) {
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69 | throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument');
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70 | }
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71 |
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72 | return _intersect2d(w, x, y, z);
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73 | } else if (w.length === 3) {
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74 | if (!_3d(w)) {
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75 | throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument');
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76 | }
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77 | if (!_3d(x)) {
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78 | throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument');
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79 | }
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80 | if (!_3d(y)) {
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81 | throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument');
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82 | }
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83 | if (!_3d(z)) {
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84 | throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument');
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85 | }
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86 |
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87 | 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]);
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88 | } else {
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89 | throw new TypeError('Arrays with two or thee dimensional points expected');
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90 | }
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91 | },
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92 |
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93 | 'Matrix, Matrix, Matrix': function MatrixMatrixMatrix(x, y, plane) {
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94 | return matrix(intersect(x.valueOf(), y.valueOf(), plane.valueOf()));
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95 | },
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96 |
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97 | 'Matrix, Matrix, Matrix, Matrix': function MatrixMatrixMatrixMatrix(w, x, y, z) {
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98 |
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99 | return matrix(intersect(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()));
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100 | }
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101 | });
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102 |
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103 | function _isNumber(a) {
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104 |
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105 | return typeof a === 'number' || type.isBigNumber(a);
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106 | }
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107 |
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108 | function _2d(x) {
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109 | return x.length === 2 && _isNumber(x[0]) && _isNumber(x[1]);
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110 | }
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111 |
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112 | function _3d(x) {
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113 | return x.length === 3 && _isNumber(x[0]) && _isNumber(x[1]) && _isNumber(x[2]);
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114 | }
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115 |
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116 | function _4d(x) {
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117 | return x.length === 4 && _isNumber(x[0]) && _isNumber(x[1]) && _isNumber(x[2]) && _isNumber(x[3]);
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118 | }
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119 |
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120 | function _intersect2d(p1a, p1b, p2a, p2b) {
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121 | var o1 = p1a;
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122 | var o2 = p2a;
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123 | var d1 = subtract(o1, p1b);
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124 | var d2 = subtract(o2, p2b);
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125 | var det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1]));
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126 | if (smaller(abs(det), config.epsilon)) {
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127 | return null;
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128 | }
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129 | var d20o11 = multiplyScalar(d2[0], o1[1]);
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130 | var d21o10 = multiplyScalar(d2[1], o1[0]);
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131 | var d20o21 = multiplyScalar(d2[0], o2[1]);
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132 | var d21o20 = multiplyScalar(d2[1], o2[0]);
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133 | var t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det);
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134 | return add(multiply(d1, t), o1);
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135 | }
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136 |
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137 | function _intersect3dHelper(a, b, c, d, e, f, g, h, i, j, k, l) {
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138 |
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139 | var add1 = multiplyScalar(subtract(a, b), subtract(c, d));
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140 | var add2 = multiplyScalar(subtract(e, f), subtract(g, h));
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141 | var add3 = multiplyScalar(subtract(i, j), subtract(k, l));
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142 | return addScalar(addScalar(add1, add2), add3);
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143 | }
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144 |
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145 | function _intersect3d(x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) {
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146 | var d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3);
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147 | var d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1);
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148 | var d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1);
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149 | var d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3);
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150 | var d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1);
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151 | var ta = divideScalar(subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)), subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)));
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152 | var tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343);
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153 |
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154 | var pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1)));
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155 | var pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1)));
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156 | var paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1)));
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157 | var pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3)));
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158 | var pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3)));
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159 | var pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3)));
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160 | if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) {
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161 | return [pax, pay, paz];
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162 | } else {
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163 | return null;
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164 | }
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165 | }
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166 |
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167 | function _intersectLinePlane(x1, y1, z1, x2, y2, z2, x, y, z, c) {
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168 | var x1x = multiplyScalar(x1, x);
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169 | var x2x = multiplyScalar(x2, x);
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170 | var y1y = multiplyScalar(y1, y);
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171 | var y2y = multiplyScalar(y2, y);
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172 | var z1z = multiplyScalar(z1, z);
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173 | var z2z = multiplyScalar(z2, z);
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174 | var t = divideScalar(subtract(subtract(subtract(c, x1x), y1y), z1z), subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z));
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175 | var px = addScalar(x1, multiplyScalar(t, subtract(x2, x1)));
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176 | var py = addScalar(y1, multiplyScalar(t, subtract(y2, y1)));
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177 | var pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1)));
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178 | return [px, py, pz];
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179 |
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180 |
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181 |
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182 | }
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183 |
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184 | return intersect;
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185 | }
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186 |
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187 | exports.name = 'intersect';
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188 | exports.factory = factory; |
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