1 | /*
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2 | * Project: MoleCuilder
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3 | * Description: creates and alters molecular systems
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4 | * Copyright (C) 2010 University of Bonn. All rights reserved.
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5 | * Please see the LICENSE file or "Copyright notice" in builder.cpp for details.
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6 | */
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7 |
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8 | /*
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9 | * Line.cpp
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10 | *
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11 | * Created on: Apr 30, 2010
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12 | * Author: crueger
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13 | */
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14 |
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15 | // include config.h
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16 | #ifdef HAVE_CONFIG_H
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17 | #include <config.h>
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18 | #endif
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19 |
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20 | #include "Helpers/MemDebug.hpp"
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21 |
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22 | #include "LinearAlgebra/Line.hpp"
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23 |
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24 | #include <cmath>
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25 | #include <iostream>
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26 |
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27 | #include "LinearAlgebra/Vector.hpp"
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28 | #include "Helpers/Log.hpp"
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29 | #include "Helpers/Verbose.hpp"
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30 | #include "LinearAlgebra/gslmatrix.hpp"
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31 | #include "Helpers/Info.hpp"
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32 | #include "Exceptions/LinearDependenceException.hpp"
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33 | #include "Exceptions/SkewException.hpp"
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34 | #include "LinearAlgebra/Plane.hpp"
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35 |
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36 | using namespace std;
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37 |
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38 | Line::Line(const Vector &_origin, const Vector &_direction) :
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39 | direction(new Vector(_direction))
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40 | {
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41 | direction->Normalize();
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42 | origin.reset(new Vector(_origin.partition(*direction).second));
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43 | }
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44 |
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45 | Line::Line(const Line &src) :
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46 | origin(new Vector(*src.origin)),
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47 | direction(new Vector(*src.direction))
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48 | {}
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49 |
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50 | Line::~Line()
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51 | {}
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52 |
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53 |
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54 | double Line::distance(const Vector &point) const{
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55 | // get any vector from line to point
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56 | Vector helper = point - *origin;
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57 | // partition this vector along direction
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58 | // the residue points from the line to the point
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59 | return helper.partition(*direction).second.Norm();
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60 | }
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61 |
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62 | Vector Line::getClosestPoint(const Vector &point) const{
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63 | // get any vector from line to point
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64 | Vector helper = point - *origin;
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65 | // partition this vector along direction
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66 | // add only the part along the direction
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67 | return *origin + helper.partition(*direction).first;
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68 | }
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69 |
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70 | Vector Line::getDirection() const{
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71 | return *direction;
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72 | }
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73 |
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74 | Vector Line::getOrigin() const{
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75 | return *origin;
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76 | }
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77 |
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78 | vector<Vector> Line::getPointsOnLine() const{
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79 | vector<Vector> res;
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80 | res.reserve(2);
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81 | res.push_back(*origin);
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82 | res.push_back(*origin+*direction);
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83 | return res;
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84 | }
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85 |
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86 | /** Calculates the intersection of the two lines that are both on the same plane.
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87 | * This is taken from Weisstein, Eric W. "Line-Line Intersection." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Line-LineIntersection.html
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88 | * \param *out output stream for debugging
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89 | * \param *Line1a first vector of first line
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90 | * \param *Line1b second vector of first line
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91 | * \param *Line2a first vector of second line
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92 | * \param *Line2b second vector of second line
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93 | * \return true - \a this will contain the intersection on return, false - lines are parallel
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94 | */
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95 | Vector Line::getIntersection(const Line& otherLine) const{
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96 | Info FunctionInfo(__func__);
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97 |
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98 | pointset line1Points = getPointsOnLine();
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99 |
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100 | Vector Line1a = line1Points[0];
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101 | Vector Line1b = line1Points[1];
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102 |
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103 | pointset line2Points = otherLine.getPointsOnLine();
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104 |
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105 | Vector Line2a = line2Points[0];
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106 | Vector Line2b = line2Points[1];
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107 |
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108 | Vector res;
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109 |
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110 | auto_ptr<GSLMatrix> M = auto_ptr<GSLMatrix>(new GSLMatrix(4,4));
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111 |
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112 | M->SetAll(1.);
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113 | for (int i=0;i<3;i++) {
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114 | M->Set(0, i, Line1a[i]);
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115 | M->Set(1, i, Line1b[i]);
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116 | M->Set(2, i, Line2a[i]);
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117 | M->Set(3, i, Line2b[i]);
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118 | }
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119 |
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120 | //Log() << Verbose(1) << "Coefficent matrix is:" << endl;
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121 | //for (int i=0;i<4;i++) {
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122 | // for (int j=0;j<4;j++)
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123 | // cout << "\t" << M->Get(i,j);
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124 | // cout << endl;
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125 | //}
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126 | if (fabs(M->Determinant()) > MYEPSILON) {
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127 | Log() << Verbose(1) << "Determinant of coefficient matrix is NOT zero." << endl;
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128 | throw SkewException(__FILE__,__LINE__);
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129 | }
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130 |
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131 | Log() << Verbose(1) << "INFO: Line1a = " << Line1a << ", Line1b = " << Line1b << ", Line2a = " << Line2a << ", Line2b = " << Line2b << "." << endl;
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132 |
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133 |
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134 | // constuct a,b,c
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135 | Vector a = Line1b - Line1a;
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136 | Vector b = Line2b - Line2a;
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137 | Vector c = Line2a - Line1a;
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138 | Vector d = Line2b - Line1b;
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139 | Log() << Verbose(1) << "INFO: a = " << a << ", b = " << b << ", c = " << c << "." << endl;
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140 | if ((a.NormSquared() < MYEPSILON) || (b.NormSquared() < MYEPSILON)) {
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141 | res.Zero();
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142 | Log() << Verbose(1) << "At least one of the lines is ill-defined, i.e. offset equals second vector." << endl;
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143 | throw LinearDependenceException(__FILE__,__LINE__);
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144 | }
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145 |
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146 | // check for parallelity
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147 | Vector parallel;
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148 | double factor = 0.;
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149 | if (fabs(a.ScalarProduct(b)*a.ScalarProduct(b)/a.NormSquared()/b.NormSquared() - 1.) < MYEPSILON) {
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150 | parallel = Line1a - Line2a;
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151 | factor = parallel.ScalarProduct(a)/a.Norm();
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152 | if ((factor >= -MYEPSILON) && (factor - 1. < MYEPSILON)) {
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153 | res = Line2a;
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154 | Log() << Verbose(1) << "Lines conincide." << endl;
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155 | return res;
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156 | } else {
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157 | parallel = Line1a - Line2b;
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158 | factor = parallel.ScalarProduct(a)/a.Norm();
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159 | if ((factor >= -MYEPSILON) && (factor - 1. < MYEPSILON)) {
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160 | res = Line2b;
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161 | Log() << Verbose(1) << "Lines conincide." << endl;
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162 | return res;
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163 | }
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164 | }
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165 | Log() << Verbose(1) << "Lines are parallel." << endl;
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166 | res.Zero();
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167 | throw LinearDependenceException(__FILE__,__LINE__);
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168 | }
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169 |
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170 | // obtain s
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171 | double s;
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172 | Vector temp1, temp2;
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173 | temp1 = c;
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174 | temp1.VectorProduct(b);
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175 | temp2 = a;
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176 | temp2.VectorProduct(b);
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177 | Log() << Verbose(1) << "INFO: temp1 = " << temp1 << ", temp2 = " << temp2 << "." << endl;
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178 | if (fabs(temp2.NormSquared()) > MYEPSILON)
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179 | s = temp1.ScalarProduct(temp2)/temp2.NormSquared();
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180 | else
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181 | s = 0.;
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182 | Log() << Verbose(1) << "Factor s is " << temp1.ScalarProduct(temp2) << "/" << temp2.NormSquared() << " = " << s << "." << endl;
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183 |
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184 | // construct intersection
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185 | res = a;
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186 | res.Scale(s);
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187 | res += Line1a;
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188 | Log() << Verbose(1) << "Intersection is at " << res << "." << endl;
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189 |
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190 | return res;
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191 | }
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192 |
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193 | /** Rotates the vector by an angle of \a alpha around this line.
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194 | * \param rhs Vector to rotate
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195 | * \param alpha rotation angle in radian
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196 | */
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197 | Vector Line::rotateVector(const Vector &rhs, double alpha) const{
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198 | Vector helper = rhs;
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199 |
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200 | // translate the coordinate system so that the line goes through (0,0,0)
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201 | helper -= *origin;
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202 |
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203 | // partition the vector into a part that gets rotated and a part that lies along the line
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204 | pair<Vector,Vector> parts = helper.partition(*direction);
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205 |
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206 | // we just keep anything that is along the axis
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207 | Vector res = parts.first;
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208 |
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209 | // the rest has to be rotated
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210 | Vector a = parts.second;
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211 | // we only have to do the rest, if we actually could partition the vector
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212 | if(!a.IsZero()){
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213 | // construct a vector that is orthogonal to a and direction and has length |a|
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214 | Vector y = a;
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215 | // direction is normalized, so the result has length |a|
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216 | y.VectorProduct(*direction);
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217 |
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218 | res += cos(alpha) * a + sin(alpha) * y;
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219 | }
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220 |
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221 | // translate the coordinate system back
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222 | res += *origin;
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223 | return res;
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224 | }
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225 |
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226 | Plane Line::getOrthogonalPlane(const Vector &origin) const{
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227 | return Plane(getDirection(),origin);
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228 | }
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229 |
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230 | std::vector<Vector> Line::getSphereIntersections() const{
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231 | std::vector<Vector> res;
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232 |
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233 | // line is kept in normalized form, so we can skip a lot of calculations
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234 | double discriminant = 1-origin->NormSquared();
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235 | // we might have 2, 1 or 0 solutions, depending on discriminant
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236 | if(discriminant>=0){
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237 | if(discriminant==0){
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238 | res.push_back(*origin);
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239 | }
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240 | else{
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241 | Vector helper = sqrt(discriminant)*(*direction);
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242 | res.push_back(*origin+helper);
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243 | res.push_back(*origin-helper);
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244 | }
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245 | }
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246 | return res;
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247 | }
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248 |
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249 | Line makeLineThrough(const Vector &x1, const Vector &x2){
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250 | if(x1==x2){
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251 | throw LinearDependenceException(__FILE__,__LINE__);
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252 | }
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253 | return Line(x1,x1-x2);
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254 | }
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255 |
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256 | ostream& operator<<(ostream& ost, const Line& m)
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257 | {
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258 | const Vector origin = m.getOrigin();
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259 | const Vector direction = m.getDirection();
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260 | ost << "(";
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261 | for (int i=0;i<NDIM;i++) {
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262 | ost << origin[i];
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263 | if (i != 2)
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264 | ost << ",";
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265 | }
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266 | ost << ") -> (";
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267 | for (int i=0;i<NDIM;i++) {
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268 | ost << direction[i];
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269 | if (i != 2)
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270 | ost << ",";
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271 | }
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272 | ost << ")";
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273 | return ost;
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274 | };
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275 |
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