1 | #ifndef __UTILITIES_HPP__
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2 | #define __UTILITIES_HPP__
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3 |
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4 |
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5 | namespace math {
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6 |
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7 | namespace utility {
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8 |
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9 |
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10 | /*!
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11 | * \fn inline std::vector<T> LineCircleIntersection(const boost::numeric::ublas::vector<T> & A,const boost::numeric::ublas::vector<T> & B, const boost::numeric::ublas::vector<T> & C,const double R)
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12 | * \brief Compute points of intersection of circle and line defined through two poinst A and B
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13 | * \param A : a point of the line
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14 | * \param B : a point of the line
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15 | * \param C :
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16 | * \param R : circle radius
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17 | * \return a list of abscissas with respect of point A
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18 | */
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19 | template <class T> inline std::vector<T> LineCircleIntersection(const boost::numeric::ublas::vector<T> & A,
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20 | const boost::numeric::ublas::vector<T> & B,
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21 | const boost::numeric::ublas::vector<T> & C,
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22 | const double R){
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23 | std::vector<T> intersection;
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24 |
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25 | double alpha = (B[0]-A[0])*(B[0]-A[0]) + (B[1]-A[1])*(B[1]-A[1]);
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26 | double norm = std::sqrt(alpha);
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27 | double beta = 2 *(B[0]-A[0])*(A[0]-C[0]) + (B[1]-A[1])*(A[1]-C[1]);
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28 | double gamma = A[0]*A[0] + A[1]*A[1] + C[0]*C[0] + C[1]*C[1] - 2*(A[0]*C[0] + A[1]*C[1] ) - R*R;
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29 | double delta = beta*beta - 4*alpha*gamma;
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30 |
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31 | if(delta>0){
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32 | intersection.push_back( (-beta -sqrt(delta))/(2*norm) );
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33 | intersection.push_back( (-beta +sqrt(delta))/(2*norm) );
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34 | }
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35 |
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36 | return intersection;
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37 | }
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38 |
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39 | /*!
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40 | * \fn inline std::vector<T> SegmentCircleIntersection(const boost::numeric::ublas::vector<T> & A,const boost::numeric::ublas::vector<T> & B, const boost::numeric::ublas::vector<T> & C,const double R)
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41 | * \brief Compute points of intersection of circle and segment defined through two poinst A and B
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42 | * \param A : a point of the line
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43 | * \param B : a point of the line
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44 | * \param C :
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45 | * \param R : circle radius
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46 | * \return a list of abscissas with respect of point A and in taking account the hypothesis abscissas in [A,B]
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47 | */
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48 | template <class T> inline std::vector<T> SegmentCircleIntersection(const boost::numeric::ublas::vector<T> & A,
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49 | const boost::numeric::ublas::vector<T> & B,
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50 | const boost::numeric::ublas::vector<T> & C,
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51 | const double R){
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52 |
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53 |
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54 | std::vector<T> intersection;
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55 | double alpha = (B[0] - A[0]) * (B[0] - A[0]) + (B[1] - A[1]) * (B[1] - A[1]);
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56 | double norm = std::sqrt(alpha);
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57 | double beta = 2 * ((B[0] - A[0]) * (A[0] - C[0]) + (B[1] - A[1]) * (A[1] - C[1]));
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58 | double gamma = A[0] * A[0] + A[1] * A[1] + C[0] * C[0] + C[1] * C[1] - 2 * (A[0] * C[0] + A[1] * C[1]) - R * R;
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59 |
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60 | double delta = beta*beta - 4*alpha*gamma;
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61 |
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62 | if(delta>0){
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63 | intersection.push_back( (-beta -sqrt(delta))/(2*norm) );
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64 | intersection.push_back( (-beta +sqrt(delta))/(2*norm) );
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65 |
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66 | if(intersection[0]<1 && intersection[1]>0){
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67 | if(intersection[0] <0 ) intersection[0]=0;
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68 | if(intersection[1] >norm) intersection[1]=norm;
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69 | }else{
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70 | intersection.clear();
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71 | }
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72 | }
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73 |
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74 |
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75 | return intersection;
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76 | }
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77 |
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78 | /*!
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79 | * \fn inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(const RealType & pxx,const RealType & pxy,const RealType & pyy,const RealType &proba)
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80 | * \brief Convert 2D covariance to a ellipse parameters
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81 | * \param pxx : variance X
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82 | * \param pxy : covariance XY
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83 | * \param pyy : variance Y
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84 | * \param proba : percentage
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85 | * \return ublas vector containing semi-major axis, semi-minor axis and orientation of the ellipse
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86 | */
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87 | template <class RealType> inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(const RealType & pxx,const RealType & pxy,const RealType & pyy,const RealType &proba){
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88 |
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89 | boost::numeric::ublas::vector<RealType> ellipse(3);
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90 |
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91 | // le scalaire "k" definit l'ellipse avec l'equation :(x-mx)T*(1/P)*(x-mx)=k^2
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92 | double k=sqrt(-2*log(1-proba));
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93 |
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94 | // coeficient de correlation
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95 | double ro = pxy / sqrt(pxx * pyy);
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96 | if ( fabs( ro ) > 1 )
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97 | {
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98 | std::cout << "ro=" << ro << "pxx=" << pxx << "pxy=" << pxy << "pyy=" << pyy << std::endl;
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99 | throw math_error("Cov2Ellipse: correlation coefficient is not included between -1 and 1. Covariance matrix is not defined positive");
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100 | }
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101 | double a = 1/(pxx*(1- ro * ro));
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102 | double b = -ro/(sqrt(pyy*pxx)*(1- ro * ro));
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103 | double c = 1/(pyy*(1- ro * ro));
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104 |
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105 | // calcul des deux valeurs propres
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106 | // la gde vp (lambda1) est associee au petit axe.
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107 | double delta = (a-c)*(a-c)+4*b*b;
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108 | double lambda1 = 0.5*(a+c+sqrt(delta));
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109 | double lambda2 = 0.5*(a+c-sqrt(delta));
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110 |
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111 | // vecteur directeur du grand axe
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112 | double aux = (lambda2-a)/b;
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113 | double deno=sqrt(1+aux*aux);
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114 | double Ux = 1/deno;
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115 | double Uy = aux/deno;
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116 |
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117 | // longueur des axes dans le repere propre
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118 | double axeX = k/sqrt(lambda2); // demi axe
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119 | double axeY = k/sqrt(lambda1); // demi axe
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120 |
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121 | ellipse(2) = - atan2(Uy, Ux);//heading
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122 | ellipse(0) = axeY * 2 * 3; // width x3 (sigma) si PROBA = 0.4 ellipsoide a deux dimensions (test du khi2)
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123 | ellipse(1) = axeX * 2 * 3; //height
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124 |
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125 | // heading = - atan2(Uy, Ux);
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126 | // width = axeY * 2 * 3; // x3 (sigma) si PROBA = 0.4 ellipsoide a deux dimensions (test du khi2)
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127 | // height = axeX * 2 * 3;
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128 |
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129 | return ellipse;
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130 | }
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131 |
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132 | /*!
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133 | * \fn inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(boost::numeric::ublas::matrix<RealType> P,const RealType &proba)
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134 | * \brief Convert 2D covariance to a ellipse parameters
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135 | * \param P : 2D covariance matrix
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136 | * \param proba :
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137 | * \return ublas vector containing semi-major axis, semi-minor axis and orientation of the ellipse
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138 | */
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139 | template <class RealType> inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(boost::numeric::ublas::matrix<RealType> P,const RealType &proba){
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140 | if(P.size1()==2 & P.size2()==2) throw math_error("Cov2Ellipse: covariance is not a 2D square matrix");
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141 | return Cov2Ellipse(P(0,0),P(0,1),P(1,1),proba);
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142 | }
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143 |
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144 | };
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145 | };
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146 | #endif
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