1 | // %pacpus:license{
|
---|
2 | // This file is part of the PACPUS framework distributed under the
|
---|
3 | // CECILL-C License, Version 1.0.
|
---|
4 | // %pacpus:license}
|
---|
5 | /// @file
|
---|
6 | /// @author Firstname Surname <firstname.surname@utc.fr>
|
---|
7 | /// @date Month, Year
|
---|
8 | /// @version $Id: utilities.hpp 76 2013-01-10 17:05:10Z kurdejma $
|
---|
9 | /// @copyright Copyright (c) UTC/CNRS Heudiasyc 2006 - 2013. All rights reserved.
|
---|
10 | /// @brief Brief description.
|
---|
11 | ///
|
---|
12 | /// Detailed description.
|
---|
13 |
|
---|
14 | #ifndef __UTILITIES_HPP__
|
---|
15 | #define __UTILITIES_HPP__
|
---|
16 |
|
---|
17 |
|
---|
18 | namespace math {
|
---|
19 |
|
---|
20 | namespace utility {
|
---|
21 |
|
---|
22 |
|
---|
23 | /*!
|
---|
24 | * \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)
|
---|
25 | * \brief Compute points of intersection of circle and line defined through two poinst A and B
|
---|
26 | * \param A : a point of the line
|
---|
27 | * \param B : a point of the line
|
---|
28 | * \param C :
|
---|
29 | * \param R : circle radius
|
---|
30 | * \return a list of abscissas with respect of point A
|
---|
31 | */
|
---|
32 | template <class T> inline std::vector<T> LineCircleIntersection(const boost::numeric::ublas::vector<T> & A,
|
---|
33 | const boost::numeric::ublas::vector<T> & B,
|
---|
34 | const boost::numeric::ublas::vector<T> & C,
|
---|
35 | const double R){
|
---|
36 | std::vector<T> intersection;
|
---|
37 |
|
---|
38 | double alpha = (B[0]-A[0])*(B[0]-A[0]) + (B[1]-A[1])*(B[1]-A[1]);
|
---|
39 | double norm = std::sqrt(alpha);
|
---|
40 | double beta = 2 *(B[0]-A[0])*(A[0]-C[0]) + (B[1]-A[1])*(A[1]-C[1]);
|
---|
41 | 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;
|
---|
42 | double delta = beta*beta - 4*alpha*gamma;
|
---|
43 |
|
---|
44 | if(delta>0){
|
---|
45 | intersection.push_back( (-beta -sqrt(delta))/(2*norm) );
|
---|
46 | intersection.push_back( (-beta +sqrt(delta))/(2*norm) );
|
---|
47 | }
|
---|
48 |
|
---|
49 | return intersection;
|
---|
50 | }
|
---|
51 |
|
---|
52 | /*!
|
---|
53 | * \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)
|
---|
54 | * \brief Compute points of intersection of circle and segment defined through two poinst A and B
|
---|
55 | * \param A : a point of the line
|
---|
56 | * \param B : a point of the line
|
---|
57 | * \param C :
|
---|
58 | * \param R : circle radius
|
---|
59 | * \return a list of abscissas with respect of point A and in taking account the hypothesis abscissas in [A,B]
|
---|
60 | */
|
---|
61 | template <class T> inline std::vector<T> SegmentCircleIntersection(const boost::numeric::ublas::vector<T> & A,
|
---|
62 | const boost::numeric::ublas::vector<T> & B,
|
---|
63 | const boost::numeric::ublas::vector<T> & C,
|
---|
64 | const double R){
|
---|
65 |
|
---|
66 |
|
---|
67 | std::vector<T> intersection;
|
---|
68 | double alpha = (B[0] - A[0]) * (B[0] - A[0]) + (B[1] - A[1]) * (B[1] - A[1]);
|
---|
69 | double norm = std::sqrt(alpha);
|
---|
70 | double beta = 2 * ((B[0] - A[0]) * (A[0] - C[0]) + (B[1] - A[1]) * (A[1] - C[1]));
|
---|
71 | 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;
|
---|
72 |
|
---|
73 | double delta = beta*beta - 4*alpha*gamma;
|
---|
74 |
|
---|
75 | if(delta>0){
|
---|
76 | intersection.push_back( (-beta -sqrt(delta))/(2*norm) );
|
---|
77 | intersection.push_back( (-beta +sqrt(delta))/(2*norm) );
|
---|
78 |
|
---|
79 | if(intersection[0]<1 && intersection[1]>0){
|
---|
80 | if(intersection[0] <0 ) intersection[0]=0;
|
---|
81 | if(intersection[1] >norm) intersection[1]=norm;
|
---|
82 | }else{
|
---|
83 | intersection.clear();
|
---|
84 | }
|
---|
85 | }
|
---|
86 |
|
---|
87 |
|
---|
88 | return intersection;
|
---|
89 | }
|
---|
90 |
|
---|
91 | /*!
|
---|
92 | * \fn inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(const RealType & pxx,const RealType & pxy,const RealType & pyy,const RealType &proba)
|
---|
93 | * \brief Convert 2D covariance to a ellipse parameters
|
---|
94 | * \param pxx : variance X
|
---|
95 | * \param pxy : covariance XY
|
---|
96 | * \param pyy : variance Y
|
---|
97 | * \param proba : percentage
|
---|
98 | * \return ublas vector containing semi-major axis, semi-minor axis and orientation of the ellipse
|
---|
99 | */
|
---|
100 | template <class RealType> inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(const RealType & pxx,const RealType & pxy,const RealType & pyy,const RealType &proba){
|
---|
101 |
|
---|
102 | boost::numeric::ublas::vector<RealType> ellipse(3);
|
---|
103 |
|
---|
104 | // le scalaire "k" definit l'ellipse avec l'equation :(x-mx)T*(1/P)*(x-mx)=k^2
|
---|
105 | double k=sqrt(-2*log(1-proba));
|
---|
106 |
|
---|
107 | // coeficient de correlation
|
---|
108 | double ro = pxy / sqrt(pxx * pyy);
|
---|
109 | if ( fabs( ro ) > 1 )
|
---|
110 | {
|
---|
111 | std::cout << "ro=" << ro << "pxx=" << pxx << "pxy=" << pxy << "pyy=" << pyy << std::endl;
|
---|
112 | throw math_error("Cov2Ellipse: correlation coefficient is not included between -1 and 1. Covariance matrix is not defined positive");
|
---|
113 | }
|
---|
114 | double a = 1/(pxx*(1- ro * ro));
|
---|
115 | double b = -ro/(sqrt(pyy*pxx)*(1- ro * ro));
|
---|
116 | double c = 1/(pyy*(1- ro * ro));
|
---|
117 |
|
---|
118 | // calcul des deux valeurs propres
|
---|
119 | // la gde vp (lambda1) est associee au petit axe.
|
---|
120 | double delta = (a-c)*(a-c)+4*b*b;
|
---|
121 | double lambda1 = 0.5*(a+c+sqrt(delta));
|
---|
122 | double lambda2 = 0.5*(a+c-sqrt(delta));
|
---|
123 |
|
---|
124 | // vecteur directeur du grand axe
|
---|
125 | double aux = (lambda2-a)/b;
|
---|
126 | double deno=sqrt(1+aux*aux);
|
---|
127 | double Ux = 1/deno;
|
---|
128 | double Uy = aux/deno;
|
---|
129 |
|
---|
130 | // longueur des axes dans le repere propre
|
---|
131 | double axeX = k/sqrt(lambda2); // demi axe
|
---|
132 | double axeY = k/sqrt(lambda1); // demi axe
|
---|
133 |
|
---|
134 | ellipse(2) = - atan2(Uy, Ux);//heading
|
---|
135 | ellipse(0) = axeY * 2 * 3; // width x3 (sigma) si PROBA = 0.4 ellipsoide a deux dimensions (test du khi2)
|
---|
136 | ellipse(1) = axeX * 2 * 3; //height
|
---|
137 |
|
---|
138 | // heading = - atan2(Uy, Ux);
|
---|
139 | // width = axeY * 2 * 3; // x3 (sigma) si PROBA = 0.4 ellipsoide a deux dimensions (test du khi2)
|
---|
140 | // height = axeX * 2 * 3;
|
---|
141 |
|
---|
142 | return ellipse;
|
---|
143 | }
|
---|
144 |
|
---|
145 | /*!
|
---|
146 | * \fn inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(boost::numeric::ublas::matrix<RealType> P,const RealType &proba)
|
---|
147 | * \brief Convert 2D covariance to a ellipse parameters
|
---|
148 | * \param P : 2D covariance matrix
|
---|
149 | * \param proba :
|
---|
150 | * \return ublas vector containing semi-major axis, semi-minor axis and orientation of the ellipse
|
---|
151 | */
|
---|
152 | template <class RealType> inline boost::numeric::ublas::vector<RealType> Cov2Ellipse(boost::numeric::ublas::matrix<RealType> P,const RealType &proba){
|
---|
153 | if(P.size1()==2 & P.size2()==2) throw math_error("Cov2Ellipse: covariance is not a 2D square matrix");
|
---|
154 | return Cov2Ellipse(P(0,0),P(0,1),P(1,1),proba);
|
---|
155 | }
|
---|
156 |
|
---|
157 | };
|
---|
158 | };
|
---|
159 | #endif
|
---|