Point Cloud Library (PCL)  1.10.0-dev
polynomial_calculations.h
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35 
36 #pragma once
37 
38 #include <pcl/common/eigen.h>
39 #include <pcl/common/bivariate_polynomial.h>
40 
41 namespace pcl
42 {
43  /** \brief This provides some functionality for polynomials,
44  * like finding roots or approximating bivariate polynomials
45  * \author Bastian Steder
46  * \ingroup common
47  */
48  template <typename real>
50  {
51  public:
52  // =====PUBLIC STRUCTS=====
53  //! Parameters used in this class
54  struct Parameters
55  {
56  Parameters () { setZeroValue (1e-6);}
57  //! Set zero_value
58  void
59  setZeroValue (real new_zero_value);
60 
61  real zero_value = {}; //!< Every value below this is considered to be zero
62  real sqr_zero_value = {}; //!< sqr of the above
63  };
64 
65  // =====PUBLIC METHODS=====
66  /** Solves an equation of the form ax^4 + bx^3 + cx^2 +dx + e = 0
67  * See http://en.wikipedia.org/wiki/Quartic_equation#Summary_of_Ferrari.27s_method */
68  inline void
69  solveQuarticEquation (real a, real b, real c, real d, real e, std::vector<real>& roots) const;
70 
71  /** Solves an equation of the form ax^3 + bx^2 + cx + d = 0
72  * See http://en.wikipedia.org/wiki/Cubic_equation */
73  inline void
74  solveCubicEquation (real a, real b, real c, real d, std::vector<real>& roots) const;
75 
76  /** Solves an equation of the form ax^2 + bx + c = 0
77  * See http://en.wikipedia.org/wiki/Quadratic_equation */
78  inline void
79  solveQuadraticEquation (real a, real b, real c, std::vector<real>& roots) const;
80 
81  /** Solves an equation of the form ax + b = 0 */
82  inline void
83  solveLinearEquation (real a, real b, std::vector<real>& roots) const;
84 
85  /** Get the bivariate polynomial approximation for Z(X,Y) from the given sample points.
86  * The parameters a,b,c,... for the polynom are returned.
87  * The order is, e.g., for degree 1: ax+by+c and for degree 2: ax²+bxy+cx+dy²+ey+f.
88  * error is set to true if the approximation did not work for any reason
89  * (not enough points, matrix not invertible, etc.) */
91  bivariatePolynomialApproximation (std::vector<Eigen::Matrix<real, 3, 1>, Eigen::aligned_allocator<Eigen::Matrix<real, 3, 1> > >& samplePoints,
92  unsigned int polynomial_degree, bool& error) const;
93 
94  //! Same as above, using a reference for the return value
95  inline bool
96  bivariatePolynomialApproximation (std::vector<Eigen::Matrix<real, 3, 1>, Eigen::aligned_allocator<Eigen::Matrix<real, 3, 1> > >& samplePoints,
97  unsigned int polynomial_degree, BivariatePolynomialT<real>& ret) const;
98 
99  //! Set the minimum value under which values are considered zero
100  inline void
101  setZeroValue (real new_zero_value) { parameters_.setZeroValue(new_zero_value); }
102 
103  protected:
104  // =====PROTECTED METHODS=====
105  //! check if std::abs(d)<zeroValue
106  inline bool
107  isNearlyZero (real d) const
108  {
109  return (std::abs (d) < parameters_.zero_value);
110  }
111 
112  //! check if sqrt(std::abs(d))<zeroValue
113  inline bool
114  sqrtIsNearlyZero (real d) const
115  {
116  return (std::abs (d) < parameters_.sqr_zero_value);
117  }
118 
119  // =====PROTECTED MEMBERS=====
121  };
122 
125 
126 } // end namespace
127 
128 #include <pcl/common/impl/polynomial_calculations.hpp>
This represents a bivariate polynomial and provides some functionality for it.
BivariatePolynomialT< real > bivariatePolynomialApproximation(std::vector< Eigen::Matrix< real, 3, 1 >, Eigen::aligned_allocator< Eigen::Matrix< real, 3, 1 > > > &samplePoints, unsigned int polynomial_degree, bool &error) const
Get the bivariate polynomial approximation for Z(X,Y) from the given sample points.
void solveLinearEquation(real a, real b, std::vector< real > &roots) const
Solves an equation of the form ax + b = 0.
This file defines compatibility wrappers for low level I/O functions.
Definition: convolution.h:45
void setZeroValue(real new_zero_value)
Set zero_value.
real zero_value
Every value below this is considered to be zero.
void solveQuarticEquation(real a, real b, real c, real d, real e, std::vector< real > &roots) const
Solves an equation of the form ax^4 + bx^3 + cx^2 +dx + e = 0 See http://en.wikipedia.org/wiki/Quartic_equation#Summary_of_Ferrari.27s_method.
void setZeroValue(real new_zero_value)
Set the minimum value under which values are considered zero.
bool sqrtIsNearlyZero(real d) const
check if sqrt(std::abs(d))<zeroValue
void solveQuadraticEquation(real a, real b, real c, std::vector< real > &roots) const
Solves an equation of the form ax^2 + bx + c = 0 See http://en.wikipedia.org/wiki/Quadratic_equation...
bool isNearlyZero(real d) const
check if std::abs(d)<zeroValue
This provides some functionality for polynomials, like finding roots or approximating bivariate polyn...
void solveCubicEquation(real a, real b, real c, real d, std::vector< real > &roots) const
Solves an equation of the form ax^3 + bx^2 + cx + d = 0 See http://en.wikipedia.org/wiki/Cubic_equati...