Point Cloud Library (PCL)  1.7.1
polynomial_calculations.h
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35 
36 #ifndef PCL_POLYNOMIAL_CALCULATIONS_H_
37 #define PCL_POLYNOMIAL_CALCULATIONS_H_
38 
39 #include <pcl/common/eigen.h>
40 #include <pcl/common/bivariate_polynomial.h>
41 
42 namespace pcl
43 {
44  /** \brief This provides some functionality for polynomials,
45  * like finding roots or approximating bivariate polynomials
46  * \author Bastian Steder
47  * \ingroup common
48  */
49  template <typename real>
51  {
52  public:
53  // =====CONSTRUCTOR & DESTRUCTOR=====
56 
57  // =====PUBLIC STRUCTS=====
58  //! Parameters used in this class
59  struct Parameters
60  {
62  //! Set zero_value
63  void
64  setZeroValue (real new_zero_value);
65 
66  real zero_value; //!< Every value below this is considered to be zero
67  real sqr_zero_value; //!< sqr of the above
68  };
69 
70  // =====PUBLIC METHODS=====
71  /** Solves an equation of the form ax^4 + bx^3 + cx^2 +dx + e = 0
72  * See http://en.wikipedia.org/wiki/Quartic_equation#Summary_of_Ferrari.27s_method */
73  inline void
74  solveQuarticEquation (real a, real b, real c, real d, real e, std::vector<real>& roots) const;
75 
76  /** Solves an equation of the form ax^3 + bx^2 + cx + d = 0
77  * See http://en.wikipedia.org/wiki/Cubic_equation */
78  inline void
79  solveCubicEquation (real a, real b, real c, real d, std::vector<real>& roots) const;
80 
81  /** Solves an equation of the form ax^2 + bx + c = 0
82  * See http://en.wikipedia.org/wiki/Quadratic_equation */
83  inline void
84  solveQuadraticEquation (real a, real b, real c, std::vector<real>& roots) const;
85 
86  /** Solves an equation of the form ax + b = 0 */
87  inline void
88  solveLinearEquation (real a, real b, std::vector<real>& roots) const;
89 
90  /** Get the bivariate polynomial approximation for Z(X,Y) from the given sample points.
91  * The parameters a,b,c,... for the polynom are returned.
92  * The order is, e.g., for degree 1: ax+by+c and for degree 2: ax²+bxy+cx+dy²+ey+f.
93  * error is set to true if the approximation did not work for any reason
94  * (not enough points, matrix not invertible, etc.) */
96  bivariatePolynomialApproximation (std::vector<Eigen::Matrix<real, 3, 1> >& samplePoints,
97  unsigned int polynomial_degree, bool& error) const;
98 
99  //! Same as above, using a reference for the return value
100  inline bool
101  bivariatePolynomialApproximation (std::vector<Eigen::Matrix<real, 3, 1> >& samplePoints,
102  unsigned int polynomial_degree, BivariatePolynomialT<real>& ret) const;
103 
104  //! Set the minimum value under which values are considered zero
105  inline void
106  setZeroValue (real new_zero_value) { parameters_.setZeroValue(new_zero_value); }
107 
108  protected:
109  // =====PROTECTED METHODS=====
110  //! check if fabs(d)<zeroValue
111  inline bool
112  isNearlyZero (real d) const
113  {
114  return (fabs (d) < parameters_.zero_value);
115  }
116 
117  //! check if sqrt(fabs(d))<zeroValue
118  inline bool
119  sqrtIsNearlyZero (real d) const
120  {
121  return (fabs (d) < parameters_.sqr_zero_value);
122  }
123 
124  // =====PROTECTED MEMBERS=====
126  };
127 
130 
131 } // end namespace
132 
133 #include <pcl/common/impl/polynomial_calculations.hpp>
134 
135 #endif