polynomial_calculations.h

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#pragma once
 
#include <pcl/common/eigen.h>
#include <pcl/common/bivariate_polynomial.h>
 
namespace pcl 
{
  /** \brief This provides some functionality for polynomials,
    *         like finding roots or approximating bivariate polynomials
    *  \author Bastian Steder 
    *  \ingroup common
    */
  template <typename real>
  class PolynomialCalculationsT 
  {
    public:
      // =====PUBLIC STRUCTS=====
      //! Parameters used in this class
      struct Parameters
      {
        Parameters () { setZeroValue (1e-6);}
        //! Set zero_value
        void
        setZeroValue (real new_zero_value);
 
        real zero_value = {};       //!< Every value below this is considered to be zero
        real sqr_zero_value = {};   //!< sqr of the above
      };
      
      // =====PUBLIC METHODS=====
      /** Solves an equation of the form ax^4 + bx^3 + cx^2 +dx + e = 0
       *  See https://en.wikipedia.org/wiki/Quartic_equation#Summary_of_Ferrari.27s_method */
      inline void
      solveQuarticEquation (real a, real b, real c, real d, real e, std::vector<real>& roots) const;
 
      /** Solves an equation of the form ax^3 + bx^2 + cx + d = 0
       *  See https://en.wikipedia.org/wiki/Cubic_equation */
      inline void
      solveCubicEquation (real a, real b, real c, real d, std::vector<real>& roots) const;
 
      /** Solves an equation of the form ax^2 + bx + c = 0
       *  See https://en.wikipedia.org/wiki/Quadratic_equation */
      inline void
      solveQuadraticEquation (real a, real b, real c, std::vector<real>& roots) const;
 
      /** Solves an equation of the form ax + b = 0 */
      inline void
      solveLinearEquation (real a, real b, std::vector<real>& roots) const;
      
      /** Get the bivariate polynomial approximation for Z(X,Y) from the given sample points.
       *  The parameters a,b,c,... for the polynom are returned.
       *  The order is, e.g., for degree 1: ax+by+c and for degree 2: ax²+bxy+cx+dy²+ey+f.
       *  error is set to true if the approximation did not work for any reason
       *  (not enough points, matrix not invertible, etc.) */
      inline 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;
      
      //! Same as above, using a reference for the return value
      inline bool
      bivariatePolynomialApproximation (std::vector<Eigen::Matrix<real, 3, 1>, Eigen::aligned_allocator<Eigen::Matrix<real, 3, 1> > >& samplePoints,
                                        unsigned int polynomial_degree, BivariatePolynomialT<real>& ret) const;
 
      //! Set the minimum value under which values are considered zero
      inline void
      setZeroValue (real new_zero_value) { parameters_.setZeroValue(new_zero_value); }
      
    protected:  
      // =====PROTECTED METHODS=====
      //! check if std::abs(d)<zeroValue
      inline bool
      isNearlyZero (real d) const 
      { 
        return (std::abs (d) < parameters_.zero_value);
      }
      
      //! check if sqrt(std::abs(d))<zeroValue
      inline bool
      sqrtIsNearlyZero (real d) const 
      { 
        return (std::abs (d) < parameters_.sqr_zero_value);
      }
      
      // =====PROTECTED MEMBERS=====
      Parameters parameters_;
  };
 
  using PolynomialCalculationsd = PolynomialCalculationsT<double>;
  using PolynomialCalculations = PolynomialCalculationsT<float>;
 
}  // end namespace
 
#include <pcl/common/impl/polynomial_calculations.hpp>