ImplicitPolynomial3Shape.h

#pragma once

#if defined(ImplicitPolynomial3Shape_RECURSES)
#error Recursive header files inclusion detected in ImplicitPolynomial3Shape.h
#else // defined(ImplicitPolynomial3Shape_RECURSES)

#define ImplicitPolynomial3Shape_RECURSES

#if !defined ImplicitPolynomial3Shape_h

#define ImplicitPolynomial3Shape_h

// Inclusions
#include <iostream>
#include "DGtal/base/Common.h"
#include "DGtal/base/BasicFunctors.h"
#include "DGtal/base/CPredicate.h"
#include "DGtal/kernel/NumberTraits.h"
#include "DGtal/math/MPolynomial.h"
#include "DGtal/shapes/implicit/CImplicitFunction.h"

namespace DGtal
{


  template < typename TSpace >
  class ImplicitPolynomial3Shape
  {

  public:
    typedef ImplicitPolynomial3Shape<TSpace> Self;
    typedef TSpace Space;
    typedef typename Space::RealPoint RealPoint;
    typedef typename Space::RealVector RealVector;
    typedef typename RealPoint::Coordinate Ring;
    typedef typename Space::Integer Integer;
    typedef MPolynomial< 3, Ring > Polynomial3;
    typedef Ring Value;

    BOOST_STATIC_ASSERT(( Space::dimension == 3 ));

    ImplicitPolynomial3Shape( const Polynomial3 & poly );

    ImplicitPolynomial3Shape & operator= ( const ImplicitPolynomial3Shape & other );

    ~ImplicitPolynomial3Shape();

    void init( const Polynomial3 & poly );

    // ----------------------- Interface --------------------------------------
  public:

    double operator()(const RealPoint &aPoint) const;

    bool isInside(const RealPoint &aPoint) const;

    Orientation orientation(const RealPoint &aPoint) const;

    inline
    RealVector gradient( const RealPoint &aPoint ) const;

// ------------------------------------------------------------ Added by Anis Benyoub

    inline
    double meanCurvature( const RealPoint &aPoint ) const;


    inline
    double gaussianCurvature( const RealPoint &aPoint ) const;

    inline
    RealPoint  nearestPoint(  const RealPoint &aPoint, 
                              const double accuracy, 
                              const int maxIter  , 
                              const double gamma ) const;



    // ----------------------- Interface --------------------------------------
  public:

    void selfDisplay ( std::ostream & out ) const;

    bool isValid() const;

    // ------------------------- Protected Datas ------------------------------
  private:
    // ------------------------- Private Datas --------------------------------
  private:
    Polynomial3 myPolynomial;

    // Partial deriatives
    Polynomial3 myFx;
    Polynomial3 myFy;
    Polynomial3 myFz;

    Polynomial3 myFxx;
    Polynomial3 myFxy;
    Polynomial3 myFxz;

    Polynomial3 myFyx;
    Polynomial3 myFyy;
    Polynomial3 myFyz;

    Polynomial3 myFzx;
    Polynomial3 myFzy;
    Polynomial3 myFzz;


    // Precomputed Polynoms useful for curvature computations
    Polynomial3 myUpPolynome;
    Polynomial3 myLowPolynome;


    // ------------------------- Hidden services ------------------------------
  protected:

    ImplicitPolynomial3Shape();

  private:


  }; // end of class ImplicitPolynomial3Shape


  template <typename T>
  std::ostream &
  operator<< ( std::ostream & out, const ImplicitPolynomial3Shape<T> & object );

} // namespace DGtal


// Includes inline functions.
#include "DGtal/shapes/implicit/ImplicitPolynomial3Shape.ih"

//                                                                           //

#endif // !defined ImplicitPolynomial3Shape_h

#undef ImplicitPolynomial3Shape_RECURSES
#endif // else defined(ImplicitPolynomial3Shape_RECURSES)