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gaussian_2D.h

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#ifndef __GAUSSIAN_2D__
#define __GAUSSIAN_2D__

#include <math.h>

#include "base_2D.h"

namespace Function_2D{

/*
  ############
  # Gaussian #
  ############
*/

  
  class Gaussian:public Base_2D{

  public:
    inline Gaussian::Gaussian(const real_type in_offset_x = 0,
                              const real_type in_offset_y = 0,
                              const real_type in_scale_x = 1,
                              const real_type in_scale_y = 1,
                              const real_type in_rotation_angle = 0,
                              const real_type out_offset = 0,
                              const real_type out_scale = 1);

    static inline real_type base_value(const real_type x,
                                       const real_type y);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;


  
  };




  
/*
  #######################
  # Normalized gaussian #
  #######################
*/


  class Normalized_gaussian:public Filter_interface_2D{

  public:
    inline Normalized_gaussian(const real_type center_x = 0,
                               const real_type center_y = 0,
                               const real_type sigma_x = 1,
                               const real_type sigma_y = 1,
                               const real_type orientation_angle = 0);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;
  };



/*
  ###########################
  # FFT normalized gaussian #
  ###########################
*/


  class FFT_normalized_gaussian:public Filter_interface_2D{

  public:
    inline FFT_normalized_gaussian(const real_type center_x = 0,
                                   const real_type center_y = 0,
                                   const real_type sigma_x = 1,
                                   const real_type sigma_y = 1,
                                   const real_type orientation_angle = 0);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;
  };



  
/*
  #########################
  # Gaussian x-derivative #
  #########################
*/


  class Gaussian_x_derivative:public Base_2D{

  public:
    inline Gaussian_x_derivative::
    Gaussian_x_derivative(const real_type in_offset_x = 0,
                          const real_type in_offset_y = 0,
                          const real_type in_scale_x = 1,
                          const real_type in_scale_y = 1,
                          const real_type in_rotation_angle = 0,
                          const real_type out_offset = 0,
                          const real_type out_scale = 1);

    static inline real_type base_value(const real_type x,
                                       const real_type y);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;


  
  };


  
/*
  ####################################
  # Normalized gaussian x-derivative #
  ####################################
*/


  class Normalized_gaussian_x_derivative:public Filter_interface_2D{

  public:
    inline Normalized_gaussian_x_derivative(const real_type center_x = 0,
                                            const real_type center_y = 0,
                                            const real_type sigma_x = 1,
                                            const real_type sigma_y = 1,
                                            const real_type orientation_angle = 0);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;
  };





  
/*
  #########################
  # Gaussian y-derivative #
  #########################
*/


  class Gaussian_y_derivative:public Base_2D{

  public:
    inline Gaussian_y_derivative::
    Gaussian_y_derivative(const real_type in_offset_x = 0,
                          const real_type in_offset_y = 0,
                          const real_type in_scale_x = 1,
                          const real_type in_scale_y = 1,
                          const real_type in_rotation_angle = 0,
                          const real_type out_offset = 0,
                          const real_type out_scale = 1);

    static inline real_type base_value(const real_type x,
                                       const real_type y);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;


  
  };


  
/*
  ####################################
  # Normalized gaussian y-derivative #
  ####################################
*/


  class Normalized_gaussian_y_derivative:public Filter_interface_2D{

  public:
    inline Normalized_gaussian_y_derivative(const real_type center_x = 0,
                                            const real_type center_y = 0,
                                            const real_type sigma_x = 1,
                                            const real_type sigma_y = 1,
                                            const real_type orientation_angle=0);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;
  };



  
/*
  #############################
  # Gaussian x-2nd-derivative #
  #############################
*/


  class Gaussian_x_2nd_derivative:public Base_2D{

  public:
    inline Gaussian_x_2nd_derivative::
    Gaussian_x_2nd_derivative(const real_type in_offset_x = 0,
                              const real_type in_offset_y = 0,
                              const real_type in_scale_x = 1,
                              const real_type in_scale_y = 1,
                              const real_type in_rotation_angle = 0,
                              const real_type out_offset = 0,
                              const real_type out_scale = 1);
    
    static inline real_type base_value(const real_type x,
                                       const real_type y);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;


  
  };


  
/*
  ########################################
  # Normalized gaussian x-2nd_derivative #
  ########################################
*/


  class Normalized_gaussian_x_2nd_derivative:public Filter_interface_2D{

  public:
    inline Normalized_gaussian_x_2nd_derivative(const real_type center_x = 0,
                                                const real_type center_y = 0,
                                                const real_type sigma_x = 1,
                                                const real_type sigma_y = 1,
                                                const real_type orientation_angle = 0);
    
  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;
  };







  

  class Gaussian_step:public Base_2D{

  public:
    inline Gaussian_step::Gaussian_step(const real_type in_offset_x = 0,
                                        const real_type in_offset_y = 0,
                                        const real_type in_scale_x = 1,
                                        const real_type in_scale_y = 1,
                                        const real_type in_rotation_angle = 0,
                                        const real_type out_offset = 0,
                                        const real_type out_scale = 1);

    static inline real_type base_value(const real_type x,
                                       const real_type y);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;


  
  };




  
/*
  ############################
  # Normalized gaussian step #
  ############################
*/


  class Normalized_gaussian_step:public Filter_interface_2D{

  public:
    inline Normalized_gaussian_step(const real_type center_x = 0,
                                    const real_type center_y = 0,
                                    const real_type sigma_x = 1,
                                    const real_type sigma_y = 1,
                                    const real_type orientation_angle = 0);

  protected:
    virtual inline real_type base_value_proxy(const real_type x,
                                              const real_type y) const;
  };


  

/*
  ###########################################################
  ###########################################################
  ###########################################################
  ##############                               ##############
  ##############  I M P L E M E N T A T I O N  ##############
  ##############                               ##############
  ###########################################################
  ###########################################################
  ###########################################################
*/




/*
  ############
  # Gaussian #
  ############
*/
  
  Gaussian::Gaussian(const real_type in_offset_x,
                     const real_type in_offset_y,
                     const real_type in_scale_x,
                     const real_type in_scale_y,
                     const real_type in_rotation_angle,
                     const real_type out_offset,
                     const real_type out_scale):
    Base_2D(in_offset_x,in_offset_y,
            in_scale_x,in_scale_y,
            in_rotation_angle,
            out_offset,out_scale){}

  Gaussian::real_type Gaussian::base_value_proxy(const real_type x,
                                                 const real_type y) const{

    return Gaussian::base_value(x,y);
  }

  Gaussian::real_type Gaussian::base_value(const real_type x,
                                           const real_type y){
    return exp(-(x*x + y*y));
  }



  
/*
  #######################
  # Normalized gaussian #
  #######################
*/

  Normalized_gaussian::
  Normalized_gaussian(const real_type center_x,
                      const real_type center_y,
                      const real_type sigma_x,
                      const real_type sigma_y,
                      const real_type orientation_angle):
    Filter_interface_2D(center_x,center_y,
                        sigma_x,sigma_y,
                        M_SQRT1_2,M_SQRT1_2,
                        orientation_angle,
                        0.5/M_PI){}

  Normalized_gaussian::real_type
  Normalized_gaussian::base_value_proxy(const real_type x,
                                        const real_type y) const{

    return Gaussian::base_value(x,y);
  }



/*
  ###########################
  # FFT normalized gaussian #
  ###########################
*/

  FFT_normalized_gaussian::
  FFT_normalized_gaussian(const real_type center_x,
                          const real_type center_y,
                          const real_type sigma_x,
                          const real_type sigma_y,
                          const real_type orientation_angle):
    Filter_interface_2D(center_x,center_y,
                        sigma_x,sigma_y,
                        M_SQRT2*M_PI,M_SQRT2*M_PI,
                        orientation_angle,
                        1){
    output_scale = 1;
  }

  FFT_normalized_gaussian::real_type
  FFT_normalized_gaussian::base_value_proxy(const real_type x,
                                            const real_type y) const{
    
    FFT_normalized_gaussian* proxy = const_cast<FFT_normalized_gaussian*>(this);
    proxy->output_scale = 1;
    return Gaussian::base_value(x,y);
  }



  /*
    #########################
    # Gaussian x-derivative #
    #########################
  */

  Gaussian_x_derivative::Gaussian_x_derivative(const real_type in_offset_x,
                                               const real_type in_offset_y,
                                               const real_type in_scale_x,
                                               const real_type in_scale_y,
                                               const real_type in_rotation_angle,
                                               const real_type out_offset,
                                               const real_type out_scale):
    Base_2D(in_offset_x,in_offset_y,
            in_scale_x,in_scale_y,
            in_rotation_angle,
            out_offset,out_scale){}

  Gaussian_x_derivative::real_type
  Gaussian_x_derivative::base_value_proxy(const real_type x,
                                          const real_type y) const{
    
    return Gaussian_x_derivative::base_value(x,y);
  }

  Gaussian_x_derivative::real_type
  Gaussian_x_derivative::base_value(const real_type x,
                                    const real_type y){
    
    return -2*x*exp(-(x*x + y*y));
  }


  

  /*
    ####################################
    # Normalized gaussian x-derivative #
    ####################################
  */
  
  Normalized_gaussian_x_derivative::
  Normalized_gaussian_x_derivative(const real_type center_x,
                                   const real_type center_y,
                                   const real_type sigma_x,
                                   const real_type sigma_y,
                                   const real_type orientation_angle):
    Filter_interface_2D(center_x,center_y,
                        sigma_x,sigma_y,
                        M_SQRT1_2,M_SQRT1_2,
                        orientation_angle,
                        0.5/M_PI){}

  Normalized_gaussian_x_derivative::real_type
  Normalized_gaussian_x_derivative::base_value_proxy(const real_type x,
                                                     const real_type y) const{

    return Gaussian_x_derivative::base_value(x,y)*input_scale_x;
  }

  

  /*
    #########################
    # Gaussian y-derivative #
    #########################
  */

  Gaussian_y_derivative::Gaussian_y_derivative(const real_type in_offset_x,
                                               const real_type in_offset_y,
                                               const real_type in_scale_x,
                                               const real_type in_scale_y,
                                               const real_type in_rotation_angle,
                                               const real_type out_offset,
                                               const real_type out_scale):
    Base_2D(in_offset_x,in_offset_y,
            in_scale_x,in_scale_y,
            in_rotation_angle,
            out_offset,out_scale){}

  Gaussian_y_derivative::real_type
  Gaussian_y_derivative::base_value_proxy(const real_type x,
                                          const real_type y) const{
    
    return Gaussian_y_derivative::base_value(x,y);
  }

  Gaussian_y_derivative::real_type
  Gaussian_y_derivative::base_value(const real_type x,
                                    const real_type y){
    
    return -2*y*exp(-(x*x + y*y));
  }


  

  /*
    ####################################
    # Normalized gaussian y-derivative #
    ####################################
  */
  
  Normalized_gaussian_y_derivative::
  Normalized_gaussian_y_derivative(const real_type center_x,
                                   const real_type center_y,
                                   const real_type sigma_x,
                                   const real_type sigma_y,
                                   const real_type orientation_angle):
    Filter_interface_2D(center_x,center_y,
                        sigma_x,sigma_y,
                        M_SQRT1_2,M_SQRT1_2,
                        orientation_angle,
                        0.5/M_PI){}

  Normalized_gaussian_y_derivative::real_type
  Normalized_gaussian_y_derivative::base_value_proxy(const real_type x,
                                                     const real_type y) const{
    
    return Gaussian_y_derivative::base_value(x,y)*input_scale_x;
  }



  /*
    #############################
    # Gaussian x-2nd_derivative #
    #############################
  */

  Gaussian_x_2nd_derivative::Gaussian_x_2nd_derivative(const real_type in_offset_x,
                                               const real_type in_offset_y,
                                               const real_type in_scale_x,
                                               const real_type in_scale_y,
                                               const real_type in_rotation_angle,
                                               const real_type out_offset,
                                               const real_type out_scale):
    Base_2D(in_offset_x,in_offset_y,
            in_scale_x,in_scale_y,
            in_rotation_angle,
            out_offset,out_scale){}

  Gaussian_x_2nd_derivative::real_type
  Gaussian_x_2nd_derivative::base_value_proxy(const real_type x,
                                          const real_type y) const{
    
    return Gaussian_x_2nd_derivative::base_value(x,y);
  }

  Gaussian_x_2nd_derivative::real_type
  Gaussian_x_2nd_derivative::base_value(const real_type x,
                                        const real_type y){
    
    return (4*x*x-2)*exp(-(x*x + y*y));
  }


  
  

  /*
    ########################################
    # Normalized gaussian x-2nd_derivative #
    ########################################
  */
  
  Normalized_gaussian_x_2nd_derivative::
  Normalized_gaussian_x_2nd_derivative(const real_type center_x,
                                       const real_type center_y,
                                       const real_type sigma_x,
                                       const real_type sigma_y,
                                       const real_type orientation_angle):
    Filter_interface_2D(center_x,center_y,
                        sigma_x,sigma_y,
                        M_SQRT1_2,M_SQRT1_2,
                        orientation_angle,
                        0.5/M_PI){}

  Normalized_gaussian_x_2nd_derivative::real_type
  Normalized_gaussian_x_2nd_derivative::base_value_proxy(const real_type x,
                                                         const real_type y) const{
    
    return Gaussian_x_2nd_derivative::base_value(x,y)*input_scale_x*input_scale_x;
  }

  
  

  /*
    #################
    # Gaussian step #
    #################
  */
  
  Gaussian_step::Gaussian_step(const real_type in_offset_x,
                               const real_type in_offset_y,
                               const real_type in_scale_x,
                               const real_type in_scale_y,
                               const real_type in_rotation_angle,
                               const real_type out_offset,
                               const real_type out_scale):
    Base_2D(in_offset_x,in_offset_y,
            in_scale_x,in_scale_y,
            in_rotation_angle,
            out_offset,out_scale){}

  Gaussian_step::real_type
  Gaussian_step::base_value_proxy(const real_type x,
                                  const real_type y) const{
    
    return Gaussian_step::base_value(x,y);
  }

  Gaussian_step::real_type Gaussian_step::base_value(const real_type x,
                                                     const real_type y){

    const real_type s = (x==0) ? 0 : ((x>0) ? 1 : -1);
    return s*exp(-(x*x + y*y));
  }



  
/*
  ############################
  # Normalized gaussian step #
  ############################
*/

  Normalized_gaussian_step::
  Normalized_gaussian_step(const real_type center_x,
                           const real_type center_y,
                           const real_type sigma_x,
                           const real_type sigma_y,
                           const real_type orientation_angle):
    Filter_interface_2D(center_x,center_y,
                        sigma_x,sigma_y,
                        M_SQRT1_2,M_SQRT1_2,
                        orientation_angle,
                        0.5/M_PI){}

  Normalized_gaussian_step::real_type
  Normalized_gaussian_step::base_value_proxy(const real_type x,
                                             const real_type y) const{
    
    return Gaussian_step::base_value(x,y);
  }


}
  
#endif

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