text: /*
  Copyright (c) 2013, Michael Kazhdan
  All rights reserved.
  
  Redistribution and use in source and binary forms, with or without modification,
  are permitted provided that the following conditions are met:
  
  Redistributions of source code must retain the above copyright notice, this list of
  conditions and the following disclaimer. Redistributions in binary form must reproduce
  the above copyright notice, this list of conditions and the following disclaimer
  in the documentation and/or other materials provided with the distribution. 
  
  Neither the name of the Johns Hopkins University nor the names of its contributors
  may be used to endorse or promote products derived from this software without specific
  prior written permission. 
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO THE IMPLIED WARRANTIES 
  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  TO, PROCUREMENT OF SUBSTITUTE  GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  DAMAGE.
  */
  #ifndef ROTATION_GRID_INCLUDED
  #define ROTATION_GRID_INCLUDED
  
  
  #include "CubeGrid.h"
  #ifndef PI
  #define PI 3.1415926535897932384
  #endif 
  
  
  // This templated class represents a function on the group of rotations, where index (i,j,k) corresponds
  // to the rotation with Euler coefficients:
  //			theta =2PI*j/r
  //			phi   =PI*(2i+1)/(2r)
  //			psi   =2PI*k/r
  // where r is the resolution of the sampling.
  
  template< class Real=float >
  class RotationGrid : public CubeGrid< Real >{
  public:
  	using CubeGrid< Real >::res;
  	using CubeGrid< Real >::values;
  	using CubeGrid< Real >::resize;
  	RotationGrid( void );
  	RotationGrid( int res );
  	~RotationGrid( void );
  
  	// Returns a reference to the indexed  array element
  	Real& operator() (const int& x,const int& y,const int& z);
  	Real operator() (const int& x,const int& y,const int& z) const;
  	// Returns the linear interpolation of the value at the spedified index
  	Real sample( Real x , Real y , Real z ) const;
  
  	// Sets the matrix coordinates of the Euler angle (theta,phi,psi)
  	static void SetCoordinates(const Real& theta,const Real& phi,const Real& psi,Real matrix[3][3]);
  	// Sets the coordinates (theta,phi,psi) associated to the specified rotation matrix
  	static void SetCoordinates(const Real matrix[3][3],Real& theta,Real& phi,Real& psi);
  	// Sets the matrix coordinates of the the rotation about the specified axis with the
  	// specified angle
  	static void SetCoordinates(const Real axis[3],const Real& angle,Real matrix[3][3]);
  
  	// Sets the matrix coordinates of the Euler angle indexed by (i,j,k)
  	void setCoordinates(const int& i,const int& j,const int& k,Real matrix[3][3]) const;
  	void setCoordinates(const Real& i,const Real& j,const Real& k,Real matrix[3][3]) const;
  	// Sets the coordinates (i,j,k) associated to the specified rotation matrix
  	void setCoordinates(const Real matrix[3][3],Real& i,Real& j,Real& k) const;
  
  	// Returns the square of the L2-norm of the array elements
  	Real squareNorm(void) const;
  
  	// Returns the square of the L2-difference between two arrays
  	static Real SquareDifference(const RotationGrid& g1,const RotationGrid& g2);
  
  	// Returns the dot-product of two arrays
  	static Real Dot(const RotationGrid& g1,const RotationGrid& g2);
  };
  #include "RotationGrid.inl"
  #endif // ROTATION_GRID_INCLUDED
  
  