/*=========================================================================

  Program:   Diffusion Applications
  Module:    $HeadURL$
  Language:  C++
  Date:      $Date$
  Version:   $Revision$

  Copyright (c) Brigham and Women's Hospital (BWH) All Rights Reserved.

  See License.txt or http://www.slicer.org/copyright/copyright.txt for details.

==========================================================================*/
#ifndef itkDiffusionTensor3DFSAffineTransform_h
#define itkDiffusionTensor3DFSAffineTransform_h

#include "itkDiffusionTensor3DAffineTransform.h"
#include <vnl/vnl_matrix.h>
#include <vnl/algo/vnl_real_eigensystem.h>
#include <vnl/vnl_real.h>

namespace itk
{
/**
 * \class DiffusionTensor3DFSAffineTransform
 *
 *
 * This class implements an affine transformation for diffusion tensors. It implements the
 * Finite Strain method presented in the following paper:
 * D.C. Alexander, Member IEEE, C. Pierpaoli, P.J. Basser and J.C Gee:
 * Spatial Transformations of Diffusion Tensor Magnetic Resonance Images,
 * IEEE Transactions on Medical Imaging, Vol 20, No. 11, November 2001
 *
 * Any nonsingular matrix F can be decomposed into a rigid rotation component R, and a deformation component U, where:
 * F=UR
 *
 * The tensor position is computed by the given affine transformation F but the tensor is transformed by
 * the extracted rotation matrix R where
 * R=(FF_{T}^{-1/2}F
 */
template <class TData>
class DiffusionTensor3DFSAffineTransform : public DiffusionTensor3DAffineTransform<TData>
{
public:
  typedef TData DataType;
  typedef DiffusionTensor3DFSAffineTransform Self;
  typedef DiffusionTensor3DAffineTransform<DataType> Superclass;
  typedef typename Superclass::MatrixTransformType MatrixTransformType;
  typedef typename Superclass::InternalMatrixTransformType InternalMatrixTransformType;
  typedef SmartPointer<Self> Pointer;
  typedef SmartPointer<const Self> ConstPointer;

  itkNewMacro(Self);

  /** Run-time type information (and related methods). */
  itkTypeMacro(DiffusionTensor3DFSAffineTransform, DiffusionTensor3DAffineTransform);

protected:
  void PreCompute() override;

private:
  MatrixTransformType ComputeMatrixSquareRoot(MatrixTransformType matrix);

  MatrixTransformType ComputeRotationMatrixFromTransformationMatrix();
};

} // end namespace itk

#ifndef ITK_MANUAL_INSTANTIATION
# include "itkDiffusionTensor3DFSAffineTransform.hxx"
#endif

#endif
