/*=========================================================================
 *
 *  Copyright UMC Utrecht and contributors
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *        http://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkReducedDimensionBSplineInterpolateImageFunction.txx,v $
  Date:      $Date: 2008-11-10 16:55:00 $
  Version:   $Revision: 1.21 $

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

  Portions of this code are covered under the VTK copyright.
  See VTKCopyright.txt or http://www.kitware.com/VTKCopyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef itkReducedDimensionBSplineInterpolateImageFunction_hxx
#define itkReducedDimensionBSplineInterpolateImageFunction_hxx

#include "itkReducedDimensionBSplineInterpolateImageFunction.h"
#include "itkImageRegionConstIteratorWithIndex.h"
#include "itkImageRegionIterator.h"

#include "itkVector.h"
#include "itkMath.h"
#include "itkMatrix.h"
#include <vnl/vnl_matrix_ref.h>

namespace itk
{

/**
 * Constructor
 */
template <typename TImageType, typename TCoordinate, typename TCoefficientType>
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::
  ReducedDimensionBSplineInterpolateImageFunction()
{
  m_SplineOrder = 0;
  unsigned int SplineOrder = 1;
  m_CoefficientFilter = CoefficientFilter::New();
  // ***TODO: Should we store coefficients in a variable or retrieve from filter?
  m_Coefficients = CoefficientImageType::New();
  this->SetSplineOrder(SplineOrder);
  this->m_UseImageDirection = true;
}


/**
 * Standard "PrintSelf" method
 */
template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::PrintSelf(
  std::ostream & os,
  Indent         indent) const
{
  Superclass::PrintSelf(os, indent);
  os << indent << "Spline Order: " << m_SplineOrder << std::endl;
  os << indent << "UseImageDirection = " << (this->m_UseImageDirection ? "On" : "Off") << std::endl;
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::SetInputImage(
  const TImageType * inputData)
{
  if (inputData)
  {
    m_CoefficientFilter->SetInput(inputData);

    // the Coefficient Filter requires that the spline order and the input data be set.
    // TODO:  We need to ensure that this is only run once and only after both input and
    //        spline order have been set. Should we force an update after the
    //        splineOrder has been set also?

    m_CoefficientFilter->Update();
    m_Coefficients = m_CoefficientFilter->GetOutput();

    // Call the Superclass implementation after, in case the filter
    // pulls in  more of the input image
    Superclass::SetInputImage(inputData);

    m_DataLength = inputData->GetBufferedRegion().GetSize();
  }
  else
  {
    m_Coefficients = nullptr;
  }
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::SetSplineOrder(
  unsigned int SplineOrder)
{
  if (SplineOrder == m_SplineOrder)
  {
    return;
  }

  m_SplineOrder = SplineOrder;
  m_CoefficientFilter->SetSplineOrder(SplineOrder);
  // Set spline order of coefficient filter for last dimension to zero,
  // to use nearest neighbour interpolation in the last dimension.
  m_CoefficientFilter->SetSplineOrder(ImageDimension - 1, 0);

  // this->SetPoles();
  this->GeneratePointsToIndex();
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
auto
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::EvaluateAtContinuousIndex(
  const ContinuousIndexType & x) const -> OutputType
{
  /** Allocate memory on the stack: */
  const unsigned int maxSplineOrder = 5;
  const unsigned int maxMatrixSize = (ImageDimension - 1) * (maxSplineOrder + 1);
  long               evaluateIndexData[maxMatrixSize];
  double             weightsData[maxMatrixSize];

  vnl_matrix_ref<long> EvaluateIndex(ImageDimension - 1, (m_SplineOrder + 1), evaluateIndexData);

  // compute the interpolation indexes
  this->DetermineRegionOfSupport(EvaluateIndex, x, m_SplineOrder);

  // Determine weights
  vnl_matrix_ref<double> weights(ImageDimension - 1, (m_SplineOrder + 1), weightsData);

  SetInterpolationWeights(x, EvaluateIndex, weights, m_SplineOrder);

  // Modify EvaluateIndex at the boundaries using mirror boundary conditions
  this->ApplyMirrorBoundaryConditions(EvaluateIndex, m_SplineOrder);

  // perform interpolation
  double    interpolated = 0.0;
  IndexType coefficientIndex;
  coefficientIndex[ImageDimension - 1] = vnl_math::rnd(x[ImageDimension - 1]);

  // Step through eachpoint in the N-dimensional interpolation cube.
  for (const auto & pointIndex : m_PointsToIndex)
  {
    // translate each step into the N-dimensional index.
    //      IndexType pointIndex = PointToIndex( p );

    double w = 1.0;
    for (unsigned int n = 0; n < ImageDimension - 1; ++n)
    {
      w *= weights[n][pointIndex[n]];
      coefficientIndex[n] = EvaluateIndex[n][pointIndex[n]]; // Build up ND index for coefficients.
    }
    // Convert our step p to the appropriate point in ND space in the
    // m_Coefficients cube.
    interpolated += w * m_Coefficients->GetPixel(coefficientIndex);
  }
  return (interpolated);
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
auto
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::
  EvaluateDerivativeAtContinuousIndex(const ContinuousIndexType & x) const -> CovariantVectorType
{
  /** Allocate memory on the stack: */
  const unsigned int maxSplineOrder = 5;
  const unsigned int maxMatrixSize = (ImageDimension - 1) * (maxSplineOrder + 1);
  long               evaluateIndexData[maxMatrixSize];
  double             weightsData[maxMatrixSize];
  double             weightsDerivativeData[maxMatrixSize];

  vnl_matrix_ref<long> EvaluateIndex(ImageDimension - 1, (m_SplineOrder + 1), evaluateIndexData);

  // compute the interpolation indexes
  // TODO: Do we need to revisit region of support for the derivatives?
  this->DetermineRegionOfSupport(EvaluateIndex, x, m_SplineOrder);

  // Determine weights
  vnl_matrix_ref<double> weights(ImageDimension - 1, (m_SplineOrder + 1), weightsData);

  SetInterpolationWeights(x, EvaluateIndex, weights, m_SplineOrder);

  vnl_matrix_ref<double> weightsDerivative(ImageDimension - 1, (m_SplineOrder + 1), weightsDerivativeData);
  SetDerivativeWeights(x, EvaluateIndex, weightsDerivative, (m_SplineOrder));

  // Modify EvaluateIndex at the boundaries using mirror boundary conditions
  this->ApplyMirrorBoundaryConditions(EvaluateIndex, m_SplineOrder);

  const InputImageType * const                 inputImage = this->GetInputImage();
  const typename InputImageType::SpacingType & spacing = inputImage->GetSpacing();

  // Calculate derivative
  CovariantVectorType derivativeValue{};
  IndexType           coefficientIndex;
  coefficientIndex[ImageDimension - 1] = vnl_math::rnd(x[ImageDimension - 1]);
  for (unsigned int n = 0; n < ImageDimension - 1; ++n)
  {
    for (const auto & pointIndex : m_PointsToIndex)
    {
      double tempValue = 1.0;
      for (unsigned int n1 = 0; n1 < ImageDimension - 1; ++n1)
      {
        coefficientIndex[n1] = EvaluateIndex[n1][pointIndex[n1]];

        if (n1 == n)
        {
          // w *= weights[ n ][ m_PointsToIndex[ p ][ n ] ];
          tempValue *= weightsDerivative[n1][pointIndex[n1]];
        }
        else
        {
          tempValue *= weights[n1][pointIndex[n1]];
        }
      }
      derivativeValue[n] += m_Coefficients->GetPixel(coefficientIndex) * tempValue;
    }
    derivativeValue[n] /= spacing[n]; // take spacing into account
  }

  if (this->m_UseImageDirection)
  {
    return inputImage->TransformLocalVectorToPhysicalVector(derivativeValue);
  }

  return derivativeValue;
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::SetInterpolationWeights(
  const ContinuousIndexType & x,
  const vnl_matrix<long> &    EvaluateIndex,
  vnl_matrix<double> &        weights,
  unsigned int                splineOrder) const
{
  // For speed improvements we could make each case a separate function and use
  // function pointers to reference the correct weight order.
  // Left as is for now for readability.
  double w, w2, w4, t, t0, t1;

  switch (splineOrder)
  {
    case 3:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        w = x[n] - (double)EvaluateIndex[n][1];
        weights[n][3] = (1.0 / 6.0) * w * w * w;
        weights[n][0] = (1.0 / 6.0) + 0.5 * w * (w - 1.0) - weights[n][3];
        weights[n][2] = w + weights[n][0] - 2.0 * weights[n][3];
        weights[n][1] = 1.0 - weights[n][0] - weights[n][2] - weights[n][3];
      }
      break;
    case 0:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        weights[n][0] = 1; // implements nearest neighbor
      }
      break;
    case 1:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        w = x[n] - (double)EvaluateIndex[n][0];
        weights[n][1] = w;
        weights[n][0] = 1.0 - w;
      }
      break;
    case 2:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        /* x */
        w = x[n] - (double)EvaluateIndex[n][1];
        weights[n][1] = 0.75 - w * w;
        weights[n][2] = 0.5 * (w - weights[n][1] + 1.0);
        weights[n][0] = 1.0 - weights[n][1] - weights[n][2];
      }
      break;
    case 4:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        /* x */
        w = x[n] - (double)EvaluateIndex[n][2];
        w2 = w * w;
        t = (1.0 / 6.0) * w2;
        weights[n][0] = 0.5 - w;
        weights[n][0] *= weights[n][0];
        weights[n][0] *= (1.0 / 24.0) * weights[n][0];
        t0 = w * (t - 11.0 / 24.0);
        t1 = 19.0 / 96.0 + w2 * (0.25 - t);
        weights[n][1] = t1 + t0;
        weights[n][3] = t1 - t0;
        weights[n][4] = weights[n][0] + t0 + 0.5 * w;
        weights[n][2] = 1.0 - weights[n][0] - weights[n][1] - weights[n][3] - weights[n][4];
      }
      break;
    case 5:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        /* x */
        w = x[n] - (double)EvaluateIndex[n][2];
        w2 = w * w;
        weights[n][5] = (1.0 / 120.0) * w * w2 * w2;
        w2 -= w;
        w4 = w2 * w2;
        w -= 0.5;
        t = w2 * (w2 - 3.0);
        weights[n][0] = (1.0 / 24.0) * (1.0 / 5.0 + w2 + w4) - weights[n][5];
        t0 = (1.0 / 24.0) * (w2 * (w2 - 5.0) + 46.0 / 5.0);
        t1 = (-1.0 / 12.0) * w * (t + 4.0);
        weights[n][2] = t0 + t1;
        weights[n][3] = t0 - t1;
        t0 = (1.0 / 16.0) * (9.0 / 5.0 - t);
        t1 = (1.0 / 24.0) * w * (w4 - w2 - 5.0);
        weights[n][1] = t0 + t1;
        weights[n][4] = t0 - t1;
      }
      break;
    default:
      // SplineOrder not implemented yet.
      ExceptionObject err(__FILE__, __LINE__);
      err.SetLocation(ITK_LOCATION);
      err.SetDescription("SplineOrder must be between 0 and 5. Requested spline order has not been implemented yet.");
      throw err;
      break;
  }
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::SetDerivativeWeights(
  const ContinuousIndexType & x,
  const vnl_matrix<long> &    EvaluateIndex,
  vnl_matrix<double> &        weights,
  unsigned int                splineOrder) const
{
  // For speed improvements we could make each case a separate function and use
  // function pointers to reference the correct weight order.
  // Another possiblity would be to loop inside the case statement (reducing the number
  // of switch statement executions to one per routine call.
  // Left as is for now for readability.
  double w, w1, w2, w3, w4, w5, t, t0, t1, t2;
  int    derivativeSplineOrder = (int)splineOrder - 1;

  switch (derivativeSplineOrder)
  {

    // Calculates B(splineOrder) ( (x + 1/2) - xi) - B(splineOrder -1) ( (x - 1/2) - xi)
    case -1:
      // Why would we want to do this?
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        weights[n][0] = 0.0;
      }
      break;
    case 0:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        weights[n][0] = -1.0;
        weights[n][1] = 1.0;
      }
      break;
    case 1:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        w = x[n] + 0.5 - (double)EvaluateIndex[n][1];
        // w2 = w;
        w1 = 1.0 - w;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w;
        weights[n][2] = w;
      }
      break;
    case 2:

      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        w = x[n] + .5 - (double)EvaluateIndex[n][2];
        w2 = 0.75 - w * w;
        w3 = 0.5 * (w - w2 + 1.0);
        w1 = 1.0 - w2 - w3;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w2;
        weights[n][2] = w2 - w3;
        weights[n][3] = w3;
      }
      break;
    case 3:

      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        w = x[n] + 0.5 - (double)EvaluateIndex[n][2];
        w4 = (1.0 / 6.0) * w * w * w;
        w1 = (1.0 / 6.0) + 0.5 * w * (w - 1.0) - w4;
        w3 = w + w1 - 2.0 * w4;
        w2 = 1.0 - w1 - w3 - w4;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w2;
        weights[n][2] = w2 - w3;
        weights[n][3] = w3 - w4;
        weights[n][4] = w4;
      }
      break;
    case 4:
      for (unsigned int n = 0; n < ImageDimension - 1; ++n)
      {
        w = x[n] + .5 - (double)EvaluateIndex[n][3];
        t2 = w * w;
        t = (1.0 / 6.0) * t2;
        w1 = 0.5 - w;
        w1 *= w1;
        w1 *= (1.0 / 24.0) * w1;
        t0 = w * (t - 11.0 / 24.0);
        t1 = 19.0 / 96.0 + t2 * (0.25 - t);
        w2 = t1 + t0;
        w4 = t1 - t0;
        w5 = w1 + t0 + 0.5 * w;
        w3 = 1.0 - w1 - w2 - w4 - w5;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w2;
        weights[n][2] = w2 - w3;
        weights[n][3] = w3 - w4;
        weights[n][4] = w4 - w5;
        weights[n][5] = w5;
      }
      break;

    default:
      // SplineOrder not implemented yet.
      ExceptionObject err(__FILE__, __LINE__);
      err.SetLocation(ITK_LOCATION);
      err.SetDescription(
        "SplineOrder (for derivatives) must be between 1 and 5. Requested spline order has not been implemented yet.");
      throw err;
      break;
  }
}


// Generates m_PointsToIndex;
template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::GeneratePointsToIndex()
{
  // number of neighborhood points used for interpolation
  const auto maxNumberInterpolationPoints =
    static_cast<unsigned int>(Math::UnsignedPower(m_SplineOrder + 1, ImageDimension - 1));

  // m_PointsToIndex is used to convert a sequential location to an N-dimension
  // index vector.  This is precomputed to save time during the interpolation routine.
  m_PointsToIndex.resize(maxNumberInterpolationPoints);
  for (unsigned int p = 0; p < maxNumberInterpolationPoints; ++p)
  {
    int           pp = p;
    unsigned long indexFactor[ImageDimension - 1];
    indexFactor[0] = 1;
    for (int j = 1; j < static_cast<int>(ImageDimension - 1); ++j)
    {
      indexFactor[j] = indexFactor[j - 1] * (m_SplineOrder + 1);
    }
    for (int j = (static_cast<int>(ImageDimension) - 2); j >= 0; j--)
    {
      m_PointsToIndex[p][j] = pp / indexFactor[j];
      pp = pp % indexFactor[j];
    }
  }
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::DetermineRegionOfSupport(
  vnl_matrix<long> &          evaluateIndex,
  const ContinuousIndexType & x,
  unsigned int                splineOrder) const
{
  long indx;

  // compute the interpolation indexes
  for (unsigned int n = 0; n < ImageDimension - 1; ++n)
  {
    if (splineOrder & 1) // Use this index calculation for odd splineOrder
    {
      indx = (long)std::floor((float)x[n]) - splineOrder / 2;
      for (unsigned int k = 0; k <= splineOrder; ++k)
      {
        evaluateIndex[n][k] = indx++;
      }
    }
    else // Use this index calculation for even splineOrder
    {
      indx = (long)std::floor((float)(x[n] + 0.5)) - splineOrder / 2;
      for (unsigned int k = 0; k <= splineOrder; ++k)
      {
        evaluateIndex[n][k] = indx++;
      }
    }
  }
}


template <typename TImageType, typename TCoordinate, typename TCoefficientType>
void
ReducedDimensionBSplineInterpolateImageFunction<TImageType, TCoordinate, TCoefficientType>::
  ApplyMirrorBoundaryConditions(vnl_matrix<long> & evaluateIndex, unsigned int splineOrder) const
{
  for (unsigned int n = 0; n < ImageDimension - 1; ++n)
  {
    long dataLength2 = 2 * m_DataLength[n] - 2;

    // apply the mirror boundary conditions
    // TODO:  We could implement other boundary options beside mirror
    if (m_DataLength[n] == 1)
    {
      for (unsigned int k = 0; k <= splineOrder; ++k)
      {
        evaluateIndex[n][k] = 0;
      }
    }
    else
    {
      for (unsigned int k = 0; k <= splineOrder; ++k)
      {
        // btw - Think about this couldn't this be replaced with a more elagent modulus method?
        evaluateIndex[n][k] = (evaluateIndex[n][k] < 0L)
                                ? (-evaluateIndex[n][k] - dataLength2 * ((-evaluateIndex[n][k]) / dataLength2))
                                : (evaluateIndex[n][k] - dataLength2 * (evaluateIndex[n][k] / dataLength2));
        if ((long)m_DataLength[n] <= evaluateIndex[n][k])
        {
          evaluateIndex[n][k] = dataLength2 - evaluateIndex[n][k];
        }
      }
    }
  }
}


} // namespace itk

#endif
