text: /*=========================================================================
   *
   *  Copyright NumFOCUS
   *
   *  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.
   *
   *=========================================================================*/
  #ifndef itkBSplineTransform_h
  #define itkBSplineTransform_h
  
  #include "itkBSplineBaseTransform.h"
  
  namespace itk
  {
  /** \class BSplineTransform
   * \brief Deformable transform using a BSpline representation
   *
   * This class encapsulates a deformable transform of points from one
   * N-dimensional space to another N-dimensional space.
   * The deformation field is modelled using B-splines.
   * A deformation is defined on a sparse regular grid of control points
   * \f$ \vec{\lambda}_j \f$ and is varied by defining a deformation
   * \f$ \vec{g}(\vec{\lambda}_j) \f$ of each control point.
   * The deformation \f$ D(\vec{x}) \f$ at any point \f$ \vec{x} \f$
   * is obtained by using a B-spline interpolation kernel.
   *
   * The deformation field grid is defined by a user specified transform
   * domain (origin, physical dimensions, direction) and B-spline mesh size
   * where the mesh size is the number of polynomial patches comprising the
   * finite domain of support.  The relationship between the mesh size (
   * number of polynomial pieces) and the number of control points in any
   * given dimension is
   *
   * mesh size = number of control points - spline order
   *
   * Each grid/control point has associated with it
   * N deformation coefficients \f$ \vec{\delta}_j \f$, representing the N
   * directional components of the deformation. Deformation outside the grid
   * plus support region for the BSpline interpolation is assumed to be zero.
   *
   * The parameters for this transform is N x N-D grid of spline coefficients.
   * The user specifies the parameters as one flat array: each N-D grid
   * is represented by an array in the same way an N-D image is represented
   * in the buffer; the N arrays are then concatenated together to form
   * a single array.
   *
   * The following illustrates the typical usage of this class:
   * \code
     using TransformType = BSplineTransform<double,2,3>;
     TransformType::Pointer transform = TransformType::New();
  
     transform->SetTransformDomainOrigin( origin );
     transform->SetTransformDomainPhysicalDimensions( physicalDimensions );
     transform->SetTransformDomainDirection( direction );
     transform->SetTransformDomainMeshSize( meshSize );
  
     // NB: The region must be set first before setting the parameters
  
     TransformType::ParametersType parameters( transform->GetNumberOfParameters() );
  
     // Fill the parameters with values
  
     transform->SetParameters( parameters )
  
     outputPoint = transform->TransformPoint( inputPoint );
  
     \endcode
   *
   * An alternative way to set the B-spline coefficients is via array of
   * images. The fixed parameters of the transform are taken
   * directly from the first image. It is assumed that the subsequent images
   * are the same buffered region. The following illustrates the API:
   * \code
  
     TransformType::ImageConstPointer images[2];
  
     // Fill the images up with values
  
     transform->SetCoefficientImages( images );
     outputPoint = transform->TransformPoint( inputPoint );
  
     \endcode
   *
   * \warning Use either the SetParameters() or SetCoefficientImages()
   * API. Mixing the two modes may results in unexpected results.
   *
   * The class is templated coordinate representation type (float or double),
   * the space dimension and the spline order.
   *
   * \ingroup ITKTransform
   */
  template <typename TParametersValueType = double, unsigned int NDimensions = 3, unsigned int VSplineOrder = 3>
  class ITK_TEMPLATE_EXPORT BSplineTransform
    : public BSplineBaseTransform<TParametersValueType, NDimensions, VSplineOrder>
  {
  public:
    ITK_DISALLOW_COPY_AND_MOVE(BSplineTransform);
  
    /** Standard class type aliases. */
    using Self = BSplineTransform;
    using Superclass = BSplineBaseTransform<TParametersValueType, NDimensions, VSplineOrder>;
    using Pointer = SmartPointer<Self>;
    using ConstPointer = SmartPointer<const Self>;
  
    /** New macro for creation of through the object factory. */
    itkNewMacro(Self);
  
    /** Run-time type information (and related methods). */
    itkTypeMacro(BSplineTransform, BSplineBaseTransform);
  
    /** Dimension of the domain space. */
    static constexpr unsigned int SpaceDimension = NDimensions;
  
    /** The BSpline order. */
    static constexpr unsigned int SplineOrder = VSplineOrder;
  
    /** Standard scalar type for this class. */
    using ScalarType = typename Superclass::ScalarType;
  
    /** Standard parameters container. */
    using ParametersType = typename Superclass::ParametersType;
    using ParametersValueType = typename Superclass::ParametersValueType;
    using FixedParametersType = typename Superclass::FixedParametersType;
    using FixedParametersValueType = typename Superclass::FixedParametersValueType;
  
    /** Standard Jacobian container. */
    using JacobianType = typename Superclass::JacobianType;
    using JacobianPositionType = typename Superclass::JacobianPositionType;
    using InverseJacobianPositionType = typename Superclass::InverseJacobianPositionType;
  
    /** The number of parameters defining this transform. */
    using NumberOfParametersType = typename Superclass::NumberOfParametersType;
  
    /** Standard vector type for this class. */
    using InputVectorType = typename Superclass::InputVectorType;
    using OutputVectorType = typename Superclass::OutputVectorType;
  
    /** Standard covariant vector type for this class. */
    using InputCovariantVectorType = typename Superclass::InputCovariantVectorType;
    using OutputCovariantVectorType = typename Superclass::OutputCovariantVectorType;
  
    /** Standard vnl_vector type for this class. */
    using InputVnlVectorType = typename Superclass::InputVnlVectorType;
    using OutputVnlVectorType = typename Superclass::OutputVnlVectorType;
  
    /** Standard coordinate point type for this class. */
    using InputPointType = typename Superclass::InputPointType;
    using OutputPointType = typename Superclass::OutputPointType;
  
  
    std::string
    GetTransformTypeAsString() const override;
  
    /** This method sets the fixed parameters of the transform.
     * For a BSpline deformation transform, the fixed parameters are the
     * following: grid size, grid origin, grid spacing, and grid direction.
     * However, all of these are set via the much more intuitive
     * SetTransformDomainXXX() functions
     *
     * The fixed parameters are the three times the size of the templated
     * dimensions.  This function has the effect of make the following non-
     * existing functional calls:
     *   transform->SetGridSpacing( spacing );
     *   transform->SetGridOrigin( origin );
     *   transform->SetGridDirection( direction );
     *   transform->SetGridRegion( bsplineRegion );
     *
     * With recent updates to this transform, however, all these parameters
     * are set indirectly by setting the transform domain parameters unless
     * the user sets them with SetFixedParameters().
     *
     * This function was added to allow the transform to work with the
     * itkTransformReader/Writer I/O filters.
     *
     */
    void
    SetFixedParameters(const FixedParametersType & parameters) override;
  
    /** Parameters as SpaceDimension number of images. */
    using ImageType = typename Superclass::ImageType;
    using ImagePointer = typename Superclass::ImagePointer;
    using CoefficientImageArray = typename Superclass::CoefficientImageArray;
  
    /** Set the array of coefficient images.
     *
     * This is an alternative API for setting the BSpline coefficients
     * as an array of SpaceDimension images. The fixed parameters are
     * taken from the first image. It is assumed that
     * the buffered region of all the subsequent images are the same
     * as the first image. Note that no error checking is done.
     *
     * Warning: use either the SetParameters() or SetCoefficientImages()
     * API. Mixing the two modes may results in unexpected results.
     */
    void
    SetCoefficientImages(const CoefficientImageArray & images) override;
  
    /** Typedefs for specifying the extent of the grid. */
    using RegionType = typename Superclass::RegionType;
  
    using IndexType = typename Superclass::IndexType;
    using SizeType = typename Superclass::SizeType;
    using SpacingType = typename Superclass::SpacingType;
    using DirectionType = typename Superclass::DirectionType;
    using OriginType = typename Superclass::OriginType;
  
    /** Interpolation weights function type. */
    using WeightsFunctionType = typename Superclass::WeightsFunctionType;
  
    using WeightsType = typename Superclass::WeightsType;
    using ContinuousIndexType = typename Superclass::ContinuousIndexType;
  
    /** Parameter index array type. */
    using ParameterIndexArrayType = typename Superclass::ParameterIndexArrayType;
  
    /**
     * Transform points by a BSpline deformable transformation.
     * On return, weights contains the interpolation weights used to compute the
     * deformation and indices of the x (zeroth) dimension coefficient parameters
     * in the support region used to compute the deformation.
     * Parameter indices for the i-th dimension can be obtained by adding
     * ( i * this->GetNumberOfParametersPerDimension() ) to the indices array.
     */
    using Superclass::TransformPoint;
    void
    TransformPoint(const InputPointType &    inputPoint,
                   OutputPointType &         outputPoint,
                   WeightsType &             weights,
                   ParameterIndexArrayType & indices,
                   bool &                    inside) const override;
  
    /** Compute the Jacobian in one position. */
    void
    ComputeJacobianWithRespectToParameters(const InputPointType &, JacobianType &) const override;
  
    /** Return the number of parameters that completely define the Transfom. */
    NumberOfParametersType
    GetNumberOfParameters() const override;
  
    /** Return the number of parameters per dimension. */
    NumberOfParametersType
    GetNumberOfParametersPerDimension() const override;
  
    using PhysicalDimensionsType = typename Superclass::SpacingType;
    using PixelType = typename Superclass::PixelType;
  
    using MeshSizeType = typename Superclass::MeshSizeType;
  
    /** Function to specify the transform domain origin. */
    virtual void
    SetTransformDomainOrigin(const OriginType &);
  
    /** Function to retrieve the transform domain origin. */
    virtual OriginType
    GetTransformDomainOrigin() const;
  
    /** Function to specify the transform domain physical dimensions. */
    virtual void
    SetTransformDomainPhysicalDimensions(const PhysicalDimensionsType &);
  
    /** Function to retrieve the transform domain physical dimensions. */
    virtual PhysicalDimensionsType
    GetTransformDomainPhysicalDimensions() const;
  
    /** Function to specify the transform domain direction. */
    virtual void
    SetTransformDomainDirection(const DirectionType &);
  
    /** Function to retrieve the transform domain direction. */
    virtual DirectionType
    GetTransformDomainDirection() const;
  
    /** Function to specify the transform domain mesh size. */
    virtual void
    SetTransformDomainMeshSize(const MeshSizeType &);
  
    /** Function to retrieve the transform domain mesh size. */
    virtual MeshSizeType
    GetTransformDomainMeshSize() const;
  
  protected:
    /** Print contents of an BSplineTransform. */
    void
    PrintSelf(std::ostream & os, Indent indent) const override;
  
    BSplineTransform();
    ~BSplineTransform() override = default;
  
  private:
    /** Construct control point grid size from transform domain information in the fixed parameters. */
    void
    SetCoefficientImageInformationFromFixedParameters() override;
  
    /** Methods have empty implementations */
    void
    SetFixedParametersGridSizeFromTransformDomainInformation() const override{};
    void
    SetFixedParametersGridOriginFromTransformDomainInformation() const override{};
    void
    SetFixedParametersGridSpacingFromTransformDomainInformation() const override
    {}
    void
    SetFixedParametersGridDirectionFromTransformDomainInformation() const override{};
  
    /** Check if a continuous index is inside the valid region. */
    bool
    InsideValidRegion(ContinuousIndexType &) const override;
  
    void
    SetFixedParametersFromCoefficientImageInformation();
  
    void
    SetFixedParametersFromTransformDomainInformation(const OriginType &             meshOrigin,
                                                     const PhysicalDimensionsType & meshPhysical,
                                                     const DirectionType &          meshDirection,
                                                     const MeshSizeType &           meshSize);
  
  }; // class BSplineTransform
  } // namespace itk
  
  #ifndef ITK_MANUAL_INSTANTIATION
  #  include "itkBSplineTransform.hxx"
  #endif
  
  #endif /* itkBSplineTransform_h */
  