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/*=========================================================================
*
* 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
*
* https://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 itkFourierSeriesPath_h
#define itkFourierSeriesPath_h
#include "itkParametricPath.h"
#include "itkVectorContainer.h"
#include "itkIndex.h"
namespace itk
{
/**
* \class FourierSeriesPath
* \brief Represent a closed path through ND Space by its frequency components
*
* This class is intended to represent closed parametric paths through an image
* which are defined by their Fourier coefficients (frequency components). The
* paths must be closed and defined over the interval [0,1], where the paths'
* values at input 0 and input 1 are identical. The user can control how many
* harmonics (how high of frequency components) are represented by a given
* instantiation of this class. Classic applications of this class include
* smoothing other closed paths (by finding and using only the first n harmonics
* of their frequency components) and interpolating exact derivatives of other
* closed paths by first converting the other paths to FourierSeriesPaths, which
* have an exactly defined algebraic derivative. (As many harmonics as are
* necessary to adequately approximate the original path should be used when
* approximating derivatives.)
*
* \sa OrthogonallyCorrectedParametricPath
* \sa EllipseParametricPath
* \sa PolyLineParametricPath
* \sa ParametricPath
* \sa ChainCodePath
* \sa Path
* \sa ContinuousIndex
* \sa Index
* \sa Offset
* \sa Vector
*
* \ingroup PathObjects
* \ingroup ITKPath
*/
template <unsigned int VDimension>
class ITK_TEMPLATE_EXPORT FourierSeriesPath : public ParametricPath<VDimension>
{
public:
ITK_DISALLOW_COPY_AND_MOVE(FourierSeriesPath);
/** Standard class type aliases. */
using Self = FourierSeriesPath;
using Superclass = ParametricPath<VDimension>;
using Pointer = SmartPointer<Self>;
using ConstPointer = SmartPointer<const Self>;
/** \see LightObject::GetNameOfClass() */
itkOverrideGetNameOfClassMacro(FourierSeriesPath);
/** Input type */
using typename Superclass::InputType;
/** Output type */
using typename Superclass::OutputType;
/** Basic data-structure types used */
using ContinuousIndexType = ContinuousIndex<double, VDimension>;
using IndexType = Index<VDimension>;
using OffsetType = Offset<VDimension>;
using VectorType = Vector<double, VDimension>;
using CoefficientsType = VectorContainer<unsigned int, VectorType>;
using CoefficientsPointer = typename CoefficientsType::Pointer;
/** Return the location of the parametric path at the specified location. */
OutputType
Evaluate(const InputType & input) const override;
/** Evaluate the first derivative of the ND output with respect to the 1D
* input. This is an exact, algebraic function. */
VectorType
EvaluateDerivative(const InputType & input) const override;
/** Add another harmonic's frequency coefficients. */
void
AddHarmonic(const VectorType & CosCoefficients, const VectorType & SinCoefficients);
/** Clear all frequency coefficients (including the "DC" coefficients). */
void
Clear()
{
m_CosCoefficients->Initialize();
m_SinCoefficients->Initialize();
this->Modified();
}
/** New() method for dynamic construction */
itkNewMacro(Self);
/** Needed for Pipelining */
void
Initialize() override
{
this->Clear();
}
protected:
FourierSeriesPath();
~FourierSeriesPath() override = default;
void
PrintSelf(std::ostream & os, Indent indent) const override;
private:
CoefficientsPointer m_CosCoefficients{};
CoefficientsPointer m_SinCoefficients{};
};
} // end namespace itk
#ifndef ITK_MANUAL_INSTANTIATION
# include "itkFourierSeriesPath.hxx"
#endif
#endif
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