/*=========================================================================
 *
 *  Copyright Insight Software Consortium
 *
 *  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 itkParametricPath_h
#define itkParametricPath_h

#include "itkImageBase.h"
#include "itkPath.h"
#include "itkContinuousIndex.h"
#include "itkOffset.h"
#include "itkVector.h"

namespace itk
{
/** \class ParametricPath
 * \brief  Represent a parametric path through ND Space
 *
 * This virtual class is intended to represent a parametric path through an
 * image.   A parametric path maps a single floating-point 1D parameter (usually
 * designated as either time or arc-length) to a floating-point ND point in
 * continuous image index space. This mapping is done via the abstract
 * Evaluate() method, which must be overridden in all instantiable subclasses.
 * Parametric paths are required to be continuous.  They may be open or form a
 * closed loop. A parametric path may cross itself several times, although the
 * end point is constrained to have a unique spatial location unless it is
 * shared with and only with the starting point (a path tracing the number "9,"
 * starting at the bottom and ending in the middle of the right side, would
 * therefore be illegal).  Classic applications of this class include the
 * representation of contours in 2D images and path smoothing.  Another use of a
 * path is to guide the movement of an iterator through an image.
 *
 * \sa EllipseParametricPath
 * \sa PolyLineParametricPath
 * \sa FourierSeriesPath
 * \sa OrthogonallyCorrectedParametricPath
 * \sa ChainCodePath
 * \sa Path
 * \sa ContinuousIndex
 * \sa Index
 * \sa Offset
 * \sa Vector
 *
 * \ingroup PathObjects
 * \ingroup ITKPath
 */
template< unsigned int VDimension >
class ITK_TEMPLATE_EXPORT ParametricPath:public
  Path< double, ContinuousIndex< SpacePrecisionType, VDimension >, VDimension >
{
public:
  ITK_DISALLOW_COPY_AND_ASSIGN(ParametricPath);

  /** Standard class type aliases. */
  using Self = ParametricPath;
  /** All paths must be mapable to index space */
  using ContinuousIndexType = ContinuousIndex< SpacePrecisionType,VDimension >;
  using Superclass = Path< double, ContinuousIndexType, VDimension >;

  using Pointer = SmartPointer< Self >;
  using ConstPointer = SmartPointer< const Self >;

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

  /** Input type */
  using InputType = typename Superclass::InputType;

  /** Output type */
  using OutputType = typename Superclass::OutputType;

  using IndexType = Index<  VDimension >;
  using OffsetType = Offset< VDimension >;
  using VectorType = Vector< double, VDimension >;

  /** Return the nearest index to the parametric path at the specified location.
   * This is a wrapper to Evaluate(). */
  IndexType EvaluateToIndex(const InputType & input) const override;

  /** Increment the input variable passed by reference such that the ND index of
   * the path  moves to its next vertex-connected (8-connected in 2D) neighbor.
   * Return the Index-space offset of the path from its prior input to its new
   * input.  If the path is unable to increment, input is not changed and an
   * offset of Zero is returned. Children are not required to implement bounds
   * checking.
   *
   * This is a fairly slow, iterative algorithm that numerically converges to
   * the next index along the path, in a vertex-connected (8-connected in 2D)
   * fashion.  When possible, children of this class should overload this
   * function with something more efficient.
   *
   * WARNING:  This default implementation REQUIRES that the ND endpoint of
   * the path be either unique or coincident only with the startpoint, since it
   * uses the endpoint as a stopping condition. */
  OffsetType IncrementInput(InputType & input) const override;

  /** Evaluate the first derivative of the ND output with respect to the 1D
    * input.  This is a very simple and naive numerical derivative, and it
    * should be overloaded with a proper closed-form derivative function in
    * all children.  Nevertheless, users who need to create their own parametric
    * classes for their private research need not reimplement this function if
    * their work does not need the derivative operator. */
  virtual VectorType EvaluateDerivative(const InputType & input) const;

  itkSetMacro(DefaultInputStepSize, InputType)
  itkGetConstReferenceMacro(DefaultInputStepSize, InputType)

protected:
  ParametricPath();
  ~ParametricPath() override = default;
  void PrintSelf(std::ostream & os, Indent indent) const override;

  /** Default 1D input increment amount to trace along the path.  Also, the
   * value used by the defualt implementation of EvaluateDerivative() for
   * numerically approximating the derivative with the change over a single
   * default-sized step.  (NOTE that the default implementation of
   * EvaluateDerivative() should never be used in practice, but users or lazzy
   * developers may nevertheless unwisely choose to do so anyway.)  For integer-
   * input-types, 1 is probably the correct value.  For double-input-types,
   * either 1 or 0.1 are probably good values.  This value should be set in the
   * constructor of all instantiable children.  Values set in child constructors
   * overwrite values set in parent constructors. */
  InputType m_DefaultInputStepSize;
};

} // namespace itk

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

#endif // itkParametricPath.h
