/*=========================================================================
 *
 * 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 itkFEMElement3DC0LinearTriangular_h
#define itkFEMElement3DC0LinearTriangular_h

#include "itkFEMElementStd.h"
#include "ITKFEMExport.h"

namespace itk
{
namespace fem
{
/**
 * \class Element3DC0LinearTriangular
 * \brief 3-noded, linear, C0 continuous finite element in 2D space.
 *
 * The ordering of the nodes is counter clockwise. That is the nodes
 * should be defined in the following order:
 *
 *  (0,1)
 *  2
 *  *
 *  |\
 *  | \
 *  |  \
 *  |   \
 *  |    \
 *  |     \
 *  *------*
 *  0      1
 *  (0,0)  (0,1)
 *
 * \ingroup ITKFEM
 */

class ITKFEM_EXPORT Element3DC0LinearTriangular : public ElementStd<3, 3>
{
public:
  /** Standard class type aliases. */
  using Self = Element3DC0LinearTriangular;
  using TemplatedParentClass = ElementStd<3, 3>;
  using Superclass = TemplatedParentClass;
  using Pointer = SmartPointer<Self>;
  using ConstPointer = SmartPointer<const Self>;

  /** \see LightObject::GetNameOfClass() */
  itkOverrideGetNameOfClassMacro(Element3DC0LinearTriangular);

  // ////////////////////////////////////////////////////////////////////////
  /*
   * Methods related to numeric integration
   */

  enum
  {
    DefaultIntegrationOrder = 1
  };

  /** Get the Integration point and weight */
  void
  GetIntegrationPointAndWeight(unsigned int i, VectorType & pt, Float & w, unsigned int order) const override;

  /** Get the number of integration points */
  unsigned int
  GetNumberOfIntegrationPoints(unsigned int order) const override;

  // ////////////////////////////////////////////////////////////////////////
  /*
   * Methods related to the geometry of an element
   */

  /** Return the shape functions used to interpolate across the element */
  VectorType
  ShapeFunctions(const VectorType & pt) const override;

  /** Return the shape functions derivatives in the shapeD matrix */
  void
  ShapeFunctionDerivatives(const VectorType & pt, MatrixType & shapeD) const override;

  /** Convert from global to local coordinates */
  bool
  GetLocalFromGlobalCoordinates(const VectorType & globalPt, VectorType & localPt) const override;

  /** Compute the determinate of the Jacobian matrix */
  Float
  JacobianDeterminant(const VectorType & pt, const MatrixType * pJ = nullptr) const override;

  /** Compute the inverse of the Jacobian matrix */
  void
  JacobianInverse(const VectorType & pt, MatrixType & invJ, const MatrixType * pJ = nullptr) const override;

  /** Define the edges and nodes that correspond to the edges */
  void
  PopulateEdgeIds() override;

  /**
   * Normal of the triangle element
   */
  void
  ComputeNormalDirection(const VectorType & v1, const VectorType & v2, const VectorType & v3, VectorType & n) const;

  /**
   * Project the point x onto the plane containing the triangle element
   */
  void
  GeneralizedProjectPoint(const VectorType & x,
                          const VectorType & origin,
                          const VectorType & normal,
                          VectorType &       xproj) const;

  /** Return the determinate of a 2x2 matrix */
  itk::fem::Element::Float
  Determinant2x2(const VectorType & c1, const VectorType & c2) const;

  /**
   * Constants for integration rules.
   */
  static const Float trigGaussRuleInfo[6][7][4];

  /**
   * Array that holds number of integration point for each order
   * of numerical integration.
   */
  static const unsigned int Nip[6];

protected:
  void
  PrintSelf(std::ostream & os, Indent indent) const override;
};
} // end namespace fem
} // end namespace itk

#endif // itkFEMElement3DC0LinearTriangular_h