affinegeometry.hh

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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
#ifndef DUNE_GEOMETRY_AFFINEGEOMETRY_HH
#define DUNE_GEOMETRY_AFFINEGEOMETRY_HH

#include <cmath>

#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>

#include <dune/geometry/type.hh>
#include <dune/geometry/utility/defaultmatrixhelper.hh>

namespace Dune
{

  // External Forward Declarations
  // -----------------------------

  namespace Geo
  {

    template< typename Implementation >
    class ReferenceElement;

    template< class ctype, int dim >
    class ReferenceElementImplementation;

    template< class ctype, int dim >
    struct ReferenceElements;

  }


  template< class ct, int mydim, int cdim>
  class AffineGeometry
  {
  public:

    typedef ct ctype;

    static const int mydimension= mydim;

    static const int coorddimension = cdim;

    typedef FieldVector< ctype, mydimension > LocalCoordinate;

    typedef FieldVector< ctype, coorddimension > GlobalCoordinate;

    typedef ctype Volume;

    typedef FieldMatrix< ctype, mydimension, coorddimension > JacobianTransposed;

    typedef FieldMatrix< ctype, coorddimension, mydimension > JacobianInverseTransposed;

    typedef FieldMatrix< ctype, coorddimension, mydimension > Jacobian;

    typedef FieldMatrix< ctype, mydimension, coorddimension > JacobianInverse;

  private:
    typedef Geo::ReferenceElement< Geo::ReferenceElementImplementation< ctype, mydimension > > ReferenceElement;

    typedef Geo::ReferenceElements< ctype, mydimension > ReferenceElements;

    // Helper class to compute a matrix pseudo inverse
    typedef Impl::FieldMatrixHelper< ct > MatrixHelper;

  public:
    AffineGeometry () = default;

    AffineGeometry ( const ReferenceElement &refElement, const GlobalCoordinate &origin,
                     const JacobianTransposed &jt )
      : refElement_(refElement), origin_(origin), jacobianTransposed_(jt)
    {
      integrationElement_ = MatrixHelper::rightInvA( jacobianTransposed_, jacobianInverseTransposed_ );
    }

    AffineGeometry ( Dune::GeometryType gt, const GlobalCoordinate &origin,
                     const JacobianTransposed &jt )
      : AffineGeometry(ReferenceElements::general( gt ), origin, jt)
    { }

    template< class CoordVector >
    AffineGeometry ( const ReferenceElement &refElement, const CoordVector &coordVector )
      : refElement_(refElement), origin_(coordVector[0])
    {
      for( int i = 0; i < mydimension; ++i )
        jacobianTransposed_[ i ] = coordVector[ i+1 ] - origin_;
      integrationElement_ = MatrixHelper::rightInvA( jacobianTransposed_, jacobianInverseTransposed_ );
    }

    template< class CoordVector >
    AffineGeometry ( Dune::GeometryType gt, const CoordVector &coordVector )
      : AffineGeometry(ReferenceElements::general( gt ), coordVector)
    { }

    bool affine () const { return true; }

    Dune::GeometryType type () const { return refElement_.type(); }

    int corners () const { return refElement_.size( mydimension ); }

    GlobalCoordinate corner ( int i ) const
    {
      return global( refElement_.position( i, mydimension ) );
    }

    GlobalCoordinate center () const { return global( refElement_.position( 0, 0 ) ); }

    GlobalCoordinate global ( const LocalCoordinate &local ) const
    {
      GlobalCoordinate global( origin_ );
      jacobianTransposed_.umtv( local, global );
      return global;
    }

    LocalCoordinate local ( const GlobalCoordinate &global ) const
    {
      LocalCoordinate local;
      jacobianInverseTransposed_.mtv( global - origin_, local );
      return local;
    }

    ctype integrationElement ([[maybe_unused]] const LocalCoordinate &local) const
    {
      return integrationElement_;
    }

    Volume volume () const
    {
      return integrationElement_ * refElement_.volume();
    }

    const JacobianTransposed &jacobianTransposed ([[maybe_unused]] const LocalCoordinate &local) const
    {
      return jacobianTransposed_;
    }

    const JacobianInverseTransposed &jacobianInverseTransposed ([[maybe_unused]] const LocalCoordinate &local) const
    {
      return jacobianInverseTransposed_;
    }

    Jacobian jacobian ([[maybe_unused]] const LocalCoordinate &local) const
    {
      return jacobianTransposed_.transposed();
    }

    JacobianInverse jacobianInverse ([[maybe_unused]] const LocalCoordinate &local) const
    {
      return jacobianInverseTransposed_.transposed();
    }

    friend ReferenceElement referenceElement ( const AffineGeometry &geometry )
    {
      return geometry.refElement_;
    }

  private:
    ReferenceElement refElement_;
    GlobalCoordinate origin_;
    JacobianTransposed jacobianTransposed_;
    JacobianInverseTransposed jacobianInverseTransposed_;
    ctype integrationElement_;
  };

} // namespace Dune

#endif // #ifndef DUNE_GEOMETRY_AFFINEGEOMETRY_HH