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:
#ifndef DUNE_GEOMETRY_AFFINEGEOMETRY_HH
#define DUNE_GEOMETRY_AFFINEGEOMETRY_HH
 
#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>
 
#include <dune/geometry/type.hh>
#include <dune/geometry/genericgeometry/geometrytraits.hh>
#include <dune/geometry/genericgeometry/matrixhelper.hh>
 
namespace Dune
{
 
  // External Forward Declarations
  // -----------------------------
 
  template< class ctype, int dim >
  class ReferenceElement;
 
  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 FieldMatrix< ctype, mydimension, coorddimension > JacobianTransposed;
 
    typedef FieldMatrix< ctype, coorddimension, mydimension > JacobianInverseTransposed;
 
  private:
    typedef Dune::ReferenceElement< ctype, mydimension > ReferenceElement;
 
    typedef Dune::ReferenceElements< ctype, mydimension > ReferenceElements;
 
    // Helper class to compute a matrix pseudo inverse
    typedef GenericGeometry::MatrixHelper< GenericGeometry::DuneCoordTraits< ct > > MatrixHelper;
 
  public:
    AffineGeometry ( const ReferenceElement &refElement, const GlobalCoordinate &origin,
                     const JacobianTransposed &jt )
      : refElement_(&refElement), origin_(origin), jacobianTransposed_(jt)
    {
      integrationElement_ = MatrixHelper::template rightInvA< mydimension, coorddimension >( jacobianTransposed_, jacobianInverseTransposed_ );
    }
 
    AffineGeometry ( Dune::GeometryType gt, const GlobalCoordinate &origin,
                     const JacobianTransposed &jt )
      : refElement_( &ReferenceElements::general( gt ) ), origin_(origin), jacobianTransposed_( jt )
    {
      integrationElement_ = MatrixHelper::template rightInvA< mydimension, coorddimension >( jacobianTransposed_, jacobianInverseTransposed_ );
    }
 
    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::template rightInvA< mydimension, coorddimension >( jacobianTransposed_, jacobianInverseTransposed_ );
    }
 
    template< class CoordVector >
    AffineGeometry ( Dune::GeometryType gt, const CoordVector &coordVector )
      : refElement_(&ReferenceElements::general( gt )), origin_(coordVector[0] )
    {
      for( int i = 0; i < mydimension; ++i )
        jacobianTransposed_[ i ] = coordVector[ i+1 ] - origin_;
      integrationElement_ = MatrixHelper::template rightInvA< mydimension, coorddimension >( jacobianTransposed_, jacobianInverseTransposed_ );
    }
 
    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 ( const LocalCoordinate &local ) const
    {
      DUNE_UNUSED_PARAMETER(local);
      return integrationElement_;
    }
 
    ctype volume () const
    {
      return integrationElement_ * refElement_->volume();
    }
 
    const JacobianTransposed &jacobianTransposed ( const LocalCoordinate &local ) const
    {
      DUNE_UNUSED_PARAMETER(local);
      return jacobianTransposed_;
    }
 
    const JacobianInverseTransposed &jacobianInverseTransposed ( const LocalCoordinate &local ) const
    {
      DUNE_UNUSED_PARAMETER(local);
      return jacobianInverseTransposed_;
    }
 
  private:
    const ReferenceElement* refElement_;
    GlobalCoordinate origin_;
    JacobianTransposed jacobianTransposed_;
    JacobianInverseTransposed jacobianInverseTransposed_;
    ctype integrationElement_;
 
  };
 
} // namespace Dune
 
#endif // #ifndef DUNE_GEOMETRY_AFFINEGEOMETRY_HH