BarycentricTraits.cpp

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/* This file is part of MoDELib, the Mechanics Of Defects Evolution Library.
 *
 *
 * MoDELib is distributed without any warranty under the
 * GNU General Public License (GPL) v2 <http://www.gnu.org/licenses/>.
 */
 
#ifndef  model_BarycentricTraits_cpp_
#define  model_BarycentricTraits_cpp_
 
#include <BarycentricTraits.h>
 
namespace model
{
 
    
    template<short int dim>
    typename BarycentricTraits<dim>::VectorHigherDimD BarycentricTraits<dim>::x2l(const VectorDimD& X)
    {
        return X2L* (VectorHigherDimD()<< X, 1.0).finished();
    }
 
    
    template<short int dim>
    typename BarycentricTraits<dim>::VectorHigherDimD BarycentricTraits<dim>::x2l(const double& X)
    {
        assert(dim==1);
        return X2L* (VectorHigherDimD()<< X, 1.0).finished();
    }
 
    
    template<short int dim>
    typename BarycentricTraits<dim>::VectorDimD BarycentricTraits<dim>::l2x(const VectorHigherDimD& L)
    {
        return (L2X* L).template segment<dim>(0);
    }
 
    
    template<short int dim>
    Eigen::Matrix<double,dim+1,1> BarycentricTraits<dim>::face2domainBary(const Eigen::Matrix<double,dim,1>& b1,const int& boundaryFace)
    {
        // Transform to barycentric coordinate on the volume, adding a zero on the boundaryFace-face
        Eigen::Matrix<double,dim+1,1> bary;
        for (int k=0;k<dim;++k)
        {
            bary((k<boundaryFace)? k : k+1)=b1(k);
        }
        bary(boundaryFace)=0.0;
        return bary;
    }
 
 
    
    template<short int dim>
    typename BarycentricTraits<dim>::MatrixHigherDimD BarycentricTraits<dim>::get_L2X()
    {/*!/returns the barycentric-to-standard coordinate transformation matrix.
      *
      * For example, in 2d, the transformation is:
      * \f[
      *         \left[\begin{array}{lll}
      *     v_{11}&v_{21}&v_{31}\\
      *     v_{12}&v_{22}&v_{32}\\
      *     1&1&1\\
      *     \end{array}
      *     \right]
      *     \left[\begin{array}{l}
      *     \lambda_1\\
      *     \lambda_2\\
      *     \lambda_3\\
      *     \end{array}
      *     \right]=
      *     \left[\begin{array}{c}
      *     s_1\\
      *     s_2\\
      *     1\\
      *     \end{array}
      *     \right]
      * \f]
      *
      * In the sandard domain, we now adopt the convention that, for i<n,
      * the i-th vertex is on the i-th axis at a unit distance from the
      * origin, while the n-th vertex is the origin. With this convention,
      * plugging in the coordinates of the standard vertices, we obtain:
      * \f[
      *         \underbrace{\left[\begin{array}{lll}
      *     1&0&0\\
      *     0&1&0\\
      *     1&1&1\\
      *     \end{array}
      *     \right]}_{L2X}
      *     \left[\begin{array}{l}
      *     \lambda_1\\
      *     \lambda_2\\
      *     \lambda_3\\
      *     \end{array}
      *     \right]=
      *     \left[\begin{array}{c}
      *     s_1\\
      *     s_2\\
      *     1\\
      *     \end{array}
      *     \right]
      * \f]
      */
        MatrixHigherDimD temp(MatrixHigherDimD::Identity());
        temp.template block<1,dim>(dim,0)=Eigen::Matrix<double,1,dim>::Ones();
        return temp;
    }
 
    
    template<short int dim>
    typename BarycentricTraits<dim>::MatrixHigherDimD BarycentricTraits<dim>::get_X2L()
    {/*!/returns the standard-2-barycentric coordinate transformation matrix,
      * that is the inverse ofget_L2X().
      */
        MatrixHigherDimD temp(MatrixHigherDimD::Identity());
        temp.template block<1,dim>(dim,0)= -Eigen::Matrix<double,1,dim>::Ones();
        return temp;
    }
 
    
    template<short int dim>
    typename BarycentricTraits<dim>::MatrixDimHigherDimD BarycentricTraits<dim>::get_NdA()
    {/*!/returns a matrix having in columns the non-unitary outward normals
      * in the standard simplex. The norm of the normal is the ratio between
      * the area of the face to the area of a dim-1 Simplex.
      */
        MatrixHigherDimDimD temp(-get_L2X().template block<dim+1,dim>(0,0));
        for (int r=0;r<dim;++r)
        {
            temp.row(r).normalize(); // norm of first dim-1 normals is unitary
        }
        temp.row(dim)*=-1.0; // flip direction of the inclined face normal
        return temp.transpose();
    }
 
 
 
    // Declare static data member
//    template<short int dim>
//    const typename BarycentricTraits<dim>::MatrixHigherDimD BarycentricTraits<dim>::L2X=BarycentricTraits<dim>::get_L2X();
//
//    template<short int dim>
//    const typename BarycentricTraits<dim>::MatrixHigherDimD BarycentricTraits<dim>::X2L=BarycentricTraits<dim>::get_X2L();
//
//    template<short int dim>
//    const typename BarycentricTraits<dim>::MatrixHigherDimDimD BarycentricTraits<dim>::dLdX=BarycentricTraits<dim>::X2L. template block<dim+1,dim>(0,0);
//
//    template<short int dim>
//    const typename BarycentricTraits<dim>::MatrixDimHigherDimD BarycentricTraits<dim>::NdA=BarycentricTraits<dim>::get_NdA();
 
    template struct BarycentricTraits<1>;
    template struct BarycentricTraits<2>;
    template struct BarycentricTraits<3>;
}
#endif