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A class that stores Coxeter triangulation of type \(\tilde{A}_d\). This triangulation has the greatest simplex quality out of all linear transformations of the Freudenthal-Kuhn triangulation. More...
Public Member Functions | |
| Coxeter_triangulation (std::size_t dimension) | |
| Constructor of Coxeter triangulation of a given dimension. More... | |
 Public Member Functions inherited from Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation< std::vector< int >, std::vector< std::vector< std::size_t > > > > | |
| Freudenthal_triangulation (std::size_t dimension) | |
| Constructor of the Freudenthal-Kuhn triangulation of a given dimension. More... | |
| Freudenthal_triangulation (std::size_t dimension, const Matrix &matrix) | |
| Constructor of the Freudenthal-Kuhn triangulation of a given dimension under a linear transformation by a given matrix. More... | |
| Freudenthal_triangulation (unsigned dimension, const Matrix &matrix, const Vector &offset) | |
| Constructor of the Freudenthal-Kuhn triangulation of a given dimension under an affine transformation by a given matrix and a translation vector. More... | |
| unsigned | dimension () const |
| Dimension of the triangulation. | |
| const Matrix & | matrix () const |
| Matrix that defines the linear transformation of the triangulation. | |
| const Vector & | offset () const |
| Vector that defines the offset of the triangulation. | |
| void | change_matrix (const Eigen::MatrixXd &matrix) |
| Change the linear transformation matrix to a given value. More... | |
| void | change_offset (const Eigen::VectorXd &offset) |
| Change the offset vector to a given value. More... | |
| Simplex_handle | locate_point (const Point_d &point, double scale=1) const |
| Returns the permutahedral representation of the simplex in the triangulation that contains a given query point. More... | |
| Eigen::VectorXd | cartesian_coordinates (const Vertex_handle &vertex, double scale=1) const |
| Returns the Cartesian coordinates of the given vertex. More... | |
| Eigen::VectorXd | barycenter (const Simplex_handle &simplex, double scale=1) const |
| Returns the Cartesian coordinates of the barycenter of a given simplex. More... | |
Additional Inherited Members | |
| Public Types inherited from Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation< std::vector< int >, std::vector< std::vector< std::size_t > > > > | |
| using | Simplex_handle = Permutahedral_representation< std::vector< int >, std::vector< std::vector< std::size_t > > > |
| Type of the simplices in the triangulation. | |
| using | Vertex_handle = typename Permutahedral_representation_::Vertex |
| Type of the vertices in the triangulation. | |
A class that stores Coxeter triangulation of type \(\tilde{A}_d\). This triangulation has the greatest simplex quality out of all linear transformations of the Freudenthal-Kuhn triangulation.
| Permutahedral_representation_ | Type of a simplex given by a permutahedral representation. Needs to be a model of SimplexInCoxeterTriangulation. |
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Constructor of Coxeter triangulation of a given dimension.
| [in] | dimension | The dimension of the triangulation. |