mirror of https://github.com/CGAL/cgal
69 lines
2.3 KiB
TeX
69 lines
2.3 KiB
TeX
\section{Sparse Linear Algebra}
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Parameterizing triangle meshes requires both efficient representation
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of sparse matrices and efficient iterative or direct linear
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solvers. We provide links to standard libraries ({\sc Taucs})
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and include a separate package devoted to OpenNL sparse linear solver.
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\subsection{List of Solvers and Concept}
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We provide an interface to several sparse linear solvers, as models
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of the \ccc{SparseLinearAlgebraTraits_d} concept:
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\begin{itemize}
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\item OpenNL \cite{cgal:l-nmdgp-05} is shipped with \cgal. This is the default solver:
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\ccc{OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>} in OpenNL package \\
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\ccc{OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>} in OpenNL package \\
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\item {\sc Taucs} is a state-of-the-art direct solver for sparse symmetric matrices.
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\ccc{CGAL::Taucs_solver_traits<T>} \\
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\ccc{CGAL::Taucs_symmetric_solver_traits<T>} \\
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\end{itemize}
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\subsection{{\sc Taucs} Solver Example}
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The examples provided so far use the default sparse linear solver
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OpenNL.
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\ccc{Taucs_parameterization.C} computes the default parameterization
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method (Floater Mean Value Coordinates with a circular border), but
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specifically instantiates the {\sc Taucs} solver.
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The differences with the first example \ccc{Simple_parameterization.C} are:
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\begin{ccExampleCode}
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#include <CGAL/Taucs_solver_traits.h>
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...
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//***************************************
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// Floater Mean Value Coordinates parameterization
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// (circular border) with TAUCS solver
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//***************************************
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// Circular border parameterizer (the default)
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typedef CGAL::Circular_border_arc_length_parameterizer_3<Parameterization_polyhedron_adaptor>
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Border_parameterizer;
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// TAUCS solver
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typedef CGAL::Taucs_solver_traits<double> Solver;
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// Floater Mean Value Coordinates parameterization
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// (circular border) with TAUCS solver
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typedef CGAL::Mean_value_coordinates_parameterizer_3<Parameterization_polyhedron_adaptor,
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Border_parameterizer,
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Solver>
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Parameterizer;
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Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer());
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...
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\end{ccExampleCode}
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