mirror of https://github.com/CGAL/cgal
90 lines
3.3 KiB
TeX
90 lines
3.3 KiB
TeX
\section{Sparse Linear Algebra \label{sec: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}
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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
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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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\emph{Usage:}
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OpenNL (in the version shipped with \cgal) is a lightweight sparse linear solver.
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It does not support large systems, but it is highly portable and
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supports exact number types.
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\item
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\ccAnchor{http://www.cs.tau.ac.il/~stoledo/taucs}{{\sc Taucs}}
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is a state-of-the-art direct solver for sparse symmetric matrices.
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It also includes an out-of-core general sparse solver.
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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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\emph{Usage:}
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{\sc Taucs} is very robust and supports large systems.
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On the other hand, it is not available on all platforms
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supported by \cgal\ and does not support exact number types.
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\emph{Install:}
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{\sc Taucs} can be downloaded from
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\ccAnchor{http://www.tau.ac.il/~stoledo/taucs/2.2/taucs_full.zip}
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{\ccc{http://www.tau.ac.il/~stoledo/taucs/2.2/taucs_full.zip}}.
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\end{itemize}
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\subsection{{\sc Taucs} Solver Example}
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\ccc{examples/Surface_mesh_parameterization/Taucs_parameterization.cpp} computes the
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default parameterization method (Floater mean value coordinates with a circular border),
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but specifically instantiates the {\sc Taucs} solver. Specifying a specific solver
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instead of the default one (OpenNL) means using the third parameter of
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\ccc{CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3,
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BorderParameterizer_3, SparseLinearAlgebraTraits_d>}. The differences with the first
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example \ccc{examples/Surface_mesh_parameterization/Simple_parameterization.cpp} 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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