mirror of https://github.com/CGAL/cgal
134 lines
4.3 KiB
TeX
134 lines
4.3 KiB
TeX
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% | Reference manual page: Discrete_authalic_parameterizer_3.tex
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% | 21.09.2005 Laurent Saboret, Pierre Alliez, Bruno Levy
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% | Package: Parameterization
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% |
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\RCSdef{\RCSDiscreteauthalicparameterizerRev}{$Id$}
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\RCSdefDate{\RCSDiscreteauthalicparameterizerDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefClass}{Discrete_authalic_parameterizer_3} %% add template arg's if necessary
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[class]{} %% add further index entries
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\ccDefinition
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% The section below is automatically generated. Do not edit!
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%START-AUTO(\ccDefinition)
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The class Discrete\_authalic\_parameterizer\_3 implements the Discrete Authalic Parameterization algorithm \cite{cgal:dma-ipsm-02}. This method is sometimes called {\em DAP} or just {\em Authalic parameterization}.
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DAP is a weak area-preserving parameterization. It is a compromise between area-preserving and angle-preserving.
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1 to 1 mapping is guaranteed if surface's border is mapped onto a convex polygon.
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As all parameterization algorithms of the package, this class is usually called via the global function parameterize().
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This class is a Strategy \cite{cgal:ghjv-dpero-95} called by the main parameterization algorithm Fixed\_border\_parameterizer\_3::parameterize(). Discrete\_authalic\_parameterizer\_3:\begin{itemize}
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\item provides default BorderParameterizer\_3 and SparseLinearAlgebraTraits\_d template parameters that make sense.\item implements compute\_w\_ij() to compute w\_ij = (i,j) coefficient of matrix A for j neighbor vertex of i based on Discrete Authalic Parameterization algorithm.\end{itemize}
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%END-AUTO(\ccDefinition)
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\ccInclude{CGAL/Discrete_authalic_parameterizer_3.h}
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\ccIsModel
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% The section below is automatically generated. Do not edit!
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%START-AUTO(\ccIsModel)
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Model of the ParameterizerTraits\_3 concept.
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%END-AUTO(\ccIsModel)
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\ccParameters
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The full template declaration is:
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% The section below is automatically generated. Do not edit!
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%START-AUTO(\ccParameters)
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template$<$ \\
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class ParameterizationMesh\_3, \\
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class BorderParameterizer\_3 = Circular\_border\_arc\_length\_parameterizer\_3$<$ParameterizationMesh\_3$>$, \\
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class SparseLinearAlgebraTraits\_d = OpenNL::DefaultLinearSolverTraits$<$typename ParameterizationMesh\_3::NT$>$$>$ \\
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class Discrete\_authalic\_parameterizer\_3;
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%END-AUTO(\ccParameters)
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\ccTypes
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% The section below is automatically generated. Do not edit!
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%START-AUTO(\ccTypes)
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%END-AUTO(\ccTypes)
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\ccCreation
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\ccCreationVariable{param} %% variable name used by \ccMethod below
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% The section below is automatically generated. Do not edit!
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%START-AUTO(\ccCreation)
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\ccConstructor{Discrete_authalic_parameterizer_3 (Border_param border_param = Border_param(), Sparse_LA sparse_la = Sparse_LA());}
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{
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Constructor.
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}
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\ccGlue
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\begin{description}
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\item[Parameters: ]
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\begin{description}
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\item[border\_param]Object that maps the surface's border to 2D space. \item[sparse\_la]Traits object to access a sparse linear system. \end{description}
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\end{description}
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\ccGlue
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%END-AUTO(\ccCreation)
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\ccOperations
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% The section below is automatically generated. Do not edit!
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%START-AUTO(\ccOperations)
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\ccMethod{virtual NT compute_w_ij (const Adaptor & mesh, Vertex_const_handle main_vertex_v_i, Vertex_around_vertex_const_circulator neighbor_vertex_v_j);}
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{
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Compute w\_ij = (i,j) coefficient of matrix A for j neighbor vertex of i.
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}
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\ccGlue
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%END-AUTO(\ccOperations)
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\ccSeeAlso
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\ccRefIdfierPage{CGAL::Parameterizer_traits_3} \\
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\ccRefIdfierPage{CGAL::Fixed_border_parameterizer_3} \\
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\ccRefIdfierPage{CGAL::Barycentric_mapping_parameterizer_3} \\
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\ccRefIdfierPage{CGAL::Discrete_conformal_map_parameterizer_3} \\
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\ccRefIdfierPage{CGAL::LSCM_parameterizer_3} \\
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\ccRefIdfierPage{CGAL::Mean_value_coordinates_parameterizer_3} \\
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\ccExample
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See \ccc{Authalic_parameterization.C} example.
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\end{ccRefClass}
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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% EOF
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% +------------------------------------------------------------------------+
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