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% | Reference manual page: Two_vertices_parameterizer_3.tex
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% | 21.09.2005   Laurent Saboret, Pierre Alliez, Bruno Levy
% | Package: Parameterization
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\RCSdef{\RCSTwoverticesparameterizerRev}{$Id$}
\RCSdefDate{\RCSTwoverticesparameterizerDate}{$Date$}
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\ccDefinition

Two\_vertices\_parameterizer\_3 is the default border parameterizer
for Least Squares Conformal Maps parameterization.

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The class Two\_vertices\_parameterizer\_3 parameterizes 2 extreme vertices of a 3D surface. This kind of border parameterization is used by free border parameterizations.

Implementation note: To simplify the implementation, BorderParameterizer\_3 models know only the ParameterizationMesh\_3 class. They do not know the parameterization algorithm requirements nor the kind of sparse linear system used.

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\ccInclude{CGAL/Two_vertices_parameterizer_3.h}


\ccIsModel

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Model of the BorderParameterizer\_3 concept.

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\ccHeading{Design Pattern}

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BorderParameterizer\_3 models are Strategies \cite{cgal:ghjv-dpero-95}: they implement a strategy of border parameterization for models of ParameterizationMesh\_3.

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\ccParameters

The full template declaration is:

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template$<$  \\
class ParameterizationMesh\_3$>$   \\
class Two\_vertices\_parameterizer\_3;

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\ccTypes

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\ccNestedType{Adaptor}
{
Export ParameterizationMesh\_3 template parameter.
}
\ccGlue

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\ccCreation
\ccCreationVariable{bp}  %% choose variable name for \ccMethod

\ccConstructor{Two_vertices_parameterizer_3();}{default constructor.}

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\ccOperations

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\ccMethod{Parameterizer_traits_3< Adaptor >::Error_code parameterize_border (Adaptor * mesh);}
{
Map 2 extreme vertices of the 3D mesh and mark them as {\em parameterized}.
Map 2 extreme vertices of the 3D mesh and mark them as {\em parameterized}. Return false on error.
}
\ccGlue
\ccMethod{bool is_border_convex ();}
{
Indicate if border's shape is convex. Meaningless for free border parameterization algorithms.
}
\ccGlue

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\ccSeeAlso

\ccRefIdfierPage{CGAL::Circular_border_arc_length_parameterizer_3}  \\
\ccRefIdfierPage{CGAL::Circular_border_uniform_parameterizer_3}  \\
\ccRefIdfierPage{CGAL::Square_border_arc_length_parameterizer_3}  \\
\ccRefIdfierPage{CGAL::Square_border_uniform_parameterizer_3}  \\


\ccExample

\begin{ccExampleCode}

// CGAL kernel
typedef CGAL::Cartesian<double>                         Kernel;

// Mesh true type and parameterization adaptor
typedef CGAL::Polyhedron_3<Kernel>                      Polyhedron;
typedef CGAL::Parameterization_polyhedron_adaptor_3<Polyhedron>
                                                        Parameterization_polyhedron_adaptor;

// Least Squares Conformal Maps parameterization with
// the default border parameterization: Two_vertices_parameterizer_3
typedef CGAL::LSCM_parameterizer_3<Parameterization_polyhedron_adaptor>
                                                        Parameterizer;

int main(int argc,char * argv[])
{
    Polyhedron mesh;
    ...

    // The parameterization package needs an adaptor to handle Polyhedron_3 meshes
    // The mesh must be a topological disk
    Parameterization_polyhedron_adaptor mesh_adaptor(&mesh);

    Parameterizer::Error_code err = CGAL::parameterize(&mesh_adaptor, Parameterizer());
    ...
}

\end{ccExampleCode}


\end{ccRefClass}

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