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% | Reference manual page: Umbilic_approximation.tex
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% | 15.09.2006   Marc Pouget and Frédéric Cazals
% | Package: Ridges_3
% | 
\RCSdef{\RCSUmbilicapproximationRev}{$Id$}
\RCSdefDate{\RCSUmbilicapproximationDate}{$Date$}
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\begin{ccRefClass}{Umbilic_approximation<TriangulatedSurfaceMesh,Vertex2FTPropertyMap,Vertex2VectorPropertyMap>} 
 %% add template arg's if necessary

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\ccDefinition
  
The class \ccRefName\ computes the approximation of
umbilics on a triangular polyhedral surface. 


\ccInclude{CGAL/Umbilics.h}

\ccParameters The class \ccRefName\ has three template parameters.
\ccc{TriangulatedSurfaceMesh} provides the surface. Parameters
\ccc{Vertex2FTPropertyMap} and \ccc{Vertex2VectorPropertyMap} provide
the differential properties of the surface associated to its vertices.

Requirements (checked at compile time) : the types
\ccc{TriangulatedSurfaceMesh::Traits::FT} and
\ccc{Vertex2FTPropertyMap::value_type} must coincide; the types
\ccc{TriangulatedSurfaceMesh::Traits::Vector_3} and
\ccc{Vertex2VectorPropertyMap::value_type} must coincide; the types
\ccc{TriangulatedSurfaceMesh::Vertex_handle},
\ccc{Vertex2FTPropertyMap::key_type} and
\ccc{Vertex2VectorPropertyMap::key_type} must coincide;


\ccTypes

\ccTypedef{  typedef typename TriangulatedSurfaceMesh::Traits::FT       FT;}{}

\ccCreation
\ccCreationVariable{umbilic_approximation}  %% choose variable name

\ccConstructor{Umbilic_approximation(const TriangulatedSurfaceMesh& P, 
			const Vertex2FTPropertyMap& vertex2k1_pm, 
			const Vertex2FTPropertyMap& vertex2k2_pm,
			const Vertex2VectorPropertyMap& vertex2d1_pm, 
			const Vertex2VectorPropertyMap& vertex2d2_pm);}
 {default constructor.}

\ccOperations

\ccMethod{template <class OutputIterator>  OutputIterator compute(OutputIterator it, FT size);}
{Performs the approximation, \ccc{size} determines the size of the
patches around vertices, taken as  \ccc{size} times the size of the
1-ring. Umbilics are output through the \ccc{OutputIterator} which is a
concept of output iterator of the  {\sc Stl} with value type \ccc{Umbilic*}.}

\ccSeeAlso

\ccc{Umbilic}
\ccc{TriangulatedSurfaceMesh}
\ccc{Vertex2FTPropertyMap}
\ccc{Vertex2VectorPropertyMap}


\end{ccRefClass}

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