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% | Reference manual page: ShortestPathTraits.tex
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% | Last revision: 09.07.2002   
% | Author : Pierre Angelier <Pierre.Angelier@ens.fr>
% | Maintainer: Laurent Rineau <Laurent.Rineau@ens.fr>
% | Package: Visibility_complex
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\ccRefPageBegin
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\begin{ccRefConcept}{ShortestPathTraits}
\label{pageShortestPathTraitsRef}

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\ccDefinition

The concept \ccRefName\  describes the set of requirements to be fulfilled by
any class used to instantiate the last parameter in the shortest\_path\_2 
\ccIndexMainItem[c]{shortest_path_2} function. This function computes the shortest path between
two points in a scene.
This concept inherits all the types and requirement from the
\ccc{VisibilityComplexTraits} concept and adds a few additional primitives used
specifically for shortest path computations.

We distinguish two different number types: the one used for the input data and
the one used for the distance computations during our algorithm. The latter type
has to support the square root operation whereas the first type doesn't (i.e. it 
can be of integer type).
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\ccTypes
\ccThree{ShortestPathTraits::Exact_NT }{}{}
\ccThreeToTwo

\ccNestedType{Exact_NT}{the number type used to compute distances. It must
support the square root operation.}
\ccGlue
\ccNestedType{Disk}{the disk type.}
\ccGlue
\ccNestedType{Arc_2}{the arc type. Model of the \ccc{Arc} concept.}
\ccGlue
\ccNestedType{Bitangent_2}{the bitangent type. Model of the \ccc{Bitangent}
concept.}
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\ccCreation
\ccCreationVariable{traits}

\ccConstructor{ShortestPathTraits();} {default constructor.}
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\ccOperations

\ccTagFullDeclarations
\ccMethod{Disk make_convex_from_point(Point_2 p);}{method to create a disk from a point.}
\ccGlue
\ccMethod{bool is_vertex(Disk d);}{returns true if \ccc{d} is a point. }
\ccGlue
\ccMethod{Exact_NT length(Arc_2 a, Bitangent_2 b, Bitangent_2 c);}
{returns the length of the arc \ccc{a} defined by the two bitangents \ccc{b} and
\ccc{c}.}
\ccGlue
\ccMethod{Exact_NT length(Bitangent_2 b);}{return the length of the bitangent
\ccc{b}.}

\ccTagDefaults
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\ccHasModels

\ccRefIdfierPage{CGAL::Shortest_path_point_traits<R,E>} \\
\ccRefIdfierPage{CGAL::Shortest_path_segment_traits<R,E>} \\
\ccRefIdfierPage{CGAL::Shortest_path_polygon_traits<R,E>}
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\end{ccRefConcept}
\ccRefPageEnd
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