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% | Reference manual page: VisibilityComplexTraits.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}{VisibilityComplexTraits}
\label{pageVisibilityComplexTraitsRef}

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\ccDefinition

The concept \ccRefName\  describes the set of requirements to be fulfilled by
any class used to instantiate the first template parameter of the classes
\ccc{Visibility_complex_2<Gt,It>} and
\ccc{Visibility_complex_antichain<Gt,It>}.  This concept provides the
types of the geometric primitives used in the visiblity complex and some
function object types for the required predicates on those primitives. 
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\ccTypes
\ccThree{VisibilityComplexTraits::Is_upward_directed }{}{}
\ccThreeToTwo

\ccNestedType{Point_2}{point type.}
\ccGlue
\ccNestedType{Segment_2}{segment type.}
\ccGlue
\ccNestedType{Disk}{disk type.}
\ccGlue
\ccNestedType{Bitangent_2}{model of the \ccc{Bitangent} concept. }
\ccGlue
\ccNestedType{Arc_2}{model of the \ccc{Arc} concept. }
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\ccNestedType{Orientation_object}{Must provide the operator \ccc{Orientation
operator()(Bitangent_2 a, Bitangent_2 b)}, which returns \ccc{LEFTURN,
RIGHTTURN, COLLINEAR} depending on the sign, \ccc{POSITIVE, NEGATIVE, ZERO} of
the determinant $\det(\vec{a},\vec{b})$ of the two underlying vectors of the
bitangents $a$ and $b$.}
\ccGlue
\ccNestedType{Is_upward_directed}{Must provide the operator \ccc{bool
operator()(Bitangent_2 d)}, which returns true iff. the angle of the bitangent
belongs to $[0,\pi)$. }
\ccGlue
\ccNestedType{Compare_extreme_yx}{Let \ccc{FT extreme(bool x, C c)} be a function returning
the maximal (resp. minimal) $y$-coordinate of $c$ if $x$ is false (resp. true). 
The type $C$ can be either \ccc{Disk} or \ccc{Bitangent_2}. \\
The type \ccc{Compare_extreme_yx} must provide an operator
\ccc{Comparison_result operator()(bool x , C a , bool y , D b)} which returns
the comparison result between the \ccc{compare(x,a)} and \ccc{extreme(y,b)}. The
types $C$ and $D$ can be either \ccc{Disk} or \ccc{Bitangent}. }
\ccNestedType{Is_point}{Must provide the operator \ccc{bool operator()(Disk d)},
which returns true iff. $d$ is a point.}
\ccGlue
\ccNestedType{Equal_as_segments}{Must provide the operator \ccc{bool
operator()(Bitangent_2 a, Bitangent_2 b)}, which returns true iff. the
underlying segments of $a$ and $b$ are equal.}
\ccGlue
\ccNestedType{Do_intersect}{Must provide the four operators \ccc{bool
operator()(C a, D b)}-- where the types $C, D$ are either \ccc{Disk} or
\ccc{Bitangent_2}-- which return true iff. $a$ and $b$ intersect.}
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\ccCreation
\ccCreationVariable{traits}

\ccConstructor{VisibilityComplexTraits();} {default constructor.}
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\ccHasModels

\ccRefIdfierPage{CGAL::Visibility_complex_point_traits<R>} \\
\ccRefIdfierPage{CGAL::Visibility_complex_segment_traits<R>} \\
\ccRefIdfierPage{CGAL::Visibility_complex_polygon_traits<R>} \\
\ccRefIdfierPage{CGAL::Visibility_complex_circle_traits<R>}
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\end{ccRefConcept}
\ccRefPageEnd
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