mirror of https://github.com/CGAL/cgal
123 lines
3.6 KiB
TeX
123 lines
3.6 KiB
TeX
\begin{ccRefFunctionObjectConcept}{CircularKernel::MakeXMonotone_2}
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\ccDefinition
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Splitting curves into monotone pieces.
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\ccCreationVariable{fo}
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A model \ccVar\ of this type must provide:
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\ccMemberFunction{template < class OutputIterator >
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OutputIterator
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operator()(const CircularKernel::Circular_arc_2 &ca, OutputIterator oit);}
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{Splits the arc \ccc{ca} into monotone arcs that are returned through the
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output iterator.}
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For the sake of completeness, the \ccc{operator()} must also be defined for a
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\ccc{Line_arc_2}. In this case, the input line arc itself is the only
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arc returned through the \ccc{OutputIterator}.
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\ccHasModels
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\ccc{Circular_kernel_2::Make_x_monotone_2;}
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\ccSeeAlso
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\ccRefIdfierPage{CGAL::make_x_monotone}
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\end{ccRefFunctionObjectConcept}
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\begin{ccRefFunctionObjectConcept}{CircularKernel::Intersect_2}
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\ccDefinition
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To compute intersections of objects.
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\ccRefines
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\ccc{Kernel::Intersect_2}
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\ccCreationVariable{fo}
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A model \ccVar\ of this type must provide:
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\ccMemberFunction{template < class OutputIterator >
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OutputIterator
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operator()(const CircularKernel::Line_arc_2 &l, const Type &c,
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OutputIterator points);}
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{Copies in the output iterators the intersection points between the
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two objects, sorted lexicographically. \ccc{points} iterates on
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elements of type \ccc{std::pair<CircularKernel::Circular_arc_point_2,
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int>}, where the integer is the multiplicity of the corresponding
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intersection point between \ccc{l} and \ccc{c}. }
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and
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\ccMemberFunction{template < class OutputIterator >
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OutputIterator
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operator()(const Type &c, const CircularKernel::Line_arc_2 &l);}
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{same}
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where \ccc{Type} is either \ccc{CircularKernel::Circle_2} or
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\ccc{CircularKernel::Circular_arc_2}.
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\ccMemberFunction{template < class OutputIteratorPoints,
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class OutputIteratorArcs >
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std::pair< OutputIteratorPoints, OutputIteratorArcs >
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operator()(const Type1 &obj1, const Type2 &obj2,
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OutputIteratorPoints points, OutputIteratorArcs arcs);}
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{Copies in the output iterators the intersections between the two
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objects, sorted lexicographically. \ccc{points} iterates on elements
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of type \ccc{std::pair<CircularKernel::Circular_arc_point_2, int>},
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where the integer is the multiplicity of the corresponding
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intersection point between \ccc{obj1} and \ccc{obj2}, and \ccc{arcs}
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iterates on elements of type \ccc{CircularKernel::Circular_arc_2} %(or
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%\ccc{CircularKernel::Circle_2} in the special case of two equal input circles)
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that are arcs on which \ccc{obj1} and \ccc{obj2} overlap.}
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where \ccc{Type1} and \ccc{Type2} can both be either
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\ccc{CircularKernel::Circle_2} or
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\ccc{CircularKernel::Circular_arc_2}.
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\ccHasModels
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\ccc{Circular_kernel_2::Intersect_2;}
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\ccSeeAlso
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\ccRefIdfierPage{CGAL::intersect}
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\end{ccRefFunctionObjectConcept}
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\begin{ccRefFunctionObjectConcept}{CircularKernel::Split_2}
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\ccDefinition
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To split curves at a given point.
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\ccCreationVariable{fo}
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A model \ccVar\ of this type must provide:
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\ccMemberFunction{void operator()
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(const CircularKernel::Circular_arc_2 &a,
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const CircularKernel::Circular_arc_point_2 &p,
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CircularKernel::Circular_arc_2 &a1,
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CircularKernel::Circular_arc_2 &a2);}
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{Splits arc $a$ at point $p$, which creates arcs $a1$ and $a2$.
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\ccPrecond{$a$ is $x$-monotone, and $p$ lies on $a$.}}
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\ccMemberFunction{void operator()
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(const CircularKernel::Line_arc_2 &l,
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const CircularKernel::Circular_arc_point_2 &p,
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CircularKernel::Line_arc_2 &l1, CircularKernel::Line_arc_2 &l2);}
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{Same for a line arc.}
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\ccHasModels
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\ccc{Circular_kernel_2::Split_2}
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\ccSeeAlso
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\ccRefIdfierPage{CGAL::split}
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\end{ccRefFunctionObjectConcept}
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