mirror of https://github.com/CGAL/cgal
Fixed ArrangementDirectionalXMonotoneTraits_2 concept
This commit is contained in:
Efi Fogel
parent
9369f7ba93
commit
810bc03435
|
|
@ -7,7 +7,7 @@
|
|||
\begin{ccRefConcept}{ArrangementDirectionalXMonotoneTraits_2}
|
||||
|
||||
\ccDefinition
|
||||
|
||||
% ===========
|
||||
This concept refines the basic arrangement $x$-monotone traits concept.
|
||||
A model of this concept is able to handle \emph{directed} $x$-monotone curves
|
||||
that intersect in their interior. Namely, an instance of the
|
||||
|
|
@ -16,8 +16,8 @@ that intersect in their interior. Namely, an instance of the
|
|||
(lexicographically smaller) endpoint and a \emph{right} endpoint.
|
||||
If the traits class is also a model of
|
||||
\ccc{ArrangementDirectionalXMonotoneTraits_2}, the $x$-monotone curve is
|
||||
also required to have a direction, namely one of these two endpoint is
|
||||
viewed as its \emph{source} and the other as its \emph{target}.
|
||||
also required to have a direction, namely one of these two endpoint serves
|
||||
as its \emph{source} and the other as its \emph{target}.
|
||||
|
||||
\ccRefines
|
||||
\ccc{ArrangementXMonotoneTraits_2}
|
||||
|
|
@ -29,51 +29,22 @@ viewed as its \emph{source} and the other as its \emph{target}.
|
|||
\ccThreeToTwo
|
||||
|
||||
\ccNestedType{Compare_endpoints_xy_2}
|
||||
{provides the operator~: \\
|
||||
\ccc{Comparison_result operator() (X_monotone_curve_2 c)} \\
|
||||
which accepts an input curve \ccc{c} and compare its source and target
|
||||
point. It returns \ccc{SMALLER} if the curve is directed from left to right
|
||||
(lexicographically --- i.e., in case of a vertical line segment, this means
|
||||
it is directed upward), and \ccc{LARGER} if it is directed from right to
|
||||
left.}
|
||||
{models the concept \ccc{ArrDirectionalTraits::CompareEndpointsXy_2}.}
|
||||
|
||||
\ccNestedType{Construct_opposite_2}
|
||||
{provides the operator~: \\
|
||||
\ccc{X_monotone_curve_2 operator() (X_monotone_curve_2 c)} \\
|
||||
which accepts an $x$-monotone curve \ccc{c} and returns its opposite curve,
|
||||
namely a curve whose graph is the same as \ccc{c}'s, and whose source and
|
||||
target are swapped with respect to \ccc{c}'s source and target.}
|
||||
|
||||
In addition, the two following functors, required by the concept
|
||||
\ccc{ArrangementXMonotoneTraits_2} should operate as follows:
|
||||
{models the concept \ccc{ArrDirectionalTraits::ConstructOpposite_2}.}
|
||||
|
||||
\ccNestedType{Intersect_2}
|
||||
{provides the operator (templated by the \ccc{OutputIterator} type)~: \\
|
||||
\ccc{OutputIterator operator() (X_monotone_curve_2 c1, X_monotone_curve_2 c2,
|
||||
OutputIterator oi)} \\
|
||||
which computes the intersections of \ccc{c1} and \ccc{c2} and inserts them
|
||||
{\sl in an ascending lexicographic $xy$-order} into the output iterator.
|
||||
The value-type of \ccc{OutputIterator} is \ccc{CGAL::Object}, where each
|
||||
\ccc{Object} either wraps a \ccc{pair<Point_2,Multiplicity>} instance, which
|
||||
represents an intersection point with its multiplicity (in case the
|
||||
multiplicity is undefined or not known, it should be set to $0$) or an
|
||||
\ccc{X_monotone_curve_2} instance, representing an overlapping subcurve of
|
||||
\ccc{c1} and \ccc{c2}. In the latter case, if \ccc{c1} and \ccc{c2} have the
|
||||
same direction, then the overlapping subcurves should also be directed the
|
||||
same way; otherwise, they can be associated with an arbitrary direction.
|
||||
The operator returns a past-the-end iterator for the output sequence.}
|
||||
{models the concept \ccc{ArrDirectionalTraits::Intersect_2}.}
|
||||
|
||||
\ccNestedType{Split_2}
|
||||
{provides the operator~: \\
|
||||
\ccc{void operator() (X_monotone_curve_2 c, Point_2 p,
|
||||
X_monotone_curve_2& c1, X_monotone_curve_2& c2)} \\
|
||||
which accepts an input curve \ccc{c} and a split point \ccc{p} in its
|
||||
interior. It splits \ccc{c} at the split point into two subcurves \ccc{c1}
|
||||
and \ccc{c2}, such that \ccc{p} is \ccc{c1}'s {\sl right} endpoint and
|
||||
\ccc{c2}'s {\sl left} endpoint. The direction of \ccc{c} should be preserved:
|
||||
in case \ccc{c} is directed from left to right then \ccc{p} becomes \ccc{c1}'s
|
||||
target and \ccc{c2}'s source; otherwise, \ccc{p} becomes \ccc{c2}'s
|
||||
target and \ccc{c1}'s source.}
|
||||
{models the concept \ccc{ArrDirectionalTraits::Split_2}.}
|
||||
|
||||
\ccNestedType{Are_mergeable_2}
|
||||
{models the concept \ccc{ArrDirectionalTraits::AreMergeable_2}.}
|
||||
|
||||
\ccNestedType{Merge_2}
|
||||
{models the concept \ccc{ArrDirectionalTraits::Merge_2}.}
|
||||
|
||||
\ccCreation
|
||||
\ccCreationVariable{traits}
|
||||
|
|
@ -104,7 +75,9 @@ In addition, the two following functors, required by the concept
|
|||
\ccc{CGAL::Arr_non_caching_segment_traits_2<Kernel>} \\
|
||||
\ccc{CGAL::Arr_circle_segment_traits_2<Kernel>} \\
|
||||
\ccc{CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>} \\
|
||||
\ccc{CGAL::Arr_rational_arc_traits_2<AlgKernel,NtTraits>}
|
||||
\ccc{CGAL::Arr_rational_function_traits_2<AlgKernel,NtTraits>}\\
|
||||
\ccc{CGAL::Arr_Bezier_curve_traits_2<RatKernel,AlgKernel,NtTraits>}\\
|
||||
\ccc{CGAL::Arr_algebraic_segment_traits_2<Coefficient>}
|
||||
|
||||
\ccSeeAlso
|
||||
%=========
|
||||
|
|
@ -115,3 +88,147 @@ In addition, the two following functors, required by the concept
|
|||
\end{ccRefConcept}
|
||||
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% Functors %%%%%%%%
|
||||
|
||||
%%%%%%%% Intersect_2
|
||||
% ==================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrDirectionalTraits::Intersect_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementDirectionalXMonotoneTraits_2::Intersect_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccMethod{Output_iterator operator()(ArrDirectionalTraits::X_monotone_curve_2 xc1,
|
||||
ArrDirectionalTraits::X_monotone_curve_2 xc2,
|
||||
Output_iterator& oi);}
|
||||
{computes the intersections of \ccc{xc1} and \ccc{xc2} and
|
||||
inserts them \emph{in an ascending lexicographic $xy$-order} into the
|
||||
output iterator \ccc{oi}. The value-type of \ccc{Output_iterator} is
|
||||
\ccc{CGAL::Object}, where each \ccc{Object} wraps either a
|
||||
\ccc{pair<ArrDirectionalTraits::Point_2, ArrDirectionalTraits::Multiplicity>} object, which
|
||||
represents an intersection point with its multiplicity (in case the
|
||||
multiplicity is undefined or unknown, it is set to $0$) or an
|
||||
\ccc{ArrDirectionalTraits::X_monotone_curve_2} object, representing an
|
||||
overlapping subcurve of \ccc{xc1} and \ccc{xc2}. In the latter case,
|
||||
the overlapping subcurves are given the direction of \ccc{xc1} and
|
||||
\ccc{xc2} if their directions are identical. Otherwise, the overlapping
|
||||
subcurves are given an arbitrary direction. The operator returns a
|
||||
past-the-end iterator for the output sequence.}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% Split_2
|
||||
% ==============
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrDirectionalTraits::Split_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementDirectionalXMonotoneTraits_2::Split_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\def\ccTagRmConstRefPair{\ccFalse}%
|
||||
\ccMethod{void operator()(ArrDirectionalTraits::X_monotone_curve_2 xc,
|
||||
ArrDirectionalTraits::Point_2 p,
|
||||
ArrDirectionalTraits::X_monotone_curve_2& xc1,
|
||||
ArrDirectionalTraits::X_monotone_curve_2& xc2);}
|
||||
{accepts an input curve \ccc{xc} and a split point \ccc{p} in its
|
||||
interior. It splits \ccc{xc} at the split point into two subcurves
|
||||
\ccc{xc1} and \ccc{xc2}, such that \ccc{p} is \ccc{xc1}'s \emph{right}
|
||||
endpoint and \ccc{xc2}'s \emph{left} endpoint. The direction of \ccc{xc}
|
||||
is preserved. That is, in case \ccc{xc} is directed from left to right,
|
||||
\ccc{p} becomes \ccc{xc1}'s target and \ccc{c2}'s source;
|
||||
otherwise, \ccc{p} becomes \ccc{xc2}'s target and \ccc{xc1}'s source.}%
|
||||
\ccTagDefaults
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% AreMergeable_2
|
||||
% =====================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrDirectionalTraits::AreMergeable_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementDirectionalXMonotoneTraits_2::Are_mergeable_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\def\ccTagRmConstRefPair{\ccFalse}%
|
||||
\ccMethod{bool operator()(ArrDirectionalTraits::X_monotone_curve_2 xc1,
|
||||
ArrDirectionalTraits::X_monotone_curve_2 xc2);}
|
||||
{accepts two $x$-monotone curves \ccc{xc1} and \ccc{xc2} and determines
|
||||
whether they can be merged to form a single $x$-monotone curve.
|
||||
\ccc{xc1} and \ccc{xc2} are mergeable if their underlying curves are
|
||||
identical, they share a common endpoint, and they do not bend to form
|
||||
a non-$x$-monotone curve.
|
||||
\ccPrecond{The target point of \ccc{xc1} and the source point \ccc{xc2}
|
||||
coincide or the source point of \ccc{xc2} and the target
|
||||
point \ccc{xc2} coincide.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% Merge_2
|
||||
% ==============
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrDirectionalTraits::Merge_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementDirectionalXMonotoneTraits_2::Merge_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\def\ccTagRmConstRefPair{\ccFalse}%
|
||||
\ccMethod{void operator()(ArrDirectionalTraits::X_monotone_curve_2 xc1,
|
||||
ArrDirectionalTraits::X_monotone_curve_2 xc2,
|
||||
ArrDirectionalTraits::X_monotone_curve_2& xc);}
|
||||
{accepts two \emph{mergeable} $x$-monotone curves \ccc{xc1} and
|
||||
\ccc{xc2} and asigns \ccc{xc} with the merged curve. If the target
|
||||
point of \ccc{xc1} and the source point of \ccc{xc2} coincide; then
|
||||
the source point of \ccc{xc1} and the target point of \ccc{xc2} become
|
||||
the source and target points of \ccc{xc}, respectively. If the target
|
||||
point of \ccc{xc2} and the source point of \ccc{xc1} coincide; then
|
||||
the source point of \ccc{xc2} and the target point of \ccc{xc1} become
|
||||
the source and target points of \ccc{xc}, respectively.
|
||||
\ccPrecond{\ccc{are_mergeable_2}(\ccc{xc1}, \ccc{xc2}) is true.}}
|
||||
\ccTagDefaults
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% CompareEndpointsXy_2
|
||||
% ===========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrDirectionalTraits::CompareEndpointsXy_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementDirectionalXMonotoneTraits_2::CompareEndpointsXy_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\def\ccTagRmConstRefPair{\ccFalse}%
|
||||
\ccMethod{Comparison_result operator()(ArrDirectionalTraits::X_monotone_curve_2 xc);}
|
||||
{accepts an input curve \ccc{xc} and compares its source and target
|
||||
points. It returns \ccc{SMALLER} if the curve is directed from
|
||||
lexicographically left to right, and \ccc{LARGER} if it is directed
|
||||
from lexicographically right to left.}
|
||||
|
||||
\ccTagDefaults
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% ConstructOpposite_2
|
||||
% ===========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrDirectionalTraits::ConstructOpposite_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementDirectionalXMonotoneTraits_2::ConstructOpposite_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\def\ccTagRmConstRefPair{\ccFalse}%
|
||||
\ccMethod{ArrDirectionalTraits::X_monotone_curve_2 operator()(ArrDirectionalTraits::X_monotone_curve_2 xc);}
|
||||
{accepts an $x$-monotone curve \ccc{xc} and returns its opposite curve,
|
||||
namely a curve whose graph is the same as \ccc{xc}'s, and whose source and
|
||||
target are swapped with respect to \ccc{xc}'s source and target.}
|
||||
|
||||
\ccTagDefaults
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
|
|
|||
Loading…
Reference in New Issue