mirror of https://github.com/CGAL/cgal
110 lines
4.2 KiB
TeX
110 lines
4.2 KiB
TeX
\begin{ccRefFunction}{do_intersect}
|
|
|
|
\ccUnchecked{
|
|
\ccRefLabel{Kernel::do_intersect}
|
|
\ccFunction{bool do_intersect(Type1 obj1, Type2 obj2);}
|
|
{checks whether \ccc{obj1} and \ccc{obj2} intersect.
|
|
Two objects \ccStyle{obj1} and \ccStyle{obj2} intersect if there is a point
|
|
\ccStyle{p} that is part of both \ccStyle{obj1} and \ccStyle{obj2}.
|
|
The \ccHtmlNoLinksFrom{intersection} region of those two objects is defined as the set of all
|
|
points \ccStyle{p} that are part of both \ccStyle{obj1} and \ccStyle{obj2}.
|
|
Note that for objects like triangles and polygons that enclose a
|
|
bounded region, this region is part of the object.
|
|
}}
|
|
|
|
Depending on which \cgal\ \ccHtmlNoLinksFrom{kernel} is used,
|
|
\ccStyle{Type1} and \ccStyle{Type2} can be of different types.
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\paragraph{With the basic 2D and 3D Kernel} (see Chapter~\ref{chapter-kernel-23})
|
|
|
|
\ccInclude{CGAL/intersections.h}
|
|
|
|
The types \ccStyle{Type1} and \ccStyle{Type2} can be any of the following:
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Point_2<Kernel>}
|
|
\item \ccStyle{Line_2<Kernel>}
|
|
\item \ccStyle{Ray_2<Kernel>}
|
|
\item \ccStyle{Segment_2<Kernel>}
|
|
\item \ccStyle{Triangle_2<Kernel>}
|
|
\item \ccStyle{Iso_rectangle_2<Kernel>}
|
|
\end{itemize}
|
|
|
|
Also, \ccStyle{Type1} and \ccStyle{Type2} can be both of type
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Line_2<Kernel>}
|
|
\item \ccStyle{Circle_2<Kernel>}
|
|
\end{itemize}
|
|
|
|
In three-dimensional space, the types \ccStyle{Type1} and
|
|
\ccStyle{Type2} can be any of the following:
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Plane_3<Kernel>}
|
|
\item \ccStyle{Line_3<Kernel>}
|
|
\item \ccStyle{Ray_3<Kernel>}
|
|
\item \ccStyle{Segment_3<Kernel>}
|
|
\item \ccStyle{Triangle_3<Kernel>}.
|
|
\item \ccStyle{Bbox_3}.
|
|
\end{itemize}
|
|
|
|
Also, \ccc{Type1} and \ccc{Type2} can be respectively of types
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Triangle_3<Kernel>} and \ccStyle{Tetrahedron_3<Kernel>}
|
|
\item \ccStyle{Plane_3<Kernel>} and \ccStyle{Sphere_3<Kernel>} (or the contrary)
|
|
\item \ccStyle{Sphere_3<Kernel>} and \ccStyle{Sphere_3<Kernel>}.
|
|
\end{itemize}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\paragraph{With the 2D Circular Kernel} (see Chapter~\ref{chapter-circular-kernel})
|
|
|
|
\ccInclude{CGAL/Circular_kernel_intersections.h}
|
|
|
|
If this kernel is used, in addition to the combinations of 2D types
|
|
previously listed, \ccStyle{Type1} and \ccStyle{Type2} can be any of
|
|
the following:
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Line_2<CircularKernel>}
|
|
\item \ccStyle{Circle_2<CircularKernel>}
|
|
\item \ccStyle{Line_arc_2<CircularKernel>}
|
|
\item \ccStyle{Circular_arc_2<CircularKernel>}
|
|
\end{itemize}
|
|
|
|
An example illustrating this is presented in
|
|
Chapter~\ref{chapter-circular-kernel}.
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\paragraph{With the 3D Spherical Kernel} (see Chapter~\ref{chapter-spherical-kernel})
|
|
|
|
\ccInclude{CGAL/Spherical_kernel_intersections.h}
|
|
|
|
If this kernel is used, in addition to the combinations of 3D types
|
|
previously listed, \ccStyle{Type1} and \ccStyle{Type2} can be any of
|
|
the following:
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Line_3<SphericalKernel>}
|
|
\item \ccStyle{Circle_3<SphericalKernel>}
|
|
\item \ccStyle{Plane_3<SphericalKernel>}
|
|
\item \ccStyle{Sphere_3<SphericalKernel>}
|
|
\item \ccStyle{Line_arc_3<SphericalKernel>}
|
|
\item \ccStyle{Circular_arc_3<SphericalKernel>}
|
|
\end{itemize}
|
|
|
|
An example illustrating this is presented in
|
|
Chapter~\ref{chapter-spherical-kernel}.
|
|
|
|
Also, another predicate is provided with this kernel:
|
|
|
|
\ccFunction{bool do_intersect(Type1 obj1, Type2 obj2, Type3 obj3);}
|
|
{checks whether \ccc{obj1}, \ccc{obj2} and \ccc{obj3} intersect.}
|
|
|
|
where \ccStyle{Type1}, \ccStyle{Type2} and \ccStyle{Type3} can be:
|
|
\begin{itemize}\ccTexHtml{\itemsep0pt\topsep0pt\partopsep0pt\parskip0pt\parsep0pt}{}
|
|
\item \ccStyle{Sphere_3<SphericalKernel>}
|
|
\item \ccStyle{Plane_3<SphericalKernel>}
|
|
\end{itemize}
|
|
|
|
\ccSeeAlso
|
|
\ccRefIdfierPage{CGAL::intersection}
|
|
|
|
\end{ccRefFunction}
|