cgal/Kernel_23/doc/Kernel_23/CGAL/Spherical_kernel_intersecti...

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4.5 KiB
C++

namespace CGAL {
/*!
\ingroup do_intersect_spherical_grp
\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel for details on a spherical kernel instantiation.
When using a spherical kernel, in addition to the function overloads documented \ref do_intersect_linear_grp "here",
the following function overloads are also available.
*/
/// @{
/*!
checks whether `obj1` and `obj2` intersect. Two objects `obj1` and
`obj2` intersect if there is a point `p` that is part of both `obj1`
and `obj2`. The intersection region of those two objects is defined
as the set of all points `p` that are part of both `obj1` and `obj2`.
Note that while for a polygon we consider the enclosed domain, for an
object of type `Circle_3` or `Sphere_3` only the curve
or the surface is considered.
`Type1` and `Type2` can be any of
the following:
- `Line_3<SphericalKernel>`
- `Circle_3<SphericalKernel>`
- `Plane_3<SphericalKernel>`
- `Sphere_3<SphericalKernel>`
- `Line_arc_3<SphericalKernel>`
- `Circular_arc_3<SphericalKernel>`
An example illustrating this is presented in
Chapter \ref Chapter_3D_Spherical_Geometry_Kernel.
*/
bool do_intersect(Type1<SphericalKernel> obj1, Type2<SphericalKernel> obj2);
/*!
checks whether `obj1`, `obj2` and `obj3` intersect.
`Type1`, `Type2` and `Type3` can be:
- `Sphere_3<SphericalKernel>`
- `Plane_3<SphericalKernel>`
*/
bool do_intersect(Type1<SphericalKernel> obj1, Type2<SphericalKernel> obj2, Type3<SphericalKernel> obj3);
/// @}
/*!
\ingroup intersection_spherical_grp
\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel for details on a spherical kernel instantiation.
When using a spherical kernel, in addition to the function overloads documented \ref intersection_linear_grp "here",
the following function overloads are also available.
The iterator versions of those functions can be used in conjunction
with `Dispatch_output_iterator`.
Since both the number of intersections, if any, and their types, depend
on the arguments, the function expects an output iterator on
`decltype(std::declval<Kernel::Intersect_3>()(std::declval<Type1>(), std::declval<Type2>()))`,
as presented below.
*/
/// @{
/*!
Constructs the intersection elements between the two input
objects and stores them in the OutputIterator in lexicographic order,
where both, `SphericalType1` and `SphericalType2`, can be either
- `Sphere_3<SphericalKernel>`,
- `Plane_3<SphericalKernel>`,
- `Line_3<SphericalKernel>`,
- `Circle_3<SphericalKernel>`,
- `Line_arc_3<SphericalKernel>` or
- `Circular_arc_3<SphericalKernel>`,
and depending on the types `SphericalType1` and `SphericalType2`, the computed
type can be
- `std::pair<Circular_arc_point_3<SphericalKernel>, unsigned>`,
where the unsigned integer is the multiplicity of the corresponding
intersection point between `obj1` and `obj2`,
- `SphericalType1`, when `SphericalType1` and `SphericalType2` are equal,
and if the two objets `obj1` and `obj2` are equal,
- `Line_3<SphericalKernel>` or
`Circle_3<SphericalKernel>` when `SphericalType1` and `SphericalType2`
are two-dimensional objects intersecting along a curve (2 planes, or 2
spheres, or one plane and one sphere),
- `Circular_arc_3<SphericalKernel>` in case of an overlap of
two circular arcs or
- `Line_arc_3<SphericalKernel>` in case of an overlap of two
line segments.
*/
template < typename SphericalType1, typename SphericalType1, typename OutputIterator >
OutputIterator
intersection(const SphericalType1 &obj1, const SphericalType2 &obj2,
OutputIterator intersections);
/*!
Copies in the output iterator the intersection elements between the
three objects. `intersections` iterates on
elements of type `boost::variant< Circle_3, Plane_3, Sphere_3, std::pair< Circular_arc_point_3, unsigned > >`, in lexicographic order
when this ordering is defined on the computed objects
where `Type1`, `Type2` and `Type3`
can be either
- `Sphere_3<SphericalKernel>` or
- `Plane_3<SphericalKernel>`
and depending of these types, the computed return value
- `std::pair<Circular_arc_point_3<SphericalKernel>, unsigned>`,
where the unsigned integer is the multiplicity of the corresponding
intersection point,
- `Circle_3<SphericalKernel>` or
- `Type1`, when `Type1`, `Type2` and
`Type3` are equal, and if the three objets `obj1` and `obj2`
and `obj3` are equal.
*/
template < typename Type1, typename Type2, typename Type3, typename OutputIterator >
OutputIterator
intersection(const Type1 &obj1, const Type2 &obj2, const Type3 &obj3,
OutputIterator intersections);
/// @}
} // CGAL