CGAL::intersection() (3D Spherical Kernel)

template<typename SphericalType1, typename SphericalType1, typename OutputIterator>
OutputIterator	CGAL::intersection (const SphericalType1 &obj1, const SphericalType2 &obj2, OutputIterator intersections)
	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.
template<typename Type1, typename Type2, typename Type3, typename OutputIterator>
OutputIterator	CGAL::intersection (const Type1 &obj1, const Type2 &obj2, const Type3 &obj3, OutputIterator intersections)
	Copies in the output iterator the intersection elements between the three objects.

Function Documentation

intersection() [1/2]

template<typename SphericalType1, typename SphericalType1, typename OutputIterator>

OutputIterator CGAL::intersection	(	const SphericalType1 &	obj1,
		const SphericalType2 &	obj2,
		OutputIterator	intersections )

#include <CGAL/Spherical_kernel_intersections.h>

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.

See Chapter Chapter_3D_Spherical_Geometry_Kernel for details on a spherical kernel instantiation.

When using a spherical kernel, in addition to the function overloads documented 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 types of the intersection results depend on the arguments, the function expects an output iterator on Kernel::Intersect_3(Type1, Type2) as presented below.

• 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 objects 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.

intersection() [2/2]

template<typename Type1, typename Type2, typename Type3, typename OutputIterator>

OutputIterator CGAL::intersection	(	const Type1 &	obj1,
		const Type2 &	obj2,
		const Type3 &	obj3,
		OutputIterator	intersections )

#include <CGAL/Spherical_kernel_intersections.h>

Copies in the output iterator the intersection elements between the three objects.

intersections iterates on elements of type std::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 objects obj1 and obj2 and obj3 are equal.