CGAL::surface_neighbors_3

Definition

Given a set of sample points issued from a surface and a query point p, the function surface_neighbors_3 computes the neighbors of p on the surface within the sample points. If the sampling is sufficiently dense, the neighbors are provably close to the point p on the surface (cf. the manual pages and [BF02],[Flö03]). They are defined to be the neighbors of p in the regular triangulation dual to the power diagram which is equivalent to the intersection of the Voronoi cell of the query point p with the tangent plane to the surface at p.

#include <CGAL/surface_neighbors_3.h>

template <class OutputIterator, class InputIterator, class Kernel>
OutputIterator	surface_neighbors_3 ( InputIterator first, InputIterator beyond, typename Kernel::Point_3 p, typename Kernel::Vector_3 normal, OutputIterator out, Kernel K)
		The sample points $$ are provided in the range $$[.first, beyond$$.). InputIterator::value_type is the point type Kernel::Point_3. The tangent plane is defined by the point p and the vector normal. The parameter K determines the kernel type that will instantiate the template parameter of Voronoi_intersection_2_traits_3<K>. The surface neighbors of p are computed which are the neighbors of p in the regular triangulation that is dual to the intersection of the $$3D Voronoi diagram of $$ with the tangent plane. The point sequence that is computed by the function is placed starting at out. The function returns an iterator that is placed past-the-end of the resulting point sequence.
template <class OutputIterator, class InputIterator, class ITraits>
OutputIterator	surface_neighbors_3 ( InputIterator first, InputIterator beyond, typename ITraits::Point_2 p, OutputIterator out, ITraits traits)
		the same as above only that the traits class must be instantiated by the user. ITraits must be equivalent to Voronoi_intersection_2_traits_3<K>.

The next functions return, in addition, a boolean value that certifies whether or not, the Voronoi cell of p can be affected by points that lie outside the input range, i.e. outside the ball centered on p passing through the furthest sample point from p in the range $$[.first, beyond$$.). If the sample points are collected by a $$k-nearest neighbor or a range search query, this permits to verify that a large enough neighborhood has been considered.

template <class OutputIterator, class InputIterator, class Kernel>
std::pair< OutputIterator, bool >
	surface_neighbors_certified_3 ( InputIterator first, InputIterator beyond, typename Kernel::Point_3 p, typename Kernel::Vector_3 normal, OutputIterator out, Kernel K)
		Similar to the first function. The additional third return value is true if the furthest point in the range $$[.first, beyond$$.) is further away from p than twice the distance from p to the furthest vertex of the intersection of the Voronoi cell of p with the tangent plane defined be (p,normal). It is false otherwise.
template <class OutputIterator, class InputIterator, class Kernel>
std::pair< OutputIterator, bool >
	surface_neighbors_certified_3 ( InputIterator first, InputIterator beyond, typename Kernel::Point_2 p, typename Kernel::FT max_distance, OutputIterator out, Kernel kernel)
		The same as above except that this function takes the maximal distance from p to the points in the range $$[.first, beyond$$.) as additional parameter.
template <class OutputIterator, class InputIterator, class ITraits>
std::pair< OutputIterator, bool >
	surface_neighbors_certified_3 ( InputIterator first, InputIterator beyond, typename ITraits::Point_2 p, OutputIterator out, ITraits traits)
		The same as above only that the traits class must be instantiated by the user. ITraits must be equivalent to Voronoi_intersection_2_traits_3<K>. There is no parameter max_distance.
template <class OutputIterator, class InputIterator, class ITraits>
std::pair< OutputIterator, bool >
	surface_neighbors_certified_3 ( InputIterator first, InputIterator beyond, typename ITraits::Point_2 p, typename ITraits::FT max_distance, OutputIterator out, ITraits traits)
		The same as above with the parameter max_distance.

The next function allows to filter some potential neighbors of the query point p from $$ via its three-dimensional Delaunay triangulation. All surface neighbors of p are necessarily neighbors in the Delaunay triangulation of $$ {p}.

template < class Dt, class OutputIterator >
OutputIterator	surface_neighbors_3 ( Dt dt, typename Dt::Geom_traits::Point_2 p, typename Dt::Geom_traits::Vector_3 normal, OutputIterator out, typename Dt::Face_handle start = typename Dt::Face_handle())
		computes the surface neighbor coordinates with respect to the points that are vertices of the Delaunay triangulation dt. The type Dt must be equivalent to Delaunay_triangulation_3<Gt, Tds>. The optional parameter start is used for the used as a starting place for the search of the conflict zone. It may be the result of the call dt.locate(p). This function instantiates the template parameter ITraits to be Voronoi_intersection_2_traits_3<Dt::Geom_traits>.
template < class Dt, class OutputIterator, class ITraits>
OutputIterator	surface_neighbors_3 ( Dt dt, typename Dt::Geom_traits::Point_2 p, OutputIterator out, ITraits traits, typename Dt::Face_handle start = typename Dt::Face_handle())
		The same as above only that the parameter traits instantiates the geometric traits class. Its type ITraits must be equivalent to Voronoi_intersection_2_traits_3<K>.

Requirements

1. Dt is equivalent to the class Delaunay_triangulation_3.
2. OutputIterator::value_type is equivalent to Dt::Point_3, i.e. a point type.
3. ITraits is equivalent to the class Voronoi_intersection_2_traits_3<K>.

See Also

Implementation