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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],[Flö03b]). 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 |
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The sample points P 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 P 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 |
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| 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 > |
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| 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 > |
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| 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 > |
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| 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 > |
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| The same as above with the parameter max_distance. | ||||
The next function allows to filter some potential neighbors of the query point p from P via its three-dimensional Delaunay triangulation. All surface neighbors of p are necessarily neighbors in the Delaunay triangulation of P ∪ {p}.
| template < class Dt, class OutputIterator > | ||||
| OutputIterator |
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| 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 |
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| 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>. | ||||