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| template<class CoordinateInputIterator , class ValueFunctor > |
| ValueFunctor::result_type::first_type | linear_interpolation (CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, ValueFunctor value_function) |
| | The function linear_interpolation() computes the weighted sum of the function values which must be provided via a functor.
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| template<class CoordinateInputIterator , class ValueFunctor , class GradFunctor , class Traits , class Point > |
| ValueFunctor::result_type | quadratic_interpolation (CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, GradFunctor gradient_function, const Traits &traits) |
| | The function quadratic_interpolation() generates the interpolated function value as the weighted sum of the values plus a linear term in the gradient for each entity of the entity/coordinate pairs in the range [first, beyond).
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| template<class CoordinateInputIterator , class ValueFunctor , class GradFunctor , class Traits , class Point > |
| std::pair< typename ValueFunctor::result_type, bool > | sibson_c1_interpolation (CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, GradFunctor gradient_function, const Traits &traits) |
| | The function sibson_c1_interpolation() generates the interpolated function value at the point p, using functors for the function values and the gradients, by applying Sibson's \( Z^1\) interpolant.
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| template<class CoordinateInputIterator , class ValueFunctor , class GradFunctor , class Traits , class Point > |
| ValueFunctor::result_type | sibson_c1_interpolation_square (CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, GradFunctor gradient_function, const Traits &traits) |
| | Same as sibson_c1_interpolation(), except that no square root operation is required for the number type Traits::FT.
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| template<class CoordinateInputIterator , class ValueFunctor , class GradFunctor , class Traits , class Point > |
| ValueFunctor::result_type | farin_c1_interpolation (CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, GradFunctor gradient_function, const Traits &traits) |
| | Generates the interpolated function value computed by Farin's interpolant.
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| template<class Dt , class CoordinateOutputIterator , class OutputFunctor > |
| CGAL::Triple< CoordinateOutputIterator, typename Dt::Geom_traits::FT, bool > | natural_neighbor_coordinates_2 (const Dt &dt, const typename Dt::Geom_traits::Point_2 &p, CoordinateOutputIterator out, OutputFunctor fct, typename Dt::Face_handle start=typename Dt::Face_handle()) |
| | Computes the natural neighbor coordinates for p with respect to the points in the two-dimensional Delaunay triangulation dt.
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| template<class Dt , class CoordinateOutputIterator , class OutputFunctor , class EdgeIterator > |
| CGAL::Triple< CoordinateOutputIterator, typename Dt::Geom_traits::FT, bool > | natural_neighbor_coordinates_2 (const Dt &dt, const typename Dt::Geom_traits::Point_2 &p, CoordinateOutputIterator out, OutputFunctor fct, EdgeIterator hole_begin, EdgeIterator hole_end) |
| | Computes the natural neighbor coordinates for p with respect to the points in the two-dimensional Delaunay triangulation dt.
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| template<class Dt , class CoordinateOutputIterator , class OutputFunctor > |
| CGAL::Triple< CoordinateOutputIterator, typename Dt::Geom_traits::FT, bool > | natural_neighbor_coordinates_2 (const Dt &dt, typename Dt::Vertex_handle vh, CoordinateOutputIterator out, OutputFunctor fct) |
| | Computes the natural neighbor coordinates of the point vh->point() with respect to the vertices of dt excluding vh->point().
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| template<class Rt , class CoordinateOutputIterator , class OutputFunctor > |
| CGAL::Triple< CoordinateOutputIterator, typename Rt::Geom_traits::FT, bool > | regular_neighbor_coordinates_2 (const Rt &rt, const typename Rt::Weighted_point &p, CoordinateOutputIterator out, OutputFunctor fct, typename Rt::Face_handle start=typename Rt::Face_handle()) |
| | Computes the regular neighbor coordinates for p with respect to the weighted points in the two-dimensional regular triangulation rt.
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| template<class Rt , class CoordinateOutputIterator , class OutputFunctor , class EdgeIterator , class VertexIterator > |
| CGAL::Triple< CoordinateOutputIterator, typename Traits::FT, bool > | regular_neighbor_coordinates_2 (const Rt &rt, const typename Traits::Weighted_point &p, CoordinateOutputIterator out, OutputFunctor fct, EdgeIterator hole_begin, EdgeIterator hole_end, VertexIterator hidden_vertices_begin, VertexIterator hidden_vertices_end) |
| | Computes the regular neighbor coordinates for p with respect to the weighted points in the two-dimensional regular triangulation rt.
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| template<class Rt , class CoordinateOutputIterator , class OutputFunctor > |
| CGAL::Triple< CoordinateOutputIterator, typename Rt::Geom_traits::FT, bool > | regular_neighbor_coordinates_2 (const Rt &rt, typename Rt::Vertex_handle vh, CoordinateOutputIterator out, OutputFunctor fct) |
| | Computes the regular neighbor coordinates of the point vh->point() with respect to the vertices of rt excluding vh->point().
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| template<class CoordinateInputIterator , class ValueFunctor , class Traits , class Point > |
| Traits::Vector_d | sibson_gradient_fitting (CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, const typename ValueFunctor::result_type::first_type fn, const Traits &traits) |
| | Estimates the gradient of a function at a query point.
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| template<class Dt , class GradientOutputIterator , class OutputFunctor , class ValueFunctor , class Traits > |
| GradientOutputIterator | sibson_gradient_fitting_nn_2 (const Dt &dt, GradientOutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits &traits) |
| | Estimates the function gradients at all vertices of the Delaunay triangulation dt that lie inside the convex hull, using the coordinates computed by the function CGAL::natural_neighbor_coordinates_2().
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| template<class Rt , class GradientOutputIterator , class OutputFunctor , class ValueFunctor , class Traits > |
| GradientOutputIterator | sibson_gradient_fitting_rn_2 (const Rt &rt, GradientOutputIterator out, OutputFunctor fct, ValueFunctor value_function, const Traits &traits) |
| | Estimates the function gradients at all vertices of rt that lie inside the convex hull using the coordinates computed by the functions CGAL::regular_neighbor_coordinates_2().
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| template<class OutputIterator , class InputIterator , class Kernel > |
| CGAL::Triple< OutputIterator, typename Kernel::FT, bool > | surface_neighbor_coordinates_3 (InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::Vector_3 &normal, OutputIterator out, const Kernel &K) |
| | The sample points \( \mathcal{P}\) are provided in the range [first, beyond).
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| template<class OutputIterator , class InputIterator , class ITraits > |
| CGAL::Triple< OutputIterator, typename ITraits::FT, bool > | surface_neighbor_coordinates_3 (InputIterator first, InputIterator beyond, const typename ITraits::Point_2 &p, OutputIterator out, const ITraits &traits) |
| | Same as above only that the traits class must be instantiated by the user.
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| template<class OutputIterator , class InputIterator , class Kernel > |
| CGAL::Quadruple< OutputIterator, typename Kernel::FT, bool, bool > | surface_neighbor_coordinates_certified_3 (InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::Vector_3 &normal, OutputIterator out, const Kernel &K) |
| | Similar to the first function.
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template<class OutputIterator , class InputIterator , class Kernel > |
| CGAL::Quadruple< OutputIterator, typename Kernel::FT, bool, bool > | surface_neighbor_coordinates_certified_3 (InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::FT &max_distance, OutputIterator out, const Kernel &kernel) |
| | Same as above except that this function takes the maximal distance from p to the points in the range [first, beyond) as additional parameter.
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| template<class OutputIterator , class InputIterator , class ITraits > |
| CGAL::Quadruple< OutputIterator, typename ITraits::FT, bool, bool > | surface_neighbor_coordinates_certified_3 (InputIterator first, InputIterator beyond, const typename ITraits::Point_2 &p, OutputIterator out, const ITraits &traits) |
| | Same as above only that the traits class must be instantiated by the user and without the parameter max_distance.
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template<class OutputIterator , class InputIterator , class ITraits > |
| CGAL::Quadruple< OutputIterator, typename ITraits::FT, bool, bool > | surface_neighbor_coordinates_certified_3 (InputIterator first, InputIterator beyond, const typename ITraits::Point_2 &p, const typename ITraits::FT &max_distance, OutputIterator out, const ITraits &traits) |
| | Same as above with the parameter max_distance.
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| template<class Dt , class OutputIterator > |
| CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > | surface_neighbor_coordinates_3 (const Dt &dt, const typename Dt::Geom_traits::Point_3 &p, const typename Dt::Geom_traits::Vector_3 &normal, OutputIterator out, typename Dt::Cell_handle start=typename Dt::Cell_handle()) |
| | Computes the surface neighbor coordinates with respect to the points that are vertices of the Delaunay triangulation dt.
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| template<class Dt , class OutputIterator , class ITraits > |
| CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > | surface_neighbor_coordinates_3 (const Dt &dt, const typename Dt::Geom_traits::Point_3 &p, OutputIterator out, const ITraits &traits, typename Dt::Cell_handle start=typename Dt::Cell_handle()) |
| | Same as above only that the parameter traits instantiates the geometric traits class.
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| template<class OutputIterator , class InputIterator , class Kernel > |
| OutputIterator | surface_neighbors_3 (InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::Vector_3 &normal, OutputIterator out, const Kernel &K) |
| | The sample points \( \mathcal{P}\) are provided in the range [first, beyond).
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| template<class OutputIterator , class InputIterator , class ITraits > |
| OutputIterator | surface_neighbors_3 (InputIterator first, InputIterator beyond, const typename ITraits::Point_2 &p, OutputIterator out, const ITraits &traits) |
| | Same as above only that the traits class must be instantiated by the user.
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| template<class OutputIterator , class InputIterator , class Kernel > |
| std::pair< OutputIterator, bool > | surface_neighbors_certified_3 (InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::Vector_3 &normal, OutputIterator out, const Kernel &K) |
| | Similar to the first function.
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template<class OutputIterator , class InputIterator , class Kernel > |
| std::pair< OutputIterator, bool > | surface_neighbors_certified_3 (InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::Vector_3 &normal, const typename Kernel::FT &max_distance, OutputIterator out, const Kernel &kernel) |
| | Same as above except that this function takes the maximal distance from p to the points in the range [first, beyond) as additional parameter.
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| template<class OutputIterator , class InputIterator , class ITraits > |
| std::pair< OutputIterator, bool > | surface_neighbors_certified_3 (InputIterator first, InputIterator beyond, const typename ITraits::Point_2 &p, OutputIterator out, const ITraits &traits) |
| | Same as above only that the traits class must be instantiated by the user.
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template<class OutputIterator , class InputIterator , class ITraits > |
| std::pair< OutputIterator, bool > | surface_neighbors_certified_3 (InputIterator first, InputIterator beyond, const typename ITraits::Point_2 &p, const typename ITraits::FT &max_distance, OutputIterator out, const ITraits &traits) |
| | Same as above with the parameter max_distance.
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| template<class Dt , class OutputIterator > |
| OutputIterator | surface_neighbors_3 (const Dt &dt, const typename Dt::Geom_traits::Point_3 &p, const typename Dt::Geom_traits::Vector_3 &normal, OutputIterator out, typename Dt::Cell_handle start=typename Dt::Cell_handle()) |
| | Computes the surface neighbor coordinates with respect to the points that are vertices of the Delaunay triangulation dt.
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| template<class Dt , class OutputIterator , class ITraits > |
| OutputIterator | surface_neighbors_3 (const Dt &dt, const typename ITraits::Point_2 &p, OutputIterator out, const ITraits &traits, typename Dt::Cell_handle start=typename Dt::Cell_handle()) |
| | Same as above only that the parameter traits instantiates the geometric traits class.
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