\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.3 - 2D and Surface Function Interpolation
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CGAL Namespace Reference

Namespaces

 cpp11
 
 IO
 

Classes

class  Aff_transformation_2
 
class  Aff_transformation_3
 
class  Identity_transformation
 
class  Reflection
 
class  Rotation
 
class  Scaling
 
class  Translation
 
class  Bbox_2
 
class  Bbox_3
 
class  Cartesian
 
class  Cartesian_converter
 
class  Circle_2
 
class  Circle_3
 
class  Ambient_dimension
 
class  Dimension_tag
 
class  Dynamic_dimension_tag
 
class  Feature_dimension
 
class  Direction_2
 
class  Direction_3
 
class  Exact_predicates_exact_constructions_kernel
 
class  Exact_predicates_exact_constructions_kernel_with_sqrt
 
class  Exact_predicates_inexact_constructions_kernel
 
class  Filtered_kernel_adaptor
 
class  Filtered_kernel
 
class  Filtered_predicate
 
class  Homogeneous
 
class  Homogeneous_converter
 
class  Iso_cuboid_3
 
class  Iso_rectangle_2
 
class  Kernel_traits
 
class  Line_2
 
class  Line_3
 
class  Null_vector
 
class  Origin
 
class  Plane_3
 
class  Point_2
 
class  Point_3
 
class  Projection_traits_xy_3
 
class  Projection_traits_xz_3
 
class  Projection_traits_yz_3
 
class  Ray_2
 
class  Ray_3
 
class  Segment_2
 
class  Segment_3
 
class  Simple_cartesian
 
class  Simple_homogeneous
 
class  Sphere_3
 
class  Tetrahedron_3
 
class  Triangle_2
 
class  Triangle_3
 
class  Vector_2
 
class  Vector_3
 
class  Compact_container_base
 
class  Compact_container
 
class  Compact_container_traits
 
class  Compact
 
class  Fast
 
class  Default
 
class  Fourtuple
 
class  Cast_function_object
 
class  Compare_to_less
 
class  Creator_1
 
class  Creator_2
 
class  Creator_3
 
class  Creator_4
 
class  Creator_5
 
class  Creator_uniform_2
 
class  Creator_uniform_3
 
class  Creator_uniform_4
 
class  Creator_uniform_5
 
class  Creator_uniform_6
 
class  Creator_uniform_7
 
class  Creator_uniform_8
 
class  Creator_uniform_9
 
class  Creator_uniform_d
 
class  Dereference
 
class  Get_address
 
class  Identity
 
class  Project_facet
 
class  Project_next
 
class  Project_next_opposite
 
class  Project_normal
 
class  Project_opposite_prev
 
class  Project_plane
 
class  Project_point
 
class  Project_prev
 
class  Project_vertex
 
class  In_place_list_base
 
class  In_place_list
 
class  Const_oneset_iterator
 
class  Counting_iterator
 
class  Dispatch_or_drop_output_iterator
 
class  Dispatch_output_iterator
 
class  Emptyset_iterator
 
class  Filter_iterator
 
class  Insert_iterator
 
class  Inverse_index
 
class  Join_input_iterator_1
 
class  Join_input_iterator_2
 
class  Join_input_iterator_3
 
class  N_step_adaptor
 
class  Oneset_iterator
 
class  Random_access_adaptor
 
class  Random_access_value_adaptor
 
class  Location_policy
 
class  Multiset
 
class  Object
 
class  Sixtuple
 
class  Boolean_tag
 
struct  Null_functor
 
struct  Sequential_tag
 
struct  Parallel_tag
 
class  Null_tag
 
class  Threetuple
 
class  Twotuple
 
class  Uncertain
 
class  Quadruple
 
class  Triple
 
class  Algebraic_structure_traits
 
class  Euclidean_ring_tag
 
class  Field_tag
 
class  Field_with_kth_root_tag
 
class  Field_with_root_of_tag
 
class  Field_with_sqrt_tag
 
class  Integral_domain_tag
 
class  Integral_domain_without_division_tag
 
class  Unique_factorization_domain_tag
 
class  Coercion_traits
 
class  Fraction_traits
 
class  Real_embeddable_traits
 
class  Circulator_from_container
 
class  Circulator_from_iterator
 
class  Circulator_traits
 
class  Container_from_circulator
 
struct  Circulator_tag
 
struct  Iterator_tag
 
struct  Forward_circulator_tag
 
struct  Bidirectional_circulator_tag
 
struct  Random_access_circulator_tag
 
struct  Circulator_base
 
struct  Forward_circulator_base
 
struct  Bidirectional_circulator_base
 
struct  Random_access_circulator_base
 
class  Forward_circulator_ptrbase
 
class  Bidirectional_circulator_ptrbase
 
class  Random_access_circulator_ptrbase
 
class  Color
 
class  Input_rep
 
class  Output_rep
 
class  Istream_iterator
 
class  Ostream_iterator
 
class  Verbose_ostream
 
class  Constrained_Delaunay_triangulation_2
 
struct  No_intersection_tag
 
struct  Exact_intersections_tag
 
struct  Exact_predicates_tag
 
class  Constrained_triangulation_2
 
class  Constrained_triangulation_face_base_2
 
class  Constrained_triangulation_plus_2
 
class  Delaunay_triangulation_2
 
struct  Weighted_point_mapper_2
 
class  Regular_triangulation_2
 
class  Regular_triangulation_euclidean_traits_2
 
class  Regular_triangulation_face_base_2
 
class  Regular_triangulation_filtered_traits_2
 
class  Regular_triangulation_vertex_base_2
 
class  Triangulation_2
 
class  Triangulation_cw_ccw_2
 
class  Triangulation_euclidean_traits_2
 
class  Triangulation_euclidean_traits_xy_3
 
class  Triangulation_face_base_2
 
class  Triangulation_face_base_with_info_2
 
class  Triangulation_hierarchy_2
 
class  Triangulation_hierarchy_vertex_base_2
 
class  Triangulation_vertex_base_2
 
class  Triangulation_vertex_base_with_info_2
 
class  Weighted_point
 
class  Delaunay_triangulation_3
 
class  Regular_triangulation_3
 
class  Regular_triangulation_cell_base_3
 
class  Regular_triangulation_euclidean_traits_3
 
class  Regular_triangulation_filtered_traits_3
 
class  Triangulation_3
 
class  Triangulation_cell_base_3
 
class  Triangulation_cell_base_with_circumcenter_3
 
class  Triangulation_cell_base_with_info_3
 
class  Triangulation_simplex_3
 
class  Triangulation_vertex_base_3
 
class  Triangulation_vertex_base_with_info_3
 
class  Polygon_2
 
struct  Data_access
 The struct Data_access implements a functor that allows to retrieve data from an associative container. More...
 
class  Interpolation_gradient_fitting_traits_2
 Interpolation_gradient_fitting_traits_2 is a model for the concepts InterpolationTraits and GradientFittingTraits. More...
 
class  Interpolation_traits_2
 Interpolation_traits_2 is a model for the concept InterpolationTraits and can be used to instantiate the geometric traits class of interpolation methods applied on a bivariate function over a two-dimensional domain. More...
 
class  Voronoi_intersection_2_traits_3
 Voronoi_intersection_2_traits_3 is a model for the concept RegularTriangulationTraits_2 and InterpolationTraits. More...
 

Typedefs

typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 

Functions

NT abs (const NT &x)
 
result_type compare (const NT &x, const NT &y)
 
result_type div (const NT1 &x, const NT2 &y)
 
void div_mod (const NT1 &x, const NT2 &y, result_type &q, result_type &r)
 
result_type gcd (const NT1 &x, const NT2 &y)
 
result_type integral_division (const NT1 &x, const NT2 &y)
 
NT inverse (const NT &x)
 
result_type is_negative (const NT &x)
 
result_type is_one (const NT &x)
 
result_type is_positive (const NT &x)
 
result_type is_square (const NT &x)
 
result_type is_square (const NT &x, NT &y)
 
result_type is_zero (const NT &x)
 
NT kth_root (int k, const NT &x)
 
result_type mod (const NT1 &x, const NT2 &y)
 
NT root_of (int k, InputIterator begin, InputIterator end)
 
result_type sign (const NT &x)
 
void simplify (const NT &x)
 
NT sqrt (const NT &x)
 
NT square (const NT &x)
 
double to_double (const NT &x)
 
std::pair< double, double > to_interval (const NT &x)
 
NT unit_part (const NT &x)
 
void Assert_circulator (const C &c)
 
void Assert_iterator (const I &i)
 
void Assert_circulator_or_iterator (const IC &i)
 
void Assert_input_category (const I &i)
 
void Assert_output_category (const I &i)
 
void Assert_forward_category (const IC &ic)
 
void Assert_bidirectional_category (const IC &ic)
 
void Assert_random_access_category (const IC &ic)
 
C::difference_type circulator_distance (C c, C d)
 
C::size_type circulator_size (C c)
 
bool is_empty_range (const IC &i, const IC &j)
 
iterator_traits< IC >
::difference_type 
iterator_distance (IC ic1, IC ic2)
 
Iterator_tag query_circulator_or_iterator (const I &i)
 
Circulator_tag query_circulator_or_iterator (const C &c)
 
Mode get_mode (std::ios &s)
 
Mode set_ascii_mode (std::ios &s)
 
Mode set_binary_mode (std::ios &s)
 
Mode set_mode (std::ios &s, IO::Mode m)
 
Mode set_pretty_mode (std::ios &s)
 
bool is_ascii (std::ios &s)
 
bool is_binary (std::ios &s)
 
bool is_pretty (std::ios &s)
 
Output_rep< T > oformat (const T &t)
 
Input_rep< T > iformat (const T &t)
 
Output_rep< T, F > oformat (const T &t, F)
 
ostream & operator<< (ostream &os, Class c)
 
istream & operator>> (istream &is, Class c)
 
Polynomial_traits_d
< Polynomial_d >
::Canonicalize::result_type 
canonicalize (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Compare::result_type 
compare (const Polynomial_d &p, const Polynomial_d &q)
 
Polynomial_traits_d
< Polynomial_d >
::Degree::result_type 
degree (const Polynomial_d &p, int i, index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Degree_vector::result_type 
degree_vector (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Differentiate::result_type 
differentiate (const Polynomial_d &p, index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Evaluate_homogeneous::result_type 
evaluate_homogeneous (const Polynomial_d &p, Polynomial_traits_d< Polynomial_d >::Coefficient_type u, Polynomial_traits_d< Polynomial_d >::Coefficient_type v)
 
Polynomial_traits_d
< Polynomial_d >
::Evaluate::result_type 
evaluate (const Polynomial_d &p, Polynomial_traits_d< Polynomial_d >::Coefficient_type x)
 
Polynomial_traits_d
< Polynomial_d >
::Gcd_up_to_constant_factor::result_type 
gcd_up_to_constant_factor (const Polynomial_d &p, const Polynomial_d &q)
 
Polynomial_traits_d
< Polynomial_d >
::get_coefficient::result_type 
get_coefficient (const Polynomial_d &p, int i)
 
Polynomial_traits_d
< Polynomial_d >
::get_innermost_coefficient::result_type 
get_innermost_coefficient (const Polynomial_d &p, Exponent_vector ev)
 
Polynomial_traits_d
< Polynomial_d >
::Innermost_leading_coefficient::result_type 
innermost_leading_coefficient (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Integral_division_up_to_constant_factor::result_type 
integral_division_up_to_constant_factor (const Polynomial_d &p, const Polynomial_d &q)
 
Polynomial_traits_d
< Polynomial_d >
::Invert::result_type 
invert (const Polynomial_d &p, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Is_square_free::result_type 
is_square_free (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Is_zero_at_homogeneous::result_type 
is_zero_at_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
Polynomial_traits_d
< Polynomial_d >
::Is_zero_at::result_type 
is_zero_at (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
Polynomial_traits_d
< Polynomial_d >
::Leading_coefficient::result_type 
leading_coefficient (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Make_square_free::result_type 
make_square_free (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Move::result_type 
move (const Polynomial_d &p, int i, int j)
 
Polynomial_traits_d
< Polynomial_d >
::Multivariate_content::result_type 
multivariate_content (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Negate::result_type 
negate (const Polynomial_d &p, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
int number_of_real_roots (Polynomial_d f)
 
int number_of_real_roots (InputIterator start, InputIterator end)
 
Polynomial_traits_d
< Polynomial_d >
::Permute::result_type 
permute (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
OutputIterator polynomial_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
 
OutputIterator1 polynomial_subresultants_with_cofactors (Polynomial_d p, Polynomial_d q, OutputIterator1 sres_out, OutputIterator2 coP_out, OutputIterator3 coQ_out)
 
OutputIterator principal_sturm_habicht_sequence (typename Polynomial_d f, OutputIterator out)
 
OutputIterator principal_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
 
void pseudo_division (const Polynomial_d &f, const Polynomial_d &g, Polynomial_d &q, Polynomial_d &r, Polynomial_traits_d< Polynomial_d >::Coefficient_type &D)
 
Polynomial_traits_d
< Polynomial_d >
::Pseudo_division_quotient::result_type 
pseudo_division_quotient (const Polynomial_d &p, const Polynomial_d &q)
 
Polynomial_traits_d
< Polynomial_d >
::Pseudo_division_remainder::result_type 
pseudo_division_remainder (const Polynomial_d &p, const Polynomial_d &q)
 
Polynomial_traits_d
< Polynomial_d >
::Resultant::result_type 
resultant (const Polynomial_d &p, const Polynomial_d &q)
 
Polynomial_traits_d
< Polynomial_d >
::Scale_homogeneous::result_type 
scale_homogeneous (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &u, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &v, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Scale::result_type 
scale (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &a, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Shift::result_type 
shift (const Polynomial_d &p, int i, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Sign_at_homogeneous::result_type 
sign_at_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
Polynomial_traits_d
< Polynomial_d >
::Sign_at::result_type 
sign_at (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
OutputIterator square_free_factorize (const Polynomial_d &p, OutputIterator it, Polynomial_traits_d< Polynomial >::Innermost_coefficient &a)
 
OutputIterator square_free_factorize (const Polynomial_d &p, OutputIterator it)
 
OutputIterator square_free_factorize_up_to_constant_factor (const Polynomial_d &p, OutputIterator it)
 
OutputIterator sturm_habicht_sequence (Polynomial_d f, OutputIterator out)
 
OutputIterator1 sturm_habicht_sequence_with_cofactors (Polynomial_d f, OutputIterator1 stha_out, OutputIterator2 cof_out, OutputIterator3 cofx_out)
 
CGAL::Coercion_traits
< Polynomial_traits_d
< Polynomial_d >
::Innermost_coefficient,
std::iterator_traits
< Input_iterator >::value_type >
::Type 
substitute_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
CGAL::Coercion_traits
< Polynomial_traits_d
< Polynomial_d >
::Innermost_coefficient,
std::iterator_traits
< Input_iterator >::value_type >
::Type 
substitute (const Polynomial_d &p, InputIterator begin, InputIterator end)
 
Polynomial_traits_d
< Polynomial_d >
::Swap::result_type 
swap (const Polynomial_d &p, int i, int j)
 
Polynomial_traits_d
< Polynomial_d >
::Total_degree::result_type 
total_degree (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Translate_homogeneous::result_type 
translate_homogeneous (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &u, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &v, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Translate::result_type 
translate (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &a, int index=Polynomial_traits_d< Polynomial_d >::d-1)
 
Polynomial_traits_d
< Polynomial_d >
::Univariate_content::result_type 
univariate_content (const Polynomial_d &p)
 
Polynomial_traits_d
< Polynomial_d >
::Univariate_content_up_to_constant_factor::result_type 
univariate_content_up_to_constant_factor (const Polynomial_d &p)
 
bool has_in_x_range (const Circular_arc_2< CircularKernel > &ca, const Circular_arc_point_2< CircularKernel > &p)
 
bool has_in_x_range (const Line_arc_2< CircularKernel > &ca, const Circular_arc_point_2< CircularKernel > &p)
 
bool has_on (const Circle_2< CircularKernel > &c, const Circular_arc_point_2< CircularKernel > &p)
 
OutputIterator make_x_monotone (const Circular_arc_2< CircularKernel > &ca, OutputIterator res)
 
OutputIterator make_xy_monotone (const Circular_arc_2< CircularKernel > &ca, OutputIterator res)
 
Circular_arc_point_2
< CircularKernel > 
x_extremal_point (const Circle_2< CircularKernel > &c, bool b)
 
OutputIterator x_extremal_points (const Circle_2< CircularKernel > &c, OutputIterator res)
 
Circular_arc_point_2
< CircularKernel > 
y_extremal_point (const Circle_2< CircularKernel > &c, bool b)
 
OutputIterator y_extremal_points (const Circle_2< CircularKernel > &c, OutputIterator res)
 
CGAL::Comparison_result compare_y_to_right (const Circular_arc_2< CircularKernel > &ca1, const Circular_arc_2< CircularKernel > &ca2, Circular_arc_point_2< CircularKernel > &p)
 
bool is_finite (double x)
 
bool is_finite (float x)
 
bool is_finite (long double x)
 
OutputIterator compute_roots_of_2 (const RT &a, const RT &b, const RT &c, OutputIterator oit)
 
Root_of_traits< RT >::Root_of_2 make_root_of_2 (const RT &a, const RT &b, const RT &c, bool s)
 
Root_of_traits< RT >::Root_of_2 make_root_of_2 (RT alpha, RT beta, RT gamma)
 
Root_of_traits< RT >::Root_of_2 make_sqrt (const RT &x)
 
Rational simplest_rational_in_interval (double d1, double d2)
 
Rational to_rational (double d)
 
bool is_valid (const T &x)
 
max (const T &x, const T &y)
 
min (const T &x, const T &y)
 
void hilbert_sort (RandomAccessIterator begin, RandomAccessIterator end, const Traits &traits=Default_traits, PolicyTag policy=Default_policy)
 
void spatial_sort (RandomAccessIterator begin, RandomAccessIterator end, const Traits &traits=Default_traits, PolicyTag policy=Default_policy, std::ptrdiff_t threshold_hilbert=default, std::ptrdiff_t threshold_multiscale=default, double ratio=default)
 
template<class RandomAccessIterator , class Functor , class GradFunctor , class Traits >
Functor::result_type farin_c1_interpolation (RandomAccessIterator first, RandomAccessIterator beyond, const typename std::iterator_traits< RandomAccessIterator >::value_type::second_type &norm, const typename std::iterator_traits< ForwardIterator >::value_type::first_type &p, Functor function_value, GradFunctor function_gradient, const Traits &traits)
 generates the interpolated function value computed by Farin's interpolant. More...
 
template<class ForwardIterator , class Functor >
Functor::result_type::first_type linear_interpolation (ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator >::value_type::second_type &norm, Functor function_values)
 The function linear_interpolation() computes the weighted sum of the function values which must be provided via a functor. More...
 
template<class ForwardIterator , class Functor , class GradFunctor , class Traits >
Functor::result_type quadratic_interpolation (ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator >::value_type::second_type &norm, const typename std::iterator_traits< ForwardIterator >::value_type::first_type &p, Functor function_value, GradFunctor function_gradient, 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 point of the point/coordinate pairs in the range [first, beyond). More...
 
template<class ForwardIterator , class Functor , class GradFunctor , class Traits >
std::pair< typename
Functor::result_type, bool > 
sibson_c1_interpolation (ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator >::value_type::second_type &norm, const typename std::iterator_traits< ForwardIterator >::value_type::first_type &p, Functor function_value, GradFunctor function_gradient, 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. More...
 
template<class ForwardIterator , class Functor , class GradFunctor , class Traits >
Functor::result_type sibson_c1_interpolation_square (ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator >::value_type::second_type &norm, const typename std::iterator_traits< ForwardIterator >::value_type::first_type &p, Functor function_value, GradFunctor function_gradient, const Traits &traits)
 The same as sibson_c1_interpolation() except that no square root operation is needed for FT.
 
template<class Dt , class OutputIterator >
CGAL::Triple< OutputIterator,
typename Dt::Geom_traits::FT,
bool > 
natural_neighbor_coordinates_2 (const Dt &dt, const typename Dt::Geom_traits::Point_2 &p, OutputIterator out, 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. More...
 
template<class Dt , class OutputIterator , class EdgeIterator >
CGAL::Triple< OutputIterator,
typename Dt::Geom_traits::FT,
bool > 
natural_neighbor_coordinates_2 (const Dt &dt, const typename Dt::Geom_traits::Point_2 &p, OutputIterator out, EdgeIterator hole_begin, EdgeIterator hole_end)
 The same as above. More...
 
template<class Dt , class OutputIterator >
CGAL::Triple< OutputIterator,
typename Dt::Geom_traits::FT,
bool > 
natural_neighbor_coordinates_2 (const Dt &dt, typename Dt::Vertex_handle vh, OutputIterator out)
 computes the natural neighbor coordinates of the point vh->point() with respect to the vertices of dt excluding vh->point(). More...
 
template<class Rt , class OutputIterator >
CGAL::Triple< OutputIterator,
typename Rt::Geom_traits::FT,
bool > 
regular_neighbor_coordinates_2 (const Rt &rt, const typename Rt::Weighted_point &p, OutputIterator out, 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. More...
 
template<class Rt , class OutputIterator , class EdgeIterator , class VertexIterator >
CGAL::Triple< OutputIterator,
typename Traits::FT, bool > 
regular_neighbor_coordinates_2 (const Rt &rt, const typename Traits::Weighted_point &p, OutputIterator out, EdgeIterator hole_begin, EdgeIterator hole_end, VertexIterator hidden_vertices_begin, VertexIterator hidden_vertices_end)
 The same as above. More...
 
template<class Rt , class OutputIterator >
CGAL::Triple< OutputIterator,
typename Rt::Geom_traits::FT,
bool > 
regular_neighbor_coordinates_2 (const Rt &rt, typename Rt::Vertex_handle vh, OutputIterator out)
 computes the regular neighbor coordinates of the point vh->point() with respect to the vertices of rt excluding vh->point(). More...
 
template<class ForwardIterator , class Functor , class Traits >
Traits::Vector_d sibson_gradient_fitting (ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits< ForwardIterator >::value_type::second_type &norm, const typename std::iterator_traits< ForwardIterator >::value_type::first_type &p, Functor f, const Traits &traits)
 estimates the gradient of a function at the point p given natural neighbor coordinates of p in the range [first, beyond) and the function values of the neighbors provided by the functor f. More...
 
template<class Dt , class OutputIterator , class Functor , class Traits >
OutputIterator sibson_gradient_fitting_nn_2 (const Dt &dt, OutputIterator out, Functor f, const Traits &traits)
 estimates the function gradients at all vertices of dt that lie inside the convex hull using the coordinates computed by the function PkgInterpolationNaturalNeighborCoordinates2. More...
 
template<class Rt , class OutputIterator , class Functor , class Traits >
OutputIterator sibson_gradient_fitting_rn_2 (const Rt &rt, OutputIterator out, Functor f, 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 PkgInterpolationRegularNeighborCoordinates2. More...
 
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)`. More...
 
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)
 the same as above only that the traits class must be instantiated by the user. More...
 
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. More...
 
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)
 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 >
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)
 The same as above only that the traits class must be instantiated by the user and without the parameter max_distance. More...
 
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)
 The same as above with the parameter max_distance.
 
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. More...
 
template<class Dt , class OutputIterator , class ITraits >
CGAL::Triple< OutputIterator,
typenameDt::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())
 The same as above only that the parameter traits instantiates the geometric traits class. More...
 
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). More...
 
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)
 The same as above only that the traits class must be instantiated by the user. More...
 
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. More...
 
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)
 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, const typename ITraits::Point_2 &p, OutputIterator out, const ITraits &traits)
 The same as above only that the traits class must be instantiated by the user. More...
 
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)
 The same as above with the parameter max_distance.
 
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. More...
 
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())
 The same as above only that the parameter traits instantiates the geometric traits class. More...