CGAL Namespace Reference

Namespaces
	cpp11
	IO
	Scale_space_reconstruction_3
	Shape_detection_3
	Surface_mesh_parameterization

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_kth_root
class	Exact_predicates_exact_constructions_kernel_with_root_of
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	Weighted_point_2
class	Weighted_point_3
struct	Construct_array
class	CC_safe_handle
class	Compact_container_base
class	Compact_container
class	Compact_container_traits
class	Compact
class	Fast
class	Concurrent_compact_container_traits
class	Concurrent_compact_container
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	Iterator_range
class	Location_policy
class	Multiset
class	Object
class	Sixtuple
class	Spatial_lock_grid_3
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
struct	value_type_traits
struct	value_type_traits< std::back_insert_iterator< Container > >
struct	value_type_traits< std::insert_iterator< Container > >
struct	value_type_traits< std::front_insert_iterator< Container > >
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	Modular_traits
class	Residue
class	Exponent_vector
	For a given (multivariate) monomial the vector of its exponents is called the exponent vector. More...
class	Polynomial
	An instance of the data type Polynomial represents a polynomial \( p = a_0 + a_1*x + ...a_i*x^i\) from the ring \( \mathrm{Coeff}[x]\). More...
class	Polynomial_traits_d
	A model of concept PolynomialTraits_d More...
class	Polynomial_type_generator
	This class template provides a convenient way to obtain the type representing a multivariate polynomial with d variables, where T is the innermost coefficient type. More...

Functions
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Canonicalize::result_type	canonicalize (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Compare::result_type	compare (const Polynomial_d &p, const Polynomial_d &q)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Degree::result_type	degree (const Polynomial_d &p, int i, index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Degree_vector::result_type	degree_vector (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Differentiate::result_type	differentiate (const Polynomial_d &p, index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Evaluate::result_type	evaluate (const Polynomial_d &p, Polynomial_traits_d< Polynomial_d >::Coefficient_type x)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::get_coefficient::result_type	get_coefficient (const Polynomial_d &p, int i)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::get_innermost_coefficient::result_type	get_innermost_coefficient (const Polynomial_d &p, Exponent_vector ev)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Innermost_leading_coefficient::result_type	innermost_leading_coefficient (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Invert::result_type	invert (const Polynomial_d &p, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Is_square_free::result_type	is_square_free (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Is_zero_at_homogeneous::result_type	is_zero_at_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Is_zero_at::result_type	is_zero_at (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Leading_coefficient::result_type	leading_coefficient (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Make_square_free::result_type	make_square_free (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Move::result_type	move (const Polynomial_d &p, int i, int j)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Multivariate_content::result_type	multivariate_content (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Negate::result_type	negate (const Polynomial_d &p, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<typename Polynomial_d >
int	number_of_real_roots (Polynomial_d f)
	computes the number of distinct real roots of \(f\). More...
template<typename InputIterator >
int	number_of_real_roots (InputIterator start, InputIterator end)
	computes the number of distinct real roots of \( f\) whose principal Sturm-Habicht coefficients are passed by the iterator range. More...
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Permute::result_type	permute (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	polynomial_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
	computes the polynomial subresultants of \( p\) and \( q\), with respect to the outermost variable. More...
template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	polynomial_subresultants_with_cofactors (Polynomial_d p, Polynomial_d q, OutputIterator1 sres_out, OutputIterator2 coP_out, OutputIterator3 coQ_out)
	computes the polynomial subresultants of \( p\) and \( q\), sres_out, with respect to the outermost variable, and the cofactors for \( P\), coP_out and \( Q\), coQ_out. More...
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	principal_sturm_habicht_sequence (typename Polynomial_d f, OutputIterator out)
	computes the principal Sturm-Habicht coefficients of \( f\) with respect to the outermost variable. More...
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	principal_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
	computes the principal subresultants of \( p\) and \( q\), with respect to the outermost variable. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Pseudo_division_quotient::result_type	pseudo_division_quotient (const Polynomial_d &p, const Polynomial_d &q)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Pseudo_division_remainder::result_type	pseudo_division_remainder (const Polynomial_d &p, const Polynomial_d &q)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Resultant::result_type	resultant (const Polynomial_d &p, const Polynomial_d &q)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Shift::result_type	shift (const Polynomial_d &p, int i, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Sign_at_homogeneous::result_type	sign_at_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Sign_at::result_type	sign_at (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class OutputIterator >
OutputIterator	square_free_factorize (const Polynomial_d &p, OutputIterator it, Polynomial_traits_d< Polynomial >::Innermost_coefficient &a)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class OutputIterator >
OutputIterator	square_free_factorize (const Polynomial_d &p, OutputIterator it)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class OutputIterator >
OutputIterator	square_free_factorize_up_to_constant_factor (const Polynomial_d &p, OutputIterator it)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	sturm_habicht_sequence (Polynomial_d f, OutputIterator out)
	computes the Sturm-Habicht-sequence of \( f\) with respect to the outermost variable. More...
template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	sturm_habicht_sequence_with_cofactors (Polynomial_d f, OutputIterator1 stha_out, OutputIterator2 cof_out, OutputIterator3 cofx_out)
	computes the Sturm-Habicht sequence of \( f\) stha_out, with respect to the outermost variable, and the cofactors for \( f\), cof_out and \( f'\), cofx_out. More...
template<class Polynomial_d , class InputIterator >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d , class InputIterator >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Swap::result_type	swap (const Polynomial_d &p, int i, int j)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Total_degree::result_type	total_degree (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
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)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Univariate_content::result_type	univariate_content (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Univariate_content_up_to_constant_factor::result_type	univariate_content_up_to_constant_factor (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>. More...