CGAL 4.3 - dD Geometry Kernel
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Namespaces | |
cpp11 | |
IO | |
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 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 Interval_nt< false > | Interval_nt_advanced |
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) |
T | max (const T &x, const T &y) |
T | 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 ForwardIterator > | |
Point_d< R > | center_of_sphere (ForwardIterator first, ForwardIterator last) |
returns the center of the sphere spanned by the points in A = tuple[first,last) . More... | |
Point_d< R > | lift_to_paraboloid (const Point_d< R > &p) |
returns the projection of \( p = (x_0,\ldots,x_{d-1})\) onto the paraboloid of revolution which is the point \( (p_0, \ldots,p_{d-1},\sum_{0 \le i < d}p_i^2)\) in \( (d+1)\)-space. | |
template<class ForwardIterator , class OutputIterator > | |
OutputIterator | linear_base (ForwardIterator first, ForwardIterator last, OutputIterator result) |
computes a basis of the linear space spanned by the vectors in A = tuple [first,last) and returns it via an iterator range starting in result . More... | |
Point_d< R > | midpoint (const Point_d< R > &p, const Point_d< R > &q) |
computes the midpoint of the segment \( pq\). More... | |
Point_d< R > | project_along_d_axis (const Point_d< R > &p) |
returns \( p\) projected along the \( d\)-axis onto the hyperspace spanned by the first \( d-1\) standard base vectors. | |
FT | squared_distance (Point_d< R > p, Point_d< R > q) |
computes the square of the Euclidean distance between the two points \( p\) and \( q\). More... | |
bool | do_intersect (Type1< R > obj1, Type2< R > obj2) |
checks whether obj1 and obj2 intersect. More... | |
cpp11::result_of < R::Intersect_d(Type1< R > , Type2< R >)>::type | intersection (Type1< R > f1, Type2< R > f2) |
returns the intersection between f1 and f2 . More... | |
template<class ForwardIterator > | |
bool | affinely_independent (ForwardIterator first, ForwardIterator last) |
returns true iff the points in A = tuple [first,last) are affinely independent. More... | |
template<class ForwardIterator > | |
int | affine_rank (ForwardIterator first, ForwardIterator last) |
computes the affine rank of the points in A = tuple [first,last) . More... | |
Comparison_result | compare_lexicographically (const Point_d< R > &p, const Point_d< R > &q) |
Compares the Cartesian coordinates of points p and q lexicographically in ascending order of its Cartesian components p[i] and q[i] for \( i = 0,\ldots,d-1\). More... | |
template<class ForwardIterator > | |
bool | contained_in_affine_hull (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
determines whether \( p\) is contained in the affine hull of the points in A = tuple [first,last) . More... | |
template<class ForwardIterator > | |
bool | contained_in_linear_hull (ForwardIterator first, ForwardIterator last, const Vector_d< R > &v) |
determines whether \( v\) is contained in the linear hull of the vectors in A = tuple [first,last) . More... | |
template<class ForwardIterator > | |
bool | contained_in_simplex (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
determines whether \( p\) is contained in the simplex of the points in A = tuple [first,last) . More... | |
bool | lexicographically_smaller (const Point_d< R > &p, const Point_d< R > &q) |
returns true iff p is lexicographically smaller than q with respect to Cartesian lexicographic order of points. More... | |
bool | lexicographically_smaller_or_equal (const Point_d< R > &p, const Point_d< R > &q) |
returns true iff \( p\) is lexicographically smaller than \( q\) with respect to Cartesian lexicographic order of points or equal to \( q\). More... | |
template<class ForwardIterator > | |
bool | linearly_independent (ForwardIterator first, ForwardIterator last) |
decides whether the vectors in A = tuple [first,last) are linearly independent. More... | |
template<class ForwardIterator > | |
int | linear_rank (ForwardIterator first, ForwardIterator last) |
computes the linear rank of the vectors in A = tuple [first,last) . More... | |
template<class ForwardIterator > | |
Orientation | orientation (ForwardIterator first, ForwardIterator last) |
determines the orientation of the points of the tuple A = tuple [first,last) where \( A\) consists of \( d+1\) points in \( d\)-space. More... | |
template<class ForwardIterator > | |
Bounded_side | side_of_bounded_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
returns the relative position of point p to the sphere defined by A = tuple [first,last) . More... | |
template<class ForwardIterator > | |
Oriented_side | side_of_oriented_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
returns the relative position of point p to the oriented sphere defined by the points in A = tuple [first,last) The order of the points in \( A\) is important, since it determines the orientation of the implicitly constructed sphere. More... | |