CGAL Namespace Reference

Classes
class	Aff_transformation_d
	An instance of the data type Aff_transformation_d<Kernel> is an affine transformation of \( d\)-dimensional space. More...
class	Cartesian_d
	A model for Kernel_d (and even KernelWithLifting_d) that uses Cartesian coordinates to represent the geometric objects. More...
class	Direction_d
	A Direction_d is a vector in the \( d\)-dimensional vector space where we forget about its length. More...
struct	Epeck_d
	A model for Kernel_d, minus Kernel_d::Point_of_sphere_d, that uses Cartesian coordinates to represent the geometric objects. More...
struct	Epick_d
	A model for Kernel_d that uses Cartesian coordinates to represent the geometric objects. More...
class	Homogeneous_d
	A model for a Kernel_d (and even KernelWithLifting_d) using homogeneous coordinates to represent the geometric objects. More...
class	Hyperplane_d
	An instance of data type Hyperplane_d is an oriented hyperplane in \( d\) - dimensional space. More...
class	Iso_box_d
	An object \( b\) of the data type Iso_box_d is an iso-box in the Euclidean space \( \E^d\) with edges parallel to the axes of the coordinate system. More...
class	Line_d
	An instance of data type Line_d is an oriented line in \( d\)-dimensional Euclidean space. More...
class	Linear_algebraCd
	The class Linear_algebraCd serves as the default traits class for the LA parameter of CGAL::Cartesian_d<FT,LA>. More...
class	Linear_algebraHd
	The class Linear_algebraHd serves as the default traits class for the LA parameter of CGAL::Homogeneous_d<RT,LA>. More...
class	Point_d
	An instance of data type Point_d<Kernel> is a point of Euclidean space in dimension \( d\). More...
class	Ray_d
	An instance of data type Ray_d is a ray in \( d\)-dimensional Euclidean space. More...
class	Segment_d
	An instance \( s\) of the data type Segment_d is a directed straight line segment in \( d\)-dimensional Euclidean space connecting two points \( p\) and \( q\). More...
class	Sphere_d
	An instance \( S\) of the data type Sphere_d is an oriented sphere in some \( d\)-dimensional space. More...
class	Vector_d
	An instance of data type Vector_d<Kernel> is a vector of Euclidean space in dimension \( d\). More...

Functions
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).
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.
Point_d< R >	midpoint (const Point_d< R > &p, const Point_d< R > &q)
	computes the midpoint of the segment \( pq\).
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 \( q\).
bool	do_intersect (Type1< R > obj1, Type2< R > obj2)
	checks whether obj1 and obj2 intersect.
decltype(auto)	intersection (Type1< R > f1, Type2< R > f2)
	returns the intersection between f1 and f2.
template<class ForwardIterator >
bool	affinely_independent (ForwardIterator first, ForwardIterator last)
	returns true iff the points in A = tuple [first,last) are affinely independent.
template<class ForwardIterator >
int	affine_rank (ForwardIterator first, ForwardIterator last)
	computes the affine rank of the points in A = tuple [first,last).
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 \( i = 0,\ldots,d-1\).
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).
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).
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).
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.
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 \( q\).
template<class ForwardIterator >
bool	linearly_independent (ForwardIterator first, ForwardIterator last)
	decides whether the vectors in A = tuple [first,last) are linearly independent.
template<class ForwardIterator >
int	linear_rank (ForwardIterator first, ForwardIterator last)
	computes the linear rank of the vectors in A = tuple [first,last).
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.
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).
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.