CGAL 4.4 - dD Geometry Kernel
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Classes | |
class | Cartesian_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 using homogeneous coordinates to represent the geometric objects. More... | |
class | Aff_transformation_d |
An instance of the data type Aff_transformation_d<Kernel> is an affine transformation of \( d\)-dimensional space. More... | |
class | Direction_d |
A Direction_d is a vector in the \( d\)-dimensional vector space where we forget about its length. 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 | 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... | |
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... | |
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) . 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... | |