CGAL 6.1 - dD Geometry Kernel

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Classes | Functions
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 | Bbox_d
| An object `b` of the class `Bbox_d` is a bounding box in the d-dimensional Euclidean space \( \E^d\). 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.