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CGAL 6.0 - dD Convex Hulls and Delaunay Triangulations
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Requirements of the traits class to be used with the class CGAL::Convex_hull_d.
CGAL::Cartesian_d<FT,LA> CGAL::Homogeneous_d<RT,LA> CGAL::Convex_hull_d_traits_3<R> Public Member Functions | |
| ConvexHullTraits_d () | |
| A default constructor and copy constructor is required. | |
Types | |
| typedef unspecified_type | Point_d |
| the dD point type on which the convex hull algorithm operates | |
| typedef unspecified_type | Hyperplane_d |
| a dD plane | |
| typedef unspecified_type | Vector_d |
| a dD vector | |
| typedef unspecified_type | Ray_d |
| a dD ray | |
| typedef unspecified_type | RT |
| an arithmetic ring type | |
| typedef unspecified_type | Construct_vector_d |
Function object type that provides Vector_d operator()(int d, CGAL::Null_vector), which constructs and returns the null vector. | |
| typedef unspecified_type | Construct_hyperplane_d |
Function object type that provides Hyperplane_d operator()(ForwardIterator first,
ForwardIterator last, Point_d p, CGAL::Oriented_side side), which constructs and returns a hyperplane passing through the points in tuple[first,last) and oriented such that p is on the side side of the returned hyperplane. | |
| typedef unspecified_type | Vector_to_point_d |
Function object type that provides Point_d operator()(Vector_d v), which constructs and returns the point defined by \( 0+v\). | |
| typedef unspecified_type | Point_to_vector_d |
Function object type that provides Vector_d operator()(Point_d v), which constructs and returns the vector defined by \( p-0\). | |
| typedef unspecified_type | Orientation_d |
Function object type that provides Orientation operator()(ForwardIterator first,
ForwardIterator last), which determines the orientation of the points tuple[first,last). | |
| typedef unspecified_type | Orthogonal_vector_d |
Function object type that provides Vector_d operator()(Hyperplane_d h), which constructs and returns a vector orthogonal to h and pointing from the boundary into its positive halfspace. | |
| typedef unspecified_type | Oriented_side_d |
Predicate object type that provides Oriented_side operator()(Hyperplane_d h, Point_d p), which determines the oriented side of p with respect to h. | |
| typedef unspecified_type | Has_on_positive_side_d |
Predicate object type that provides bool operator()(Hyperplane_d h, Point_d p), which return true iff p lies in the positive halfspace determined by h. | |
| typedef unspecified_type | Affinely_independent_d |
Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator last), which determines if the points tuple[first,last) are affinely independent. | |
| typedef unspecified_type | Contained_in_simplex_d |
Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator
last, Point_d p), which determines if p is contained in the closed simplex defined by the points in tuple[first,last). | |
| typedef unspecified_type | Contained_in_affined_hull_d |
Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator
last, Point_d p), which determines if p is contained in the affine hull of the points in tuple[first,last). | |
| typedef unspecified_type | Intersect_d |
Predicate object type that provides Object operator()(Ray_d r, Hyperplane_d h), which determines if r and h intersect and returns the corresponding polymorphic object. | |
Operations | |
For each of the above function and predicate object types, For example: | |
| Construct_vector_d | construct_vector_d_object () |
Function object type that provides Hyperplane_d operator()(ForwardIterator first,
ForwardIterator last, Point_d p, CGAL::Oriented_side side), which constructs and returns a hyperplane passing through the points in tuple[first,last) and oriented such that p is on the side side of the returned hyperplane.
When side==ON_ORIENTED_BOUNDARY then any hyperplane containing the tuple is returned.