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the dD point type on which the Delaunay algorithm
operates
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a dD plane
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a dD vector
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a dD ray
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a arithmetic ring type
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Function object type that provides
Vector_d operator()(int d, CGAL::Null_vector), which constructs
and returns the null vector.
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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.
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Function object type that provides
Point_d operator()(Vector_d v), which constructs and
returns the point defined by 0+v.
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Function object type that provides
Vector_d operator()(Point_d v), which constructs and returns the
vector defined by p-0.
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Function object type that provides
Orientation operator()(ForwardIterator first, ForwardIterator last), which determines the orientation of the
points tuple[first,last).
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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.
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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.
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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.
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Predicate object type that provides
bool operator()(ForwardIterator first, ForwardIterator last), which
determines if the points tuple[first,last) are affinely independent.
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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).
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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).
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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.
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The previous requirements are all identical to the concept ConvexHullTraits_d. The Delaunay class adds the following requirements.
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Predicate object type that
provides DelaunayTraits_d::Point_d operator()(Point_d p), which
determines the d-1-dimensional point from the d-dimensional point
p while discarding the last coordinate.
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Predicate object type that
provides Point_d operator()(DelaunayTraits_d::Point_d p), which
determines the d-dimensional point from the d-1-dimensional point
p while lifting it to the paraboloid of revolution.
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Predicate object type that
provides RT homogeneous(Vector_d v,int i) and int dimension(Vector_d v), where the former determines the ith
coordinate of v and the latter the dimension of v.
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A default constructor and copy constructor is required.
For each of the above function and predicate object types, Func_obj_type, a function must exist with the name func_obj_type_object that creates an instance of the function or predicate object type. For example:
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