In addition to the requirements described for the traits class of Triangulation_3, the geometric traits class of a Delaunay triangulation must fulfill the following requirements:
 
The line type.
 
 
The object type.
 
 
The ray type.
 
 
A predicate object that must provide the function operator Bounded_side operator()(Point p, Point q, Point r, Point s), which determines the bounded side of the circle defined by p, q, and r on which s lies.
 
 
A predicate object that must provide the function operator Oriented_side operator()(Point p, Point q, Point r, Point s, Point t), which determines on which side of the oriented sphere circumscribing p, q, r, s the point t lies.
 
 
A predicate object that must provide the function operator Comparison_result operator()(Point p, Point q, Point r), which compares the distance between p and q to the distance between p and r.

In addition, only when the dual operations are used, the traits class must provide the following constructor objects:
 
A constructor object that must provide the function operator Point_3 operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s), which constructs the circumcenter of four points.
 
 
A constructor object that must provide the function operators Object_3 operator()(Point_3 p), Object_3 operator()(Segment_3 s) and Object_3 operator()(Ray_3 r) that construct an object respectively from a point, a segment and a ray.
 
 
A constructor object that must provide the function operator Line_3 operator()(Point_3 p1, Point_3 p2, Point_3 p3), which constructs the line which is at the same distance from the three points.
 
 
A constructor object that must provide the function operator Ray_3 operator()(Point_3 p, Line_3 l), which constructs the ray starting at p with direction given by l.

The following functions give access to the predicate and construction objects:

 


When using the triangulation hierarchy, the traits must provide:


The following functions must be provided only if the methods of Delaunay_triangulation_3 returning elements of the Voronoi diagram are instantiated:
CGAL::Exact_predicates_inexact_constructions_kernel (recommended)
CGAL::Exact_predicates_exact_constructions_kernel (recommended for
Voronoi)
CGAL::Filtered_kernel
CGAL::Cartesian
CGAL::Simple_cartesian
CGAL::Homogeneous
CGAL::Simple_homogeneous