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ConvexHullTraits_3

Definition

Requirements of the traits class to be used with the function convex_hull_3.

Types

ConvexHullTraits_3::Point_3
The point type on which the convex hull algorithm operates

ConvexHullTraits_3::Plane_3
a 3D plane

ConvexHullTraits_3::Segment_3
a 3D segment

ConvexHullTraits_3::Triangle_3
a 3D triangle

ConvexHullTraits_3::Vector_3
a 3D vector


ConvexHullTraits_3::Construct_plane_3
Function object type that provides Plane_3 operator()(Point_3 p, Point_3 q, Point_3 r), which constructs and returns a plane passing through p, q, and r and oriented in a positive sense when seen from the positive side of the plane.


ConvexHullTraits_3::Construct_segment_3
Function object type that provides Segment_3 operator()(Point_3 p, Point_3 q), which constructs and returns the segment with source p and target q.


ConvexHullTraits_3::Construct_triangle_3
Function object type that provides Triangle_3 operator()(Point_3 p, Point_3 q, Point_3 r), which constructs and returns the triangle with vertices p, q, and r


ConvexHullTraits_3::Construct_vector_3
Function object type that provides Vector_3 operator()(Point_3 p, Point_3 q), which constructs and returns the vector q-p


ConvexHullTraits_3::Equal_3
Predicate object type that provides bool operator()(Point_3 p, Point_3 q), which determines if points p and q are equal or not


ConvexHullTraits_3::Collinear_3
Predicate object type that provides bool operator()(Point_3 p, Point_3 q, Point_3 r), which determines if points p, q and r are collinear or not


ConvexHullTraits_3::Coplanar_3
Predicate object type that provides bool operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s), which determines if points p, q, r, and s are coplanar or not


ConvexHullTraits_3::Has_on_positive_side_3
Predicate object type that provides bool operator()(Plane_3 h, Point_3 q), which determines of the point q is on the positive side of the halfspace h


ConvexHullTraits_3::Less_distance_to_point_3
Predicate object type that provides a constructor taking a single Point_3 object and bool operator()(Point_3 q, Point_3 r), which returns true iff the distance from q to p is smaller than the distance from r to p, where p is the point passed to the object at construction.


ConvexHullTraits_3::Less_signed_distance_to_plane_3
Predicate object type that provides bool operator()(Plane_3 p, Point_3 q, Point_3 r), which returns true iff the signed distance from q to p is smaller than the signed distance from r to p

To handle the degenerate case when all points are coplanar, the following three types that are default-constructable are necessary:

ConvexHullTraits_3::Traits_xy
A model of ConvexHullTraits_2 for points projected into the xy-plane


ConvexHullTraits_3::Traits_xz
A model of ConvexHullTraits_2 for points projected into the xz-plane


ConvexHullTraits_3::Traits_yz
A model of ConvexHullTraits_2 for points projected into the yz-plane

One also needs the following function object to help choose which of the above traits classes to use:

ConvexHullTraits_3::Max_coordinate_3
Function object type that provides int operator()(Vector_3 v), which returns the index (0, 1, or 2 for x, y, or z, respectively) of the coordinate of v with maximum absolute value.

These types need not be provided when it is known that the points are not all coplanar.

Creation

Only a copy constructor is required.

ConvexHullTraits_3 traits ( & ch);

Operations

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:

Construct_plane_3 traits.construct_plane_3_object ()

Has Models

CGAL::Convex_hull_traits_3<R>

Next: Convex_hull_traits_3<R>
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The CGAL Project . Tue, December 21, 2004 .