CGAL 6.0.1  3D Envelopes

#include <CGAL/Env_plane_traits_3.h>
CGAL::Arr_linear_traits_2< typename Kernel >.
The traits class template Env_plane_traits_3
models the EnvelopeTraits_3
concept, and is used for the construction of lower and upper envelopes of planes and half planes in the space.
When the template is instantiated, the template parameter Kernel
must be substituted by a CGALkernel model, the number type of which should support exact rational arithmetic, to avoid numerical errors and robustness problems. In particular, the number type should support the arithmetic operations \( +\), \( \), \( \times\), and \( \div\) without loss of precision. For optimal performance, we recommend instantiating the traits class with the predefined Exact_predicates_exact_constructions_kernel
provided by CGAL. Using this kernel guarantees exactness and robustness, while it incurs only a minor overhead (in comparison to working with a fast, inexact number type) for most inputs.
The second template parameter, namely ArrLinearTraits
, should be substituted by a 2D arrangement geometry traits class that supports unbounded linear objects, i.e, lines, rays, and segments. By default it is substituted by Arr_linear_traits_2<Kernel>
.
Note that an entire plane has no boundaries, and the projection of a halfplane is an (unbounded) line. Naturally, rays and segments may occur as a result of overlaying projections of several half planes. Indeed, Env_plane_traits_3
inherits from the traits class that substitutes ArrLinearTraits
, and extends it by adding operations on planes and half planes. The nested Xy_monotone_surface_3
and Surface_3
types refer to the same type. They are constructible from a Kernel::Plane_3
in case of an entire plane, or from Kernel::Plane_3
and Kernel::Line_2
in case of a halfplane. The line orientation determines which half is considered.
EnvelopeTraits_3
Additional Inherited Members  
Public Types inherited from CGAL::Arr_linear_traits_2< typename Kernel >  
typedef Kernel::Segment_2  Segment_2 
typedef Kernel::Ray_2  Ray_2 
typedef Kernel::Line_2  Line_2 
typedef Kernel::Point_2  Point_2 
typedef X_monotone_curve_2  Curve_2 
Public Member Functions inherited from CGAL::Arr_linear_traits_2< typename Kernel >  
class CGAL::Arr_linear_traits_2::Trim_2  trim_2_object () const 