CGAL 5.0  3D Envelopes

#include <CGAL/Env_plane_traits_3.h>
CGAL::Arr_linear_traits_2< Kernel >.
The traits class 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.
It is parameterized by a CGALkernel model, which is parameterized in turn by a number type. The number type 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.
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 Arr_linear_traits_2<Kernel>
traits class, 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.