pgl::UnboundedConvexConcept Concept Reference

Unbounded convex polyhedral primitives. More...

#include <forward.hpp>

Concept definition

template<class T>
concept UnboundedConvexConcept =
    HalfplaneConcept<T> || LineConcept<T> || OrientedLineConcept<T> ||
    RayConcept<T> || HalfplaneIntersectionConcept<T>

Detailed Description

Unbounded convex polyhedral primitives.

A half-plane, a line, a ray and a HalfplaneIntersection are each the intersection of finitely many closed half-planes, so each is convex and each is closed under the Minkowski sum with any of the others and with any bounded convex shape: the sum of two convex polyhedra is a convex polyhedron. None of them is bounded (a HalfplaneIntersection may happen to be, and is still one of these), which is exactly why their sums answer with a HalfplaneIntersection rather than a Convex.

A Disk is convex and is not one of these: it is not polyhedral, so its sums leave the shape vocabulary in every direction but four.