We prove the connexity of the boundary of each 4-dimensional cell of the 3D visibility complex of disjoint convex polyhedra. Using this property, we outline a simple algorithm for the construction of the visibility complex of k disjoint, convex polyhedra in time O(nk log n) where n is the total complexity of the polyhedra.

Closed, watertight, 3D geometries are represented by polyhedra. Current data models define these polyhedra basically as a set of polygons, leaving the test on intersecting polygons or open gaps to external validation rules. If this testing is not performed well, or not at all, non-valid polyhedra could be stored in geo-databases. This paper proposes the utilization of the Constrained Delaunay T...

The directional contact range of two convex polyhedra is the range of positions that one of the polyhedron may locate along a given straight line so that the two polyhedra are in collision. Using the contact range, one can quickly classify the positions along a line for a polyhedron as “safe” for free of collision with another polyhedron, or “unsafe” for the otherwise. This kind of contact dete...

Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice structure on the underlying matrix satisfying certain suband supermodularity constraints. Lattice polyhedra provide one of the most general frameworks of total dual integral systems. So far no combinatorial algorithm has been found for the ...

The iterated diierence of polyhedra V = P1n(P2n independently in 11] and 7] as a suucient condition for V to be exactly computable by a two-layered neural network. An algorithm checking whether V I R d is an iterated diierence of polyhedra is proposed in 11]. However, this algorithm is not practically usable because it has a high computational complexity and it was only conjectured to stop with...