Many applications in Computer Graphics require fast and robust 3D collision detection
algorithms. These algorithms can be grouped into four approaches: space–time volume …

Collision detection is a basic tool whose performance is of capital importance in order to
achieve efficiency in many robotics and computer graphics applications, such as motion …

INFORMATION TO USERS Page 1 INFORMATION TO USERS This manuscript has been
reproduced from the microfilm master. UMI films the text directly from the original or copy …

We introduce the boxtree, a versatile data structure for representing triangulated or meshed
surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient …

We consider the problem of preprocessing a scene of polyhedral models in order to perform
collision detection very e ciently for an object that moves amongst obstacles. This problem is …

Theorem 1.1 (Helly's Theorem)[49]. Suppose A is a family of at least d+ 1 convex sets in IRd,
and A is finite or each member of A is compact. Then if every d+ 1 members of A have a …

Many problems in computer graphics and computer vision require accurate global visibility
information. Previous approaches have typically been complicated to implement and …

We define the antiumbra and the antipenumbra of a convex area light source shining
through a sequence of convex area] holes in three dimensions. The antiumbra is the volume …

In this paper we study the ray-shooting problem for three special classes of polyhedral
objects in space: axis-parallel polyhedra, curtains (unbounded polygons with three edges …

To pre-process a scene for the purpose of visibility culling during walkthroughs it is
necessary to solve visibility from all the elements of a finite partition of viewpoint space …