Witness (Delaunay) Graphs

Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations. We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We study in detail two concrete examples, both related to Delaunay graphs, and consider as well some problems on stabbing geometric objects and point set discrimination, that can be naturally described in terms of witness graphs.Comment: 27 pages. JCCGG 200

The Parallel 3D Convex-Hull Problem Revisited - Revision 1

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / CCR-89-0641

The EIGHT Manual: A System for Geometric Modelling and Three-Dimensional Graphics on the Lisp Machine

We describe a simple geometric modelling system called Eight which supports interactive creation, editing, and display of three-dimensional polyhedral solids. Perspective views of a polyhedral environment may be generated, and hidden surfaces removed. Eight proved useful for creating world models, and as an underlying system for modelling object interaction in robotics research and applications. It is documented here in order to make the facility available to other members of the Artificial Intelligence Laboratory.MIT Artificial Intelligence Laborator

Folding Orthogonal Polyhedra

In this thesis, we study foldings of orthogonal polygons into orthogonal polyhedra. The particular problem examined here is whether a paper cutout of an orthogonal polygon with fold lines indicated folds up into a simple orthogonal polyhedron. The folds are orthogonal and the direction of the fold (upward or downward) is also given. We present a polynomial time algorithm to solve this problem. Next we consider the same problem with the exception that the direction of the folds are not given. We prove that this problem is NP-complete. Once it has been determined that a polygon does fold into a polyhedron, we consider some restrictions on the actual folding process, modelling the case when the polyhedron is constructed from a stiff material such as sheet metal. We show an example of a polygon that cannot be folded into a polyhedron if folds can only be executed one at a time. Removing this restriction, we show another polygon that cannot be folded into a polyhedron using rigid material

Computing the Minimum Visible Vertex Distance Between Two Nonintersecting Simple Polygons

Coordinated Science Laboratory was formerly known as Control Systems Laborator