Zonotopes as bounding volumes

Zonotopes are centrally symmetric polytopes with a very special structure: they are the Minkowski sum of line segments. In this paper we propose to use zonotopes as bounding volumes for geometry in collision detection and other applications where the spatial relationship between two pieces of geometry is important. We show how to construct optimal, or approximately optimal zonotopes enclosing given set of points or other geometry. We also show how zonotopes can be used for efficient collision testing, based on their description via their defining line segments — without ever building their explicit description as polytopes. This implicit representation adds flexibility, power, and economy to the use of zonotopes as bounding volumes.

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Leonidas J. Guibas, An Nguyen, Li Zhang
• Keywords: Algorithms, Line Segments, Minkowski Sum, SODA 2003, Symmetric Polytopes