Oriented bounding surfaces with at most six common normals

Authors:
Margot Rabl;Laureano Gonzalez-Vega;Bert Jüttler;Hans-Peter Schröcker
Affiliations:
Institute of Applied Geometry, Johannes Kepler University, Linz, Austria;Department of Mathematics, Statistics and Computing, Universidad de Cantabria, Santander, Spain;Institute of Applied Geometry, Johannes Kepler University, Linz, Austria;Institute of Basic Sciences in Engineering, Unit Geometry and CAD, University Innsbruck, Innsbruck, Austria
Venue:
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Year:
2009

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Abstract

We present a new type of oriented bounding surfaces, which is particularly well suited for shortest distance computations. The bounding surfaces are obtained by considering surfaces whose support functions are restrictions of quadratic polynomials to the unit sphere. We show that the common normals of two surfaces of this type - and hence their shortest distance - can be computed by solving a polynomial of degree six. This compares favorably with other existing bounding surfaces, such as quadric surfaces, where the computation of the common normals is known to lead to a polynomial of degree 24.