Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

Authors:
B. Llanas;M. Fernandez De Sevilla;V. Feliu
Affiliations:
Dpto. de Matemática e Informática, E.T.S.I. de Caminos, Ciudad Universitaria, 28040-Madrid, Spain and Dpto. de Ingeniería Eléctrica, E.T.S.I Industriales, Campus Universitario ...;Dpto. de Matemática e Informática, E.T.S.I. de Caminos, Ciudad Universitaria, 28040-Madrid, Spain and Dpto. de Ingeniería Eléctrica, E.T.S.I Industriales, Campus Universitario ...;Dpto. de Matemática e Informática, E.T.S.I. de Caminos, Ciudad Universitaria, 28040-Madrid, Spain and Dpto. de Ingeniería Eléctrica, E.T.S.I Industriales, Campus Universitario ...
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.