Title: Techniques for the calculation of medial surfaces of solids

Authors: G. Renner, I.A. Stroud

Addresses: Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary. ' Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary; presently, DGM-ICAP-LICP, EPFL, ME-Ecublens, CH-1015 Lausanne, Switzerland.

Abstract: The Medial Axis Transform (MAT) surface, or simply Medial Surface (MS), offers the possibility of mathematically-based volumetric reasoning about geometric models using global shape and proximity information. The MAT surface is an important tool which can be used for several applications, such as designing manufacturing applications, robot path planning and offsetting, but has the disadvantage that it is computationally intensive. This paper describes two techniques which have been developed to improve the efficiency of the calculation process of the MAT of planar polyhedral objects. The first is a thorough analysis of the cases which can arise when calculating the vertex positions of the MAT of an object as combinations of points, lines and planes. The second technique, presented here, is a divide-and-conquer method, which makes use of some properties of the MAT structure to subdivide the problem. The power of the algorithms is illustrated by some examples, which show the MAT of solid objects with complicated shape and structure.

Keywords: medial surface calculations; skeleton; medial surfaces; solids; medial axis transform surfaces; volumetric reasoning; geometric modelling; planar polyhedral objects; solid objects; shape; proximity.

DOI: 10.1504/IJCAT.2005.006471

International Journal of Computer Applications in Technology, 2005 Vol.23 No.2/3/4, pp.138 - 156

Available online: 13 Mar 2005 *

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