Differential and Topological Properties of Medial Axis Transforms

authored by

Evan C. Sherbrooke, Nicholas M. Patrikalakis, Franz Erich Wolter

Abstract

The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning, and tolerance specification. In this paper, the theory of the medial axis transform for 3-D objects is developed. For objects with piecewise C² boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed. For n-dimensional submanifolds of ℛⁿ with boundaries which are piecewise C² and completely G¹, a deformation retract is set up between each object and its medial axis, which demonstrates that if the object is path connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path connected medial axes.

External Organisation(s)

New Technologies, Inc
Massachusetts Institute of Technology

Type

Article

Journal

Graphical Models and Image Processing

Volume

58

Pages

574-592

No. of pages

19

ISSN

1077-3169

Publication date

11.1996

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Modelling and Simulation, Computer Vision and Pattern Recognition, Geometry and Topology, Computer Graphics and Computer-Aided Design

Electronic version(s)

https://doi.org/10.1006/gmip.1996.0047 (Access: Closed)