Boundary surface recovery from skeleton curves and surfaces

https://doi.org/10.1016/0167-8396(94)E0055-VGet rights and content

Abstract

Medial axis transforms, or skeletons, have many applications in computer aided geometric design and analysis. Construction of skeletons is an active area of research. We consider the inverse problem, that of recovering boundary surfaces from given skeleton elements. The skeleton of any 3D object will, in general, consist of curves and surfaces. In this paper, we first outline a method for reconstructing boundary surfaces corresponding to skeletal curves, and then extend the method for reconstruction of boundary surfaces corresponding to skeletal surfaces. Implemented examples for both curves and surfaces are included.

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    Uniqueness; There is a unique MAT for a given object [36]. Invertibility; With the axis and its radius function one can reconstruct the object by taking the union of all circles centered on the points corresponding to the axis, each with a radius given by radius function [37]. Dimensional reduction; The dimensionality of a MAT is lower than that of its object [38].

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1

Currently with Ford Motor Company, Dearborn, MI, USA.

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