Exact Cellular Decomposition of Closed Orientable Surfaces Embedded in R3.

Abstract

We address the task of coverin,q a closed orientable surface embedded in iR3 without any prior information about the surface. For applications such as paint depo­ sition, the effector (the paint atomizer) does not explic­ itly cover the target surface, but instead covers an off­ set surface - a surface that is a fixed dis tance away from the target surface. Just as Canny and others use critical points to look for changes in connectivity of the free space to ensure completeness of their roadmap al­ gor'ithms, we use critical points to identify changes in the conne ctivity of the offset surface to ensure full sur­ face coverage. The main contribution of this work is a method to construct unknow n offset surfaces using a procedure, also developed in this paper, to detect critical points.