Computer Examination of Surfaces and Morse Functions
This chapter considers the problem of encoding essential information about a compact surface in terms of a finite amount of data that can be stored and manipulated by computer. If all we want is the topological type of a surface, the genus and the orientability are sufficient. But in many applications, we would like to have a rough version of the geometry, and yet we don’t have, or don’t care about, an exact geometric description of the surface. Using Morse theory, it is possible to assign a code, or schematic representation, to a surface. We consider three problems:
How to code a Morse function on a smooth manifold, and in particular on a surface.
How to code a surface using a Morse function defined on it.
How to reconstruct a surface if we know a coding of it.
KeywordsHeight Function Compact Surface Morse Function Clinical Dentistry Klein Bottle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Japan 1997