Abstract
Morse theory describes the relationship between a function’s critical points and the homotopy type of the function’s domain. The theorems of Morse theory were developed specifically for functions on a manifold. This work adapts these theorems for use with parameterized families of implicit surfaces in computer graphics. The result is a theoretical basis for the determination of the global topology of an implicit surface, and supports the interactive modeling of implicit surfaces by direct manipulation of a topologically-correct triangulated representation.
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© 1998 Springer-Verlag Berlin Heidelberg
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Hart, J.C. (1998). Morse Theory for Implicit Surface Modeling. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_19
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DOI: https://doi.org/10.1007/978-3-662-03567-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08373-0
Online ISBN: 978-3-662-03567-2
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