On the Velocity of an Implicit Surface

Jos Stam, Ryan Schmidt

ACM Transactions on Graphics (SIGGRAPH Proceedings)


In this paper we derive an equation for the velocity of an arbitrary time-evolving implicit surface. Strictly speaking only the normal component of the velocity is unambiguously defined. This is because an implicit surface does not have a unique parametrization. However, by enforcing a constraint on the evolution of the normal field we obtain a unique tangential component. We apply our formulas to surface tracking and to the problem of computing velocity vectors of a motion blurred blobby surface. Other possible applications are mentioned at the end of the article.For access to the slides from a recent presentation on the topic, please click here.

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