A signal processing approach to fair surface design

13 years 8 months ago

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In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals – functions deﬁned on polyhedral surfaces of arbitrary topology –, we reduce the problem of surface smoothing, or fairing, to low-pass ﬁltering. We describe a very simple surface signal low-pass ﬁlter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed w...

Gabriel Taubin

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