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A Signal Processing Approach To Fair Surface Design (1995)
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| Citations: | 654 - 15 self |
BibTeX
@MISC{Taubin95asignal,
author = {Gabriel Taubin},
title = {A Signal Processing Approach To Fair Surface Design},
year = {1995}
}
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Abstract
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 without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique.
Keyphrases
fair surface design signal processing approach arbitrary topology computer graphic object modeling curve surface smoothing surface normal discontinuity polyhedral surface different type linear system computational geometry large surface interactive free-form fair surface design two-dimensional discrete surface signal function vertex location constraint surface subdivision method new tool low-pass filtering computer-aided engineering picture image generation display algorithm linear time subject descriptor space complexity algorithm cr category classical discrete fourier analysis volumetric medical data normal constraint com puter application design general term effective fair surface design technique object representation optimization-based fairing method
