Optimal Surface Smoothing as Filter Design

For a number of computational purposes, including visualization, smooth surfaces are approximated by polyhedral surfaces. An inherent problem of these approximation algorithms is that the resulting polyhedral surfaces appear faceted. A signal processing approach to smoothing polyhedral surfaces was recently introduced [10, 11]. Within this framework surface smoothing corresponds to low-pass filtering. In this paper we look at the filter design problem in more detail. We analyze the stability properties of the low-pass filter described in [10, 11], and show how to minimize its running time. Then we show that most classical techniques used to design finite impulse response (FIR) digital filters can also be used to design significantly faster smoothing filters. Finally, we describe an algorithm to estimate the power spectrum of a signal, and use it to evaluate the performance of the different filter design techniques described in the paper.