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TW 433
Tim Volodine, Denis Vanderstraeten, and D. Roose
Reconstruction and smoothing of polygonal curves
Abstract
In this paper we propose a method for piecewise linear reconstruction and subsequent smoothing of a point sampled curve. The reconstruction step is based on the meshless parameterization reconstruction algorithm proposed by Floater. The information computed in the reconstruction step is used for a least squares based discrete smoothing method, with behavior comparable to a smoothing spline. We discuss smoothing under two different constraints: one based on the sum of squared deviations and the other based on a max-norm error. The smoothing algorithm is essentially a variation on the least squares meshes concept proposed by Sorkine et al. The reconstruction and smoothing steps are conceptually similar and provide a unified approach to the reconstruction of smooth curves in an arbitrary dimensional space.
report.pdf (829K) / mailto: T. Volodine