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We discuss three different affine invariant evolution processes for smoothing planar curves. The first one is derived from ageometric heat-type flow, both the initial and the smoothed curves being differentiable. The second smoothing process is obtained from a discretization of this affine heat equation. In this case, the curves are represented by planarpolygons. The third process is based onB-spline approximations. For this process, the initial curve is a planar polygon, and the smoothed curves are differentiable and even analytic. We show that, in the limit, all three affine invariant smoothing processes collapse any initial curve into anelliptic point.
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 30, 2004
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