Discrete fairing of curves and surfaces based on linear curvature distribution

Curve and Surface Design: Saint-Malo 1999, Laurent, Sablonniere, Schumaker (eds.), pp. 371-380

In the planar case, one possibility to create a high quality curve that interpolates a given set of points is to use a clothoid spline, which is a curvature continuous curve with linear curvature segments. In the first part of the paper we develop an efficient fairing algorithm that calculates the discrete analogon of a closed clothoid spline. In the second part we show how this discrete linear curvature concept can be extended to create a fairing scheme for the construction of a triangle mesh that interpolates the vertices of a given closed polyhedron of arbitrary topology.

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