Circular spline fitting using an evolution process

Authors:
Xinghua Song;Martin Aigner;Falai Chen;Bert Jüttler
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China and Johannes Kepler University Linz, Institute of Applied Geometry, Austria;Johannes Kepler University Linz, Institute of Applied Geometry, Austria;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China;Johannes Kepler University Linz, Institute of Applied Geometry, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We propose a new method to approximate a given set of ordered data points by a spatial circular spline curve. At first an initial circular spline curve is generated by biarc interpolation. Then an evolution process based on a least-squares approximation is applied to the curve. During the evolution process, the circular spline curve converges dynamically to a stable shape. Our method does not need any tangent information. During the evolution process, the number of arcs is automatically adapted to the data such that the final curve contains as few arc arcs as possible. We prove that the evolution process is equivalent to a Gauss-Newton-type method.