Circular spline fitting using an evolution process

Xinghua Song, Martin Aigner, Falai Chen, Bert Jüttler
2009 Journal of Computational and Applied Mathematics  
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
more » ... 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. • As observed by Wang and Joe [3], arc spline curves are very useful for sweep surface modeling, since they provide highquality approximations of rotation-minimizing frames. • Circular arcs are useful as geometric primitives for algorithms from computational geometry. They combine simplicity of elementary operations with a relatively high geometry approximation power, see [4] . (B. Jüttler). 1 The closest point of a given point on a circle in space can be found by intersecting the circle with the plane spanned by the point and by the circle's axis. If the circle is described by a rational quadratic parametric representation, then this leads to a quadratic equation.
doi:10.1016/j.cam.2009.03.002 fatcat:7dxpejumdbby3crr3cznfniq5a