“Fair and robust circle splines” by Séquin and Lee

For many applications, such as aesthetic designs or camera paths, nicely rounded, smooth, interpolatory paths — free of cusps and abrupt hairpin turns — are most important. Such curves can be obtained from globally optimized minimum variation curves (MVC) [Moreton and Séquin 1992], but at high computational costs. We present a blending scheme between circles that robustly produces equally good-looking G2-continuous curves through very challenging sets of interpolation points. One basic method produces such curves in the plane, on a sphere, and in 3D space.

1. MORETON, H. P. AND SEQUIN, C. H. 1992. Functional Optimization for Fair Surface Design. Proc. ACM SIGGRAPH’92, 167–176.
2. SZILVASI-NAGY, M. AND VENDEL, T. P. 2000. Generating Curves and Swept Surfaces by Blended Circles. CAGD 17, 197–206.