Fair and robust circle splines

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.