Fair and robust circle splines

ABSTRACT

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.

REFERENCES

• 1: Henry P. Moreton , Carlo H. Séquin, Functional optimization for fair surface design, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.167-176, July 1992
• 2: Márta Szilvási-Nagy , Teréz P. Vendel, Generating curves and swept surfaces by blended circles, Computer Aided Geometric Design, v.17 n.2, p.197-206, Feb. 2000 [doi>10.1016/S0167-8396(99)00045-X]