A circle-preserving variant of the four-point subdivision scheme.

*(English)* Zbl 1079.65514
Dæhlen, Morten (ed.) et al., Mathematical methods for curves and surfaces: Tromsø 2004. Sixth international conference on mathematical methods for curves and surfaces, celebrating the 60th birthday of Tom Lyche, Tromsø, Norway, July 1–6, 2004. Brentwood, TN: Nashboro Press (ISBN 0-9728482-4-X/hbk). Modern Methods in Mathematics, 275-286 (2005).

Summary: The four-point curve subdivision scheme is one of the classic reference points of subdivision theory. It has effective C2 continuity, although the curvature at the data points actually diverges slowly to infinity as very large numbers of subdivision steps are taken. However, it has rather large longitudinal artifacts, so that points interpolated around a curve of almost constant curvature are fitted by a curve with significant variations of curvature. We describe here a geometry-sensitive variant of this scheme which does not have this problem. In fact circles are reproduced exactly with any spacing of the initial data.

##### MSC:

65D18 | Computer graphics, image analysis, and computational geometry |