The shape of spherical quartics

Authors:
Bert Jüttler;Wenping Wang
Affiliations:
Johannes Kepler University, Institute of Analysis, Department of Applied Geometry, Altenberger Str. 69, 4040 Linz, Austria;The University of Hong Kong, Department of Computer Science and Information Systems, Pokfulam Road, Hong Kong, China
Venue:
Computer Aided Geometric Design
Year:
2003

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Abstract

We discuss the problem of interpolating C1 Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves. With the help of the generalized stereographic projection (Dietz et al., 1993), we construct a two-parameter family of spherical quartics solving this problem. We study the shape of these solutions and derive criteria which guarantee solutions without cusps or self-intersections.