We consider the shape of two point Hermite interpolation on the sphere. A three-parameter family of spherical rational quartic curves has been derived. We derive the singularity conditions theoretically and discuss the shape of the solutions, which is characterized by the presence of loops and cusps on restricted as well as whole segment. Our results can be used to develop a practical scheme for spherical Hermite interpolation, which would generate quartic spherical C¹ Hermite splines.
Citation:
Zulfiqar Habib, Manabu Sakai, "Hermite Interpolation on Sphere," cgiv, pp.416-421, International Conference on Computer Graphics, Imaging and Visualization (CGIV'05), 2005