and references

Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space. (English summary) Comput. Aided Geom. Design 28 (2011), no. 2, 127–134. The authors consider special rational triangular Bézier surfaces of degree two on the sphere in standard form and they show that these surfaces are parameterized by chord length. More precisely, it is shown that the ratios of the three distances of a point to the patch vertices and the ratios of the distances of the parameter point to the three vertices of the (suitably chosen) domain triangle are identical. This observation extends an observation of Farin (2006) about rational quadratic curves representing circles to the case of surfaces. In addition, the authors discuss the relation to tripolar coordinates