Constructing easily invertible Be´zier surfaces that parameterize general quadrics
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
NURBS: From Projective Geometry to Practical Use
NURBS: From Projective Geometry to Practical Use
Bipolar and Multipolar Coordinates
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
An algorithm for parametric quadric patch construction
Computing - Geometric modelling dagstuhl 2002
Rational quadratic circles are parametrized by chord length
Computer Aided Geometric Design
Curves with rational chord-length parametrization
Computer Aided Geometric Design
Curves with chord length parameterization
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Surfaces with rational chord length parameterization
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Curves and surfaces with rational chord length parameterization
Computer Aided Geometric Design
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We consider special rational triangular Bezier surfaces of degree two on the sphere in standard form and 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, we discuss the relation to tripolar coordinates.