Real rational curves are not “unit speed”
Computer Aided Geometric Design
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
Determination and classification of triangular quadric patches
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Bipolar and Multipolar Coordinates
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
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
Complex rational Bézier curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Curves and surfaces with rational chord length parameterization
Computer Aided Geometric Design
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We consider a rational triangular Bézier surface of degree n and study conditions under which it is rationally parameterized by chord lengths (RCL surface) with respect to the reference circle. The distinguishing property of these surfaces is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the distances of the parameter point to the three vertices of the corresponding domain triangle are identical. This RCL property, which extends an observation from [10,13] about rational curves parameterized by chord lengths, was firstly observed in the surface case for patches on spheres in [2]. In the present paper, we analyze the entire family of RCL surfaces, provide their general parameterization and thoroughly investigate their properties.