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Surfaces with Rational Chord Length Parameterization [chapter]

Bohumír Bastl, Bert Jüttler, Miroslav Lávička, Zbyněk Šír
2010 Lecture Notes in Computer Science  
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.  ...  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].  ...  Lávička and ZbyněkŠír were supported by Research Plan MSM 4977751301. All authors were supported by grant 2009/05 of AKTIONÖsterreich-Tschechische Republik.  ... 
doi:10.1007/978-3-642-13411-1_2 fatcat:ix7e4iepwzbv3no65n5elv5y7a

Curves and surfaces with rational chord length parameterization

Bohumír Bastl, Bert Jüttler, Miroslav Lávička, Zbyněk Šír
2012 Computer Aided Geometric Design  
The investigation of rational varieties with chord length parameterization (shortly RCL varieties) was started by Farin (2006) who observed that rational quadratic circles in standard Bézier form are parametrized  ...  by chord length.  ...  chord length parameterization with respect to this reference triangle (in the sense of Def. 1 in  ... 
doi:10.1016/j.cagd.2011.04.003 fatcat:4rkrte3a5fc6riphzfc4yql3t4