Total positivity and convexity preservation
In this paper the author introduces a concept of \(d\)-convexity of curves in the \(d\)-dimensional space and characterizes totally positive blending systems in terms of \(d\)-convexity. He shows that for certain systems total positivity and rational convexity preservation are equivalent. He also characterizes certain convexity preserving systems in terms of weak Chebychev systems. Among other things he derives some results on Wronskians and uses them to obtain formulas for alternating functions of sequences of derivatives of Bézier curves in terms of points in the de Casteljau algorithm. These formulas generlize some earlier results of the author.
scientific article; zbMATH DE number 1251371
scientific article