Total positivity of the cubic trigonometric bézier basis

Within the general framework of quasi extended chebyshev space,we prove that the cubic trigonometric bézier basis with two shape parameters and given in han et al. (2009) forms an optimal normalized totally positive basis for,[- 2,1 ]. moreover,we show that for =- 2 or =- 2 the basis is not suited for curve design from the blossom point of view. in order to compute the corresponding cubic trigonometric bézier curves stably and efficiently,we also develop a new corner cutting algorithm. © 2014 xuli han and yuanpeng zhu.