Nonlinear Weighted Average and Blossoming
Rongin Uwitije , Xuhui Wang , Ammar Qarariyah , Jiansong Deng
Communications in Mathematics and Statistics ›› 2020, Vol. 8 ›› Issue (3) : 361 -378.
Nonlinear Weighted Average and Blossoming
In this paper, we introduce a new averaging rule, the nonlinear weighted averaging rule. As an application, this averaging rule is used to replace the midpoint averaging in the de Casteljau evaluation algorithm and with this scheme we can also generate transcendental functions which cannot be generated by the classical de Casteljau algorithm. We also investigate the properties of the curves of the functions generated by blossoming, where the results show that these curves and the classical Bézier curves have some similar properties, including variation diminishing property and endpoint interpolation. However, the curves obtained by blossoming using nonlinear weighted averaging rules induced by certain functions violate some properties like convex hull property.
Nonlinear weighted averaging rule / Midpoint averaging / De Casteljau algorithm / Bézier curves / Blossoming
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