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Curves and surfaces construction based on new basis with exponential functions. (English) Zbl 1286.65029

Introducing a certain generalization of cubic Bernstein basis functions, generalized Beźier like curves with two shape parameters and corresponding tensor product rectangular patches with four shape parameters are studied here. \(C^1\) and \(C^2\) continuity conditions for joining two such curves are given. Also, \(G^1\) and \(G^2\) continuity conditions for two such patches are obtained. Generalized Beźier like triangular patches are also studied. The shape parameters serve as tension parameters (cf. [L. Yan and J. Liang, Appl. Math. Comput. 218, No. 6, 2863–2879 (2011; Zbl 1251.65015)]).

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D07 Numerical computation using splines

Citations:

Zbl 1251.65015
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References:

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