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Delgado, J.; Orera, H.; Peña, J. M.

An evaluation algorithm for \(q\)-Bézier triangular patches formed by convex combinations. (English) Zbl 07711022

J. Comput. Appl. Math. 428, Article ID 115184, 11 p. (2023).
Summary: An extension to triangular domains of the univariate \(q\)-Bernstein basis functions is introduced and analysed. Some recurrence relations and properties such as partition of unity and degree elevation are proved for them. It is also proved that they form a basis for the space of polynomials of total degree less than or equal to \(n\) on a triangle. In addition, it is presented a de Casteljau type evaluation algorithm whose steps are all linear convex combinations.

Cited in 1 Document

MSC:

65Dxx Numerical approximation and computational geometry (primarily algorithms)
41Axx Approximations and expansions
65Fxx Numerical linear algebra

Keywords:

convex combinations; \(q\)-Bernstein basis; \(q\)-Bézier triangular patch; de Casteljau evaluation algorithm; corner cutting algorithm; degree elevation

Software:

POLYNOMIAL
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References:

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