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\(h\)-Bernstein basis functions over a triangular domain. (English) Zbl 07200766
Summary: In this paper, we introduce and study new \(h\)-Bernstein basis functions over a triangular domain. In particular, after defining the \(h\)-Bernstein polynomial functions of degree \(n\), we prove their algebraic and geometric properties, such as partition of unity and degree elevation and we show that they form a basis for the space of polynomials of total degree less than or equal to \(n\) on a triangle. Then, we propose the \(h\)-de Casteljau algorithm and we prove the Marsden identity.
MSC:
65D Numerical approximation and computational geometry (primarily algorithms)
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