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.
h-Bernstein basis functions over a triangular domain
Lamberti P.;Remogna S.;
2020-01-01
Abstract
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.
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