Journal of Computational and Applied Mathematics ( IF 2.1 ) Pub Date : 2020-10-16 , DOI: 10.1016/j.cam.2020.113245 Jan Grošelj , Hendrik Speleers
Starting from a general B-spline representation for cubic Powell–Sabin splines on arbitrary triangulations, we focus on the construction of a B-spline representation for a particular subspace defined on three-directional triangulations with super-smoothness over each of the macro-triangles. We analyze the properties of the basis and point out the relation with simplex splines. Furthermore, we provide explicit expressions for the B-spline coefficients of any element of the spline space, and derive subdivision rules under dyadic refinement. Finally, we show simple conditions ensuring global smoothness on the domain.
中文翻译:
三方向三角剖分上的超光滑三次Powell-Sabin样条:B样条表示和细分
从一般的B样条表示开始 关于任意三角剖分的三次Powell–Sabin样条曲线,我们专注于针对在三向三角剖分中定义的特定子空间的B样条表示的构造 每个宏三角形的超平滑度。我们分析了基础的属性,并指出了与单纯形样条曲线的关系。此外,我们为样条空间中任何元素的B样条系数提供了显式表达式,并在二进式细化条件下得出细分规则。最后,我们展示了简单的条件来确保全球 域上的平滑度。