5 papers
Basis construction for polynomial spline spaces over arbitrary T-meshes
Shicong Zhong, Bingru Huang, Falai Chen
This paper presents the first method for constructing bases for polynomial spline spaces over an arbitrary T-meshes (PT-splines for short). We construct spline basis functions for…
Implicitization of rational hypersurfaces by syzygies with respect to coefficient ideals
Falai Chen, Yunzhi Wang
We study rational hypersurfaces defined as the closure of the image of a generically finite rational map , where $\mathscr…
Dimension Calculation for Spline Spaces over Rectilinear Partitions via Smoothing Cofactor Method
Bingru Huang, Falai Chen
This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach exten…
Dimension of Bi-degree Spline Spaces with the Highest Order of Smoothness over Hierarchical T-Meshes
Bingru Huang, Falai Chen
In this article, we study the dimension of the spline space of di-degree with the highest order of smoothness over a hierarchical T-mesh using the smoothing co…
A Preliminary Study on the Dimensional Stability Classification of Polynomial Spline Spaces over T-meshes
Bingru Huang, Falai Chen
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework.…