5 papers · 1 filter
Sharp Dimension Bounds for Spline Spaces over T-meshes with Highest Order of Smoothness
Bingru Huang, Falai Chen
The dimension of a polynomial spline space of bi-degree over a T-mesh with the highest order of smoothness depends on both mesh topology a…
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…
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…
A Preliminary Study on the Dimensional Stability Classification of Polynomial Spline Spaces over T-meshes
Bingru Huang, Falai Chen
This paper studies dimensional stability of polynomial spline spaces over T-meshes with highest-order smoothness. Dimensional stability is defined as the invariance of the dimensio…
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…