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…
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…
Basis Construction for Spline Spaces over Arbitrary Partitions from a Dimensional Stable Perspective
Bingru Huang
This paper introduces a novel framework for constructing basis functions for polynomial spline spaces of degree over arbitrary planar polygonal partitions, overturning th…
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.…