Author

Bing-Ru Huang

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Preprint Sep 2026

PH2T-splines, Part I: A Reasonable Mesh Assumption

This paper is the first in a three-part series on the construction of polynomial splines with the highest order of smoothness over hierarchical T-meshes, referred to as $\PHtwoT$-splines. For splines of bi-degree $(d,d)$, we study suitable refinement conditions for the subsequent basis construction, which requires dime...

Bing-Ru Huang, Yue Xi · 0 citations

Preprint Aug 2026

A Homological Decomposition for the Dimension and Dimensional Stability of Polynomial Spline Spaces over T-Meshes

We study the dimension and dimensional stability of polynomial spline spaces of bi-degree $(m,m')$ with prescribed smoothness orders over planar T-meshes. The homological dimension formula writes the spline dimension as the sum of an Euler characteristic term and a correction term. For a fixed ordered bi-degree, the Eu...

Bing-Ru Huang · 0 citations