基于满射条件的直和分解方法是在研究(二维)T网格上高光滑样条空间维数以及基函数过程中结合经典的光滑余因子方法以及同调代数发现的一种新的研究方法。随着在等几何分析的发展，对于三维T网格上的样条空间研究的必要性也逐步体现。故本项目拟推广基于满射条件的直和分解方法并应用于三维T网格上样条空间的维数研究中。相关工作已有一定的积累，有望完成研究目标。通过本项目的研究为三维T网格上的高光滑样条空间的理论研究提供必要的理论工具。

“The direct sum decomposition based on the surjection condition” is the theoretical tool for analyzing the dimension and basis construction of spline spaces over (2D) T-meshes with the highest smoothness order. This method is developed from the smoothing co-factor method and homological algebra.With Isogeometric analysis background, it is necessary to study spline spaces over 3D T-meshes.This application intends to research on the topics about generalizing “The direct sum decomposition based on the surjection condition” and apply it to the study of dimension of spline spaces over 3D T-meshes. Based on our previous works, the research aims in this application can be expected to be achieved and they will be the indispensable groundwork for analyzing spline spaces over 3D T-meshes.