中文摘要：

针对T样条无法精确表示双曲超越曲面的问题，构造了一种样条曲面——双奇次代数双曲T样条曲面（NUAHT样条），探讨了其细分算法和调配函数的线性无关性．通过将非均匀代数双曲B样条曲~（NUAHB样条曲面）定义在T网上，给出了双奇次NUAHT样条的定义；基于NUAHB样条的节点插入公式，提出NUAHT样条的一种局部细分算法；并证明了NUAHT样条的调配函数线性无关的充要条件，即由NUAHT样条转化为NUAHB样条曲面的过渡矩阵是满秩矩阵．最后，通过实例验证了曲面构建和细分算法的有效性．

英文摘要：

Since T-splines cannot represent hyperbolic spline surfaces exactly, this paper presents a kind of spline surfaces, called non-uniform algebraic hyperbolic T-spline surfaces （NUAH T-splines for short） of odd bi-degree. The NUAH T-splines are defined by applying the T-spline framework to the non-uniform al- gebraic hyperbolic B-spline surfaces （NUAH B-spline surfaces）. Based on the knot insertion of NUAH B-splines, a local refinement algorithm for NUAH T-splines of odd bi-degree is shown. This paper proves that, for any NUAH T-spline of odd bi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAH T-spline-to-NUAH B-spline transformation matrix. Finally, the examples verify the effectiveness of the local refinement algorithm of NUAH T-splines.