The Analysis of T-spline Blending Functions Linear Independence
The Analysis of T-spline Blending Functions Linear Independence
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DOI：
10.3722/cadaps.2011.735-745
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发表时间：
2011
影响因子：
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通讯作者：
Ai-zeng Wang;Zhao Gang
中科院分区：
文献类型：
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作者：
Ai-zeng Wang;Zhao Gang
摘要 2003年，Sederberg和Zheng提出了T样条，属于带T结的非均匀有理B样条。与B样条相比，T样条具有更多优势，特别是在曲面合并、局部细化和数据压缩方面。 T样条混合功能在T样条曲面建模中起着重要作用。在本文中，我们给出了 T 样条混合函数是否线性无关这一悬而未决问题的等价条件。根据等效条件，提出了一种判定T样条混合函数是否线性无关的算法。最后给出了线性独立性的充分条件，利用该充分条件可以很容易地确定某些T样条混合函数的线性独立性。给出了几个例子来说明该方法的可行性和有效性。
AbstractIn 2003, Sederberg and Zheng proposed T-splines which belongs non-uniform rational B-splines with T-knot. Compared to B-splines, T-splines have more advantages especially in the surface merging, local refinement, and data compression. The T-spline blending function plays an important role in the T-spline surface modeling. In this paper we give an equivalent condition of the open question that whether T-spline blending functions are linearly independent. According to the equivalent condition the paper presents an algorithm to determine whether T-spline blending functions are linearly independent or not. Finally, we give a sufficient condition of the linear independence, and by using the sufficient condition it can be easily to determine the linear independence of some T-spline blending functions. Several examples are given to illustrate the feasibility and effectiveness of this approach.