Generalizations of non-uniform rational B-splines via decoupling of the weights: theory, software and applications
Generalizations of non-uniform rational B-splines via decoupling of the weights: theory, software and applications
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DOI：
10.1007/s00366-019-00799-w
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发表时间：
2019-06
影响因子：
8.7
通讯作者：
A. Taheri;S. Abolghasemi;K. Suresh
中科院分区：
文献类型：
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作者：
A. Taheri;S. Abolghasemi;K. Suresh
通过对非均匀有理B样条的多重变形的研究，引入了一类新的曲线曲面。这些变化被称为广义非均匀有理B样条（GNURBS）作为一种替代的交互式形状设计工具，并在某些应用中提供改进的近似能力。GNURBS是通过解耦控制点沿沿着不同的物理坐标的权重。这个未被探索的想法带来了将权重视为附加自由度的可能性。可以看出，提出的概念有效地提高了NURBS的能力，并避免了其在特殊应用中的不足。此外，它被证明，这些新的表示只是经典NURBS的伪装形式，保证了强大的理论基础，并促进其利用。几个数值例子表明上级近似结果的GNURBS相比，NURBS在光滑和非光滑的领域。最后，为了更好地展示GNURBS与NURBS相比的行为和能力，开发并引入了一个交互式MATLAB工具箱。
We introduce a new class of curves and surfaces by exploring multiple variations of non-uniform rational B-splines. These variations which are referred to as generalized non-uniform rational B-splines (GNURBS) serve as an alternative interactive shape design tool, and provide improved approximation abilities in certain applications. GNURBS are obtained by decoupling the weights associated with control points along different physical coordinates. This unexplored idea brings the possibility of treating the weights as additional degrees of freedoms. It will be seen that this proposed concept effectively improves the capability of NURBS, and circumvents its deficiencies in special applications. Further, it is proven that these new representations are merely disguised forms of classic NURBS, guaranteeing a strong theoretical foundation, and facilitating their utilization. A few numerical examples are presented which demonstrate superior approximation results of GNURBS compared to NURBS in both cases of smooth and non-smooth fields. Finally, in order to better demonstrate the behavior and abilities of GNURBS in comparison to NURBS, an interactive MATLAB toolbox has been developed and introduced.