Surface approximations using generalized NURBS
Surface approximations using generalized NURBS
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DOI：
10.1007/s00366-021-01483-8
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发表时间：
2021-07
影响因子：
8.7
通讯作者：
A. Taheri;K. Suresh
中科院分区：
文献类型：
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作者：
A. Taheri;K. Suresh
我们将作者最近在参数曲线上引入的广义NURBS （GNURBS）概念推广到二元参数曲面。这些推广是通过沿不同物理坐标的显式或隐式权重解耦得到的。与传统的NURBS表面相比，这种解耦允许在更广泛的应用中将权重视为额外的自由度，从而提供额外的灵活性和更好的控制。提出的概念有效地提高了NURBS的性能，缓解了其在某些应用中的不足。特别是，我们将证明GNURBS可以有效地用于某些类型的曲面（如螺旋曲面、旋转曲面和最小曲面）的改进逼近。还将确定这些提出的推广可以精确地转换为等效的，但更高阶的经典NURBS曲面，从而确保强大的理论基础。最后，开发并介绍了一个全面的MATLAB工具箱GNURBS3D-Lab，以便与经典NURBS相比更好地演示GNURBS表面的行为和特性。
We extend the concept of generalized NURBS (GNURBS), recently introduced by the authors for parametric curves, to bivariate parametric surfaces. These generalizations are obtained via either explicit or implicit decoupling of the weights along different physical coordinates. This decoupling allows for treating the weights as additional degrees of freedom in a wider range of applications compared to classic NURBS surfaces, providing additional flexibility and increased control. This proposed concept effectively improves the capability of NURBS and alleviates its deficiencies in certain applications. In particular, we will demonstrate that GNURBS can be effectively used for improved approximation of certain class of surfaces such as helicoids, revolved surfaces and minimal surfaces. It will also be established that these proposed generalizations can be exactly transformed to equivalent, but higher order, classic NURBS surfaces, ensuring a strong theoretical foundation. Finally, a comprehensive MATLAB toolbox, GNURBS3D-Lab, has been developed and introduced in order to better demonstrate the behavior and properties of GNURBS surfaces compared to classic NURBS.