Designing Approximate Minimal NURBS Surfaces with Boundaries Interpolation

DOI：

 作者 单位 E-mail 吴花精灵 浙江大学 CAD&CG 国家重点实验室,浙江 杭州 310027 浙江大学 数学系 计算机图像图形研究所,浙江 杭州 310027 王国瑾 浙江大学 CAD&CG 国家重点实验室,浙江 杭州 310027 浙江大学 数学系 计算机图像图形研究所,浙江 杭州 310027 wanggj@zju.edu.cn

探索性地设计了一个插值给定边界曲线的NURBS 近似极小曲面算法,弥补了当前NURBS 系统无法有效地设计工程所急需的一般NURBS 极小曲面的缺陷.运用NURBS 曲面的节点插入、Hybrid 多项式逼近等多种技术,将NURBS 曲面转化为相对简单的分片Bézier 曲面求解,并运用各子曲面片的控制顶点优化、整体曲面不断更新的迭代方法,成功地得到高精度的近似分片Bézier 极小曲面.最后,可以按用户的各种要求选择运用相应不同的迭代逼近算法,求取插值给定边界曲线的近似NURBS 极小曲面.

We explore for designing an algorithm to construct NURBS surfaces with approximate minimal area which interpolate given boundaries, and hence supply a gap that the current NURBS system is unable to design minimal NURBS surface effectively which is urgently required for engineering. Applying multifold techniques of NURBS surfaces such as knot-inserting, Hybrid polynomial approximations, etc., one can convert a NURBS surface into Bézier patches which are relatively simple to get minimal surfaces; then by using iterative method of optimizing the control points of each sub-surface and updating the whole surface continuously, one can obtain approximate minimal Bézier patches with high-precision successfully. In the end, one could choose the corresponding iterated approximation algorithms according to various requirements of different users, to compute the NURBS surfaces with approximate minimal area which satisfy boundary position constraints.
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