| 摘要: |
| 为弥补当前NURBS 系统无法有效设计工程所急需的B 样条极小曲面的缺陷,将构造Bézier 极小曲面的 Dirichlet 方法成功地推广到了B 样条极小曲面设计.提出了插值控制网格边界的B 样条曲面模型,运用B 样条基函数的求导公式及求值割角算法,将计算极小曲面内部控制顶点的问题转化为一个线性方程组的求解,从而避免了强非线性问题所导致的困惑,极大地提高了运算效率.最后,用大量实例对理论和算法进行了验证. |
| 关键词: 计算机辅助设计 Dirichlet 方法 B 样条曲面 极小曲面 |
| DOI：10.3724/SP.J.1001.2011.04009 |
| 分类号: |
| 基金项目:国家自然科学基金(61070065, 60933007) |
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| Extending Dirichlet Approach to Design B Spline Surface of Minimal Area |
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WU Hua-Jing-Ling1,2, WANG Guo-Jin1,2
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1.State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China;2.Institute of Computer Images and Graphics, Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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| Abstract: |
| The current NURBS system is unable to design a B-spline minimal surface effectively which is required for engineering. This paper extends the Dirchlet approach, constructing Bézier minimal surface to the design of B-spline minimal surfaces successfully. The study also proposes a model of B-spline surface which interpolates its control net at the boundary, applying the derivative formulae and cutting-angle evaluation algorithms of B-spline basis. This approach transforms the problem of computing internal control points of the minimal surface to solving a system of linear equations, avoiding the bewilderment brought by a strong nonlinear problem and advancing operational efficiency greatly. Finally, with a large number of examples, the theory and algorithms are verified. |
| Key words: computer aided design Dirichlet approach B spline surface surface of minimal area |
