推广Dirichlet方法用于B样条极小曲面设计

Extending Dirichlet Approach to Design B Spline Surface of Minimal Area

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.

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 Bezier 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 .