含复杂插值曲面实体四面体网格优化方法

Method for optimizing tetrahedral mesh of object with complex interpolation surfaces

复杂插值曲面的几何形态由分布稀疏且不均匀的散乱数据点控制,含这类曲面实体的四面体网格优化在保证边界一致时存在一定的困难。提出一种将网格优化与曲面插值相结合的优化方法。借鉴Balendran提出的直接法,将正三角形结点之间的空间关系作为几何规则,以移动结点使四面体的所有侧面尽量趋近于正三角形,实现网格优化。用线性方程组表示这种几何规则,形成优化约束。将原始采样点及其它控制界面几何形态的数据转化为控制点约束,以保证边界一致性。结合优化约束与控制点约束,作为离散光滑插值(DSI)方程的约束项,实现网格优化与曲面插值的耦合。实例表明,该方法能够在保证复杂插值曲面边界一致性的前提下实现四面体网格优化。

The shape of interpolated surface is determined by sparse and scattered data points, and it is difficult to keep interfaces consistency when optimizing tetrahedral mesh of object with these kinds of surfaces. An optimization method coupled with interpolation of interface is proposed. According to direct method proposed by Balendran, a geometric criteria, which expressing the spatial relationship among nodes of equilateral triangle, is used to convert all triangles oftetrahedron to equilateral ones in order to optimize the mesh. The geometric criteria is denoted by linear equations and treated as optimization constraints. The samples and other data which controlling the shape of interfaces are treated as control point constraints to keep interfaces consistency. Through coupling aforementioned two kinds of constraints, and treating them as constraints of discrete smooth interpolation （DSI） function, mesh optimization is achieved under the condition of interfaces consistency. One case illuminates the validity of this method.