一种自由曲面自适应网格生成方法

为了在造型复杂的自由曲面上生成规整、流畅的结构化网格,提出一种自适应网格生成方法.首先,用4条边界线圈定网格划分区域;接着,将一对不相连的边界线各自分为n+1段并连接相对的分段点,得到n条曲线;然后,将这n条曲线和同向的边界线分别划分为m+1段,并以多段线连接同一相对位置上的分段点,得到另一个方向上的m条曲线.轮流对这m条曲线和n条曲线进行分段、连线等操作,优化各自的形态,直到分段点位置基本不变;最后,将分段点按照一定的规律连接成网格.在网格生成过程中,通过调整曲线的分段原则,可以实现网格大小对边界线或曲面形态的自适应;通过设定多种点阵的连接规律,可以生成多种样式的网格.案例分析表明:该方法操作难度小、生成速度快、适用范围广,生成的网格线条流畅、形状规整、形式多样,能较好地满足建筑需求.

Adaptive grid generation over free-form surfaces

To generate regular and fluent structured grids over free-form surfaces, especially complex multiple surfaces for architectural design, an adaptive grid generation method was proposed. First, the surface region to be meshed was determined by four boundary curves. Second, a pair of disconnected boundary curves was divided into n+1 segments respectively and n lines were acquired by connecting pairs of segment points on the same relative positions. Third, these n curves and the other pair of boundary curves were divided into m+1 segments respectively, and m polylines on the other direction were attained by connecting these segment points on the same relative locations. These two sets of curves were divided and reconnected in turn iteratively until the locations of segment points did not change obviously. Finally, the (m+2)×(n+2) segment points were connected into a grid in a desired pattern. During the generation, the grid size was adaptive to boundary conditions or surface shapes by adjusting the rules of curve dividing, and various girds was generated by defining different rules of point connections. The case study indicates that this method is easy to operate, fast to generate, and widely applicable, and the resulting grids have fluent lines, regular shapes, and various patterns, which can meet architectural demands.