基于中轴线的曲面网格质量优化

Surface Mesh Quality Improvement Based on Medial Axis

网格质量对数值模拟的精度和效率有着重要影响,为了提升曲面网格质量,提出一种基于中轴线的曲面网格质量优化算法,由几何特征保持和节点光顺操作组成。采用法向张量投票理论对网格节点进行分类,保证了原始网格的几何特征。节点光顺操作通过不断的调整节点位置来提升网格质量,直到网格质量的变化量小于给定的阈值。针对光滑节点,釆用二分法求解邻域多边形中轴上的最优中心点,并将该最优中心点投影回三维网格上,折痕点的最优位置则通过二次多项式插值法求得。应用实例表明,该方法在保证网格几何特征的基础上,较为明显地提升了曲面网格的质量。

Mesh quality plays an important role in the accuracy and efficiency of numerical simulation. In order to improve the quality of surface mesh, a mesh quality improvement algorithm based on medial axis is proposed, which is composed of geometric feature preservation and node smoothing operations. The normal tensor voting theory is used to classify the surface nodes, which can accurately preserve the geometric features of the original mesh. The node smooth operation improves the mesh quality by constantly adjusting the node position until the change of the mesh quality is less than the given threshold. For smoothing node, the optimal point on the medial axis of the surrounding polygon is obtained by dichotomy, and map the optimal point to original surface mesh, while the optimal location of the crease point is obtained by quadratic polynomial interpolation method. The application examples show that the method can improve the quality of the surface mesh on the basis of ensuring the geometric features of the original mesh.