一种基于邻域作用力的三维网格平滑方法

A 3D meshes smoothing method based on neighborhood forces

关键词:  六面体网格  锯齿效应  三维平滑  邻域网格  作用力

Key words:  hexahedral mesh  jagged effect  3D smoothing  neighborhood mesh  force

摘要:

针对以不规则六面体为基元的三维网格模型在对三维区域边界表达时存在锯齿现象，在保持原有网格拓扑结构不变的情况下，提出种基于离散属性数据的邻域网格相互作用力平滑方法。受磁铁"同性相斥"物理特性的启发，将三维网格模型共用顶点的邻域网格体元素根据属性值划分为不同的体块，体块之间具有相斥的作用力，根据体块对顶点的作用合力方向和大小确定网格顶点平滑移动的方向和距离。实际应用表明平滑存在着"拐点"现象，平滑系数取值接近拐点时平滑效果较好，取值偏大或偏小评价指标性能下降。

Abstract:

Hexahedral meshes are widely used to build three-dimensional (3D) geological and reservoir models. However, this voxel model, derived from rectangular grid, has jagged effects when modeling the boundary of a 3D region, which is not consistent with actual geological phenomena. To address the jagged-edge phenomena, under the condition of keeping original topology structure invariable, a smoothing algorithm is proposed based on the forces of neighborhood meshes. The algorithm is inspired by "poles repel" derived from physical properties of a magnet, and the neighboring meshes of a smoothed vertex are divided into different blocks according to their attributes. The blocks have repulsive force. The direction and magnitude of resultant force determine the vertex direction and distance of smoothing movement. The practical application shows that there is an inflection point for smoothing performance and the smoothing performs better when the smoothing coefficient closes to the inflection point; or conversely, the performance is decreasing when smoothing coefficient is away from the inflection point.