结合边折叠和局部优化的网格简化算法

Mesh simplification algorithm combined with edge collapse and local optimization

针对目前网格简化算法在将三维模型简化到较低分辨率时,网格模型的细节特征丢失、网格质量不佳的问题,提出一种保持特征的高质量网格简化算法。引入顶点近似曲率的概念,并将其与边折叠的误差矩阵结合,使得简化模型的细节特征在最大限度上得到保持。同时分析简化后三角网格的质量,对三角网格作局部优化处理,减少狭长三角形的数量,提高简化模型的网格质量。使用Apple模型和Horse模型进行实验,并与一种经典的基于边折叠的网格简化算法以及其改进算法之一进行对比。实验结果显示,两种对比算法三角网格分布过于均匀,局部细节模糊不清,而所提算法的三角网格在曲率大的区域稠密,在平坦处稀疏,细节特征清晰可辨;简化模型的几何误差的数量值与两种对比算法处于同一数量级;所提算法的简化网格的平均质量远高于两种对比算法。实验结果表明,在不扩大几何误差的情况下,所提算法不仅具有较强的细节特征保持能力,而且简化模型的网格质量较高,视觉效果较好。

Aiming at the problems that the detail features of the mesh models are lost and the qualities of meshes are bad when the three-dimensional models are simplified to a lower resolution with the mesh simplification algorithms, a high quality mesh simplification algorithm was proposed based on feature preserving. By introducing the concept of approximate curvature of the vertex and combining it with the error matrix of the edge collapse in the algorithm, the detail features of the simplified model were reserved to a great extent. At the same time, by analyzing the quality of simplified triangular mesh, optimizing triangular mesh locally, reducing the amount of narrow triangles, the quality of simplified model was improved. The proposed algorithm was tested on Apple model and Horse model, and compared with two algorithms, one of them is a classical mesh simplification algorithm based on edge collapse, the other is an improved algorithm of the classical one. The experimental results show that when the models are simplified to a lower resolution, the triangular meshes of two contrast algorithms are too evenly distributed, and the local details are not clear, while the triangular meshes of the proposed algorithm are intensive in the areas with large curvature but sparse in the flat areas, and the local details are legible. Compared with the two contrast algorithms, the geometric errors of the simplified model in the proposed algorithm are of the same magnitude; the average qualities of the simplified meshes in the proposed algorithm are much higher than those of two contrast algorithms. The results verify that not only the proposed algorithm can efficiently maintain the detail features of the original model, but also the simplified model has high quality and looks better.