基于边折叠和质点-弹簧模型的网格简化优化算法

通过边折叠实现网格曲面简化，提出了保持曲面特征的边折叠基本规则，引入边折叠顺序控制因子λ，给出了折叠点坐标获取方法，简化过程中网格边长度趋于均匀．在曲面简化基础上，利用质点-弹簧模型优化网格形状．将网格顶点邻域参数化到二维域上，在质点-弹簧模型中引入约束弹簧，约束调整网格顶点，并逆映射到三维原始曲面上，局部优化网格顶点的相邻网格；调整曲面上所有网格顶点，在全局上优化网格形状．在曲面简化优化过程中，建立原始模型曲面和简化优化后曲面之间的双向映射关系；曲面的网格顶点始终在原始模型表面上滑动，并以双向Hausdorff距离衡量、控制曲面间的形状误差．应用实例表明：文中算法稳定、高效，适合于任意复杂的二维流形网格．

Mesh Simplification and Optimization with Edge Collapse and Mass-Spring Model

Mesh simplification is realized by collapsing edges in sequence while preserving the geometric feature of surfaces through order control factors. During mesh simplification, length of its edges tends to be uniform. The simplified surfaces are optimized by a mass-spring model: neighborhood vertices of each vertex are parameterized onto a 2D plane, and a constraining spring is introduced into the model to avoid excessive movement of the central vertex; the adjusted result is inversely mapped onto the 3D original surfaces, so the meshes are locally optimal. Surfaces are globally optimized after all the vertices are locally adjusted. During mesh simplification and optimization, bidirectional mapping is fulfilled between the original surfaces and their simplified and optimized results, so vertices of the resultant surfaces are confined to slide on the original ones. Shape errors are measured and controlled by two-side Hausdorff distance. Experimental results show that the algorithm is efficient, robust and can be applied to arbitrary complex 2D manifold meshes.