基于局部多项式拟合的网格简化算法

为了提高网格简化后的三角形质量,提出了一种新的基于顶点局部多项式曲面拟合的三角网格简化算法.用三次多项式曲面拟合网格上的每个顶点及其局部邻域,计算每条边折叠的误差估计,衡量了顶点到拟合曲面的偏离程度,在算法的每次迭代中删除网格上误差估计最小的边,直到网格的顶点个数减到预先给定的数字.基于Laplace算子,增加顶点约束以及顶点邻域重心约束条件，对简化网格作一次线性整体优化.结果表明,该算法保留了更多的网格细节特征,在简化网格的三角形质量方面优于Garland的二次误差度量算法.该算法可用于快速构建模型的细节层次（LOD）模型.

Mesh simplification based on local polynomial fitting

To enhance the triangle quality of the simplified mesh,a novel triangular mesh simplification algorithm based on local polynomial fitting surface of vertices was proposed.After each vertex of the mesh and its local neighbors were fitted using cubic polynomial surface,the error estimation of each edge collapse was computed,and the deviation from the vertex to the fitting surface was measured.An edge on the mesh with the minimal error estimation was deleted in each iteration of the algorithm.When vertex number of the simplified mesh was decreased to the number given,the algorithm was stopped.Vertex constraints and barycenter constraints of vertex neighbors were added,and a global linear optimization based on Laplace operator was performed for the simplified mesh.Results show that the proposed algorithm can preserve more feature details of the mesh,has better triangle quality of the simplified mesh than Garland's quadratic error metrics algorithm,and is suitable for the rapid level of detail(LOD) modelling.