A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.

提出了一种三角形表面网格平滑方法，通过将原始最佳 Delaunay 三角剖分 (ODT) 扩展到表面网格来提高角度质量。通过求解二次优化问题来提高网格质量，该问题最小化抛物线函数与其在网格上定义的分段线性插值之间的近似插值误差。一个次优问题被推导出来，以保证一个独特的分析解决方案，与最佳解决方案相比，该解决方案在精度损失很小的情况下明显更快。除了质量改进能力外，所提出的方法还适用于去除噪声，同时忠实地保留锐利的特征，例如网格的边缘和角落。包括许多实验来证明该方法的性能。