The smoothness and angle quality of a surface mesh are two important indicators of the “goodness” of the mesh for downstream applications such as visualization and numerical simulation. We present in this paper a novel surface mesh processing method not only to reduce mesh noise but to improve angle quality as well. Our approach is based on the local surface fitting around each vertex using the least-square minimization technique. The new position of the vertex is obtained by finding the maximum inscribed circle (MIC) of the surrounding polygon and projecting the circle’s center onto the analytically fitted surface. The procedure above repeats until the maximal vertex displacement is less than a pre-defined threshold. The mesh smoothness is improved by a combined idea of surface fitting and projection, while the angle quality is achieved by utilizing the MIC-based projection scheme. Results on a variety of geometric mesh models have demonstrated the effectiveness of our method.

表面网格的平滑度和角度质量是下游应用（如可视化和数值模拟）网格“好坏”的两个重要指标。我们在本文中提出了一种新颖的表面网格处理方法，不仅可以减少网格噪声，还可以提高角度质量。我们的方法基于使用最小二乘最小化技术围绕每个顶点的局部表面拟合。顶点的新位置是通过找到周围多边形的最大内切圆 (MIC) 并将圆的中心投影到解析拟合的表面上来获得的。重复上述过程，直到最大顶点位移小于预先定义的阈值。通过曲面拟合和投影相结合的思想，提高了网格平滑度，而角度质量是通过利用基于 MIC 的投影方案来实现的。各种几何网格模型的结果证明了我们方法的有效性。