基于顶点分类的曲面三角网格模型自适应光顺研究

逆向工程中由测量数据得到的三角网格模型往往含有大量的噪声、扰动及不规则三角片，需对其进行光顺处理，以满足后续处理的使用要求。本文首先提出了一种新的网格模型顶点法矢计算公式，该公式采用网格模型中三角片面积与顶角角度综合加权，可同时反映三角片面积与顶角角度对顶点法矢的影响。在此基础上，对网格模型顶点进行了分类处理，提出了能够反映网格顶点特征性质的顶点势概念。势为1的点为特征点，势为0的点为普通点。最后，提出了一种新的自适应曲面三角网格模型光顺方法，综合了普通拉普拉斯光顺法与平均曲率法的优点。在该方法中，顶点调整方向为拉普拉斯光顺矢量在被调整顶点切平面上的分量与该点法矢的加权合成；顶点调整幅度根据顶点类别的不同而不同，特征点的调整幅度小，普通点的调整幅度大，从而可保护原有特征。实例表明，与现有方法相比，该方法在有效去除噪声，匀化三角片的同时，充分保留了初始网格模型上的特征。

Research on Adaptive Smoothing of Triangular Meshes Based on Vertice Classification

A new formula for the calculation of mesh vertex normal vector is presented. Utilizing the weight combination of areas and vertex angles of correlated mesh triangles, the formula can represent the affects of the triangle area and vertex angles. And then, a new concept and the vertex power are put forword. Based on this new concept, mesh vertices are classified. Vertices of power 1 are classified as feature ones, and power 0 common ones. Finally, a novel adaptive mesh smoothing method is devoloped. The method maintains the merits of Laplacian and mean curvature methods. In smoothing process, the vertex is regulated in the direction of combination of Laplacian smoothing and mean curvature smoothing vectors, so mesh triangles can be uniformed. Unlike the uniform displacement in Laplacian or mean curvature methods, in the method, the regulating displacements vary with the category of vertices. For feature vertices the displacement is small and for common ones the displacement is big. After smoothing process, features of the original mesh can be perfectly preserved. Compared with existing methods, the method can efficiently eliminate noises and uniform triangles and preserve features of the original meshes.