基于面法向量谱变换的网格光顺算法

摘要

Differential coordinate is a powerful tool to characterize the geometry details of the grid model. Surface normal vector is a simple calculation,and it is not affected by noise as a first-order differential coordinates which can reflect detailed features of the grid model. This paper proposes an improved mesh smoothing denoising algorithm. The surface normal vector is transformed to the frequency domain using spectral mesh processing method through the Laplacian matrix decomposition. It can get smoothing facet continuous signal by low pass filter. The grid model is built through triangle barycenter constraints. Experimental results show that the algorithm is not easily affected by the noise, more robust than the vertex normal vector, and it can overcome the problems of volume shrinkage in the process of smoothing.%微分坐标是刻画网格模型几何细节特征的有力工具，面法向量作为网格模型的一阶微分量，计算简单、不易受噪声影响，能真实反映网格模型的细节特征。基于此，提出一种改进的网格光顺去噪算法，使用信号处理技术中的谱网格处理方法，通过分解面法向量的拉普拉斯矩阵，将网格模型的面法向量变换到频谱域中，利用低频滤波器去除高频噪声得到连续的面法向量信号，基于三角面片重心约束条件重建网格顶点坐标，得到光顺的网格模型。实验结果表明，该算法使用的面法向量不易受到噪声影响，比顶点法向量更鲁棒，大幅提高了谱分解的效率，并且能克服光顺过程中产生的体积收缩、变形和过光滑等现象。