文档介绍：摘 要
随着三维扫描技术的成熟和可扫描物体复杂度的提高，三维网格模型日益成为
三维物体的一种通用表示方式，其中又以三角网格模型最为常见。作为众多网格模
型处理技术的前序步骤，三角网格模型的平滑处理己经成为数字几何处理领域的一
个研究热点。
三角网格并不是曲面的参数化表示，所以传统的基于参数曲面的光顺技术不再
完全适用。同时由于网格模型本身的性质，包括取样频率的非规整性，二维流形的
特殊性等，传统的较为成熟的基于二维图像的光顺技术也不能直接使用。这些都对
三角网格光顺处理技术提了新的要求。
在总结分析了几种常用的经典平滑算法和基本顶点扩散的偏微分方程平滑算
法的基础上，提出了与曲率相结合的基于顶点扩散的三维网格平滑算法。与曲率相
结合的基于顶点扩散的三维网格平滑算法针对噪声区域中顶点曲率变化剧烈的特
点，对这些顶点进行较大的平滑位移处理。实验结果表明，本文的算法能够在保持
三维模型几何结构特征的情况下，有效地对网格进行光滑，进一步改善对网格噪声
区域的平滑效果。
关键词：网格平滑；偏微分方程；曲率；特征保持
Abstract
With the development of 3D scan technology and the enhancement of complexity of
scannable objects, 3D mesh model has become a common representation for 3D objects,
among which, triangular mesh is most widely used. As a preceding step for many mesh
processing procedures, the research on triangular mesh fairing has already been hot in
digital geometry processing field.
Triangular mesh is not a parameterized representation of surfaces in nature,
therefore traditional fairing technology for parametric surfaces is no longer applicable. In
addition, because of the features of mesh model, including irregularity of sampling,
speciality of 2-manifold and etc., traditional mature fairing technology for 2D images can
not be directly used either, all these have made new requirements for triangular mesh
fairing.
On the basis of summary and analysis of the classic smoothing algorithms and the
vertex-based diffusion for triangular mesh smoothing by solving nonlinear discrete
partial differential equations, this paper proposes a novel smoothing algorithm for 3-D
meshes based on the vertex diffusion techniques. This proposed algorithm uses smooth
shift method to process the vertices in noise area with regard to their excessive changes
of curvature. Experimental results show that the proposed algorithm can efficiently
smooth the 3-D meshes and improve the quality in the noise area on the premise of
preserving the geometri