随着CAD/CAM的迅速发展，人们对产品的几何外形设计提出了更多更高的要求，用于产品几何外形设计的曲面光顺和过渡曲面构造方法受到了极大的重视和广泛的研究，已成为当前的研究热点。本文主要研究网格曲面光顺和过渡曲面构造方法及其在虚拟牙齿矫正系统中的应用。 　　　通过对常见网格光顺算法的研究和分析，研究并实现了基于特征域的网格模型光顺方法。该方法首先根据三角面片的法矢变化率将模型划分为非特征区域和特征区域；然后分别采用拉普拉斯算子和组合双边滤波算子进行了非特征域和特征域的三角面片法矢调整；接着在法矢调整的基础上，采用夹角和面积加权平均进行了模型顶点位置调整，实现了模型的光顺处理。牙齿模型的光顺效果显示，该方法有效可行。 　　　在对各种典型过渡曲面构造方法，如滚球法、偏微分方程法、能量法、基于脊线、裁剪线等的基本原理、特点、使用范围、优缺点进行比较和分析的基础上，重点研究了基于能量法的四边域过渡曲面构造方法，实现了牙冠间过渡曲面的构造。该方法首先提出了基于边界边比较和基于哈希表的边界提取快速算法，实现了牙冠边界的快速提取；其次，在牙冠边界提取基础上，确定了四边域结构的过渡区域；最后，根据牙冠边界顶点的法矢和曲率约束，建立了合理的能量优化模型，通过模型化简，并采用广义拉格朗日乘子法进行模型的求解，获得了过渡曲面的控制顶点，实现了牙冠间G1连续过渡曲面的可视化显示。 　　　本文采用Visual Studio 2005为开发平台实现了牙齿模型的光顺，牙冠的边界提取及牙冠间过渡曲面的构造。实验结果表明，本文提出的算法能够达到预期的效果，有较高的运行效率和较好的实用性。

With the rapid development of CAD/CAM, people bring forward higher requests to the product geometric design. Surface smoothing and blend surface constructing for the product geometric design has been received great attention and extensive research, which has become a research hotspot. This paper mainly focused on the grid surface smoothing algorithm and blend surface constructing method and its application in virtual orthodontics treatment system. 　　　On the basis of analysis of the traditional grid smoothing algorithm, a new algorithm based on the feature regions is studied and realized in this paper. Firstly, the grid model is divided into the non-characteristic and characteristic feature regions according to the variation of the normal. Secondly, the normal vector of triangular mesh is adjusted by Laplacian and combining bilateral filtering in feature regions, respectively.Finally, smoothed model is achieved through adjusting the mesh vertices according to the weighted average of the area and angle based on the normal vector adjusting. Experiment result of the dental model shows that the method is effective and feasible. 　　　Based on the comparing and analyzing of the basic principle, characteristics, applications, merits and demerits of the typical blend surface construction methods, such as Rolling-ball blends, Partial Differential Equations, Energy method, this paper mainly studied the energy-based method to construct blend surface based on quadrilateral regions and realized the blend surface construction between the crowns. Firstly, fast methods based on boundary comparing and hash map are proposed on the basis of the tranditional method, and the extraction of the crown boundary is obtained. Secondly, on the basis of the crown boundary extraction, this paper identified the quadrilateral regions as the blend area. Finally, the reasonable mathematical model is established under the constraints of boundary normal and boundary curvature.Through simplifying the mathematical model, the generalized Lagrange multiplier method is adopted to absolve the model and obtained the control points, which implements the visualization of the blend surface between the crowns. 　　　This paper selected Visual Studio 2005 as the development tool. It realized the dental model smoothing, the crown boundary extraction and blend surface construction between the crowns. The results of the experiment show that the algorithms mentioned in this paper can achieve the desired effect, which has higher proficiency and better practicability.