【作者】 聂军洪；

【导师】 周来水；

【作者基本信息】 南京航空航天大学 ， 航空宇航制造工程， 2003， 博士

【摘要】 三角网格模型是逆向工程、快速原型制造、数控加工编程、三维动画等技术中常用的模型表示方法，模型的质量直接影响到产品的质量，尤其在逆向工程中，直接通过测量数据得到高质量的网格模型几乎是不可能的。因为，测量数据中不可避免地存在各种噪声和扰动，因此在满足几何精度要求的前提下，对网格模型进行优化调整，以提高模型质量就十分必要。作者在研究消化所能收集到的国内外相关资料的基础上，对三角网格模型的外形光顺、特征修复和三角片优化等技术进行了深入研究。主要内容如下： 研究了任意拓扑结构三角网格模型的整体光顺和局部光顺调整方法。融入平均曲率光顺思想，对拉普拉斯算子进行改进，通过在法矢方向和切平面上同时对网格顶点进行移动调整，较好地达到模型外形光顺、三角片形状比较均匀的要求。 研究了三角网格模型的特征修复方法。通过依次对模型中三角片法矢和网格顶点进行调整，不仅保证了新生成网格拓扑结构不变，具有较好的光顺效果，而且调整后的模型特征清晰突出。 研究了基于边交换的三角网格模型优化调整方法。采用遗传算法按照一定准则不断进行边交换调整，提高了模型表面的光顺性。 研究了基于自适应细分的劣质三角片去除算法。首先对原始网格进行自适应细分，接下来通过边删除操作来简化细分后三角网格模型，彻底清除模型中的所有劣质三角片。 研究了任意三角网格模型重新布点的算法。通过合理规划采样方案，实现了自适应地对初始网格模型进行重新布点。能够较好地控制新生成的网格模型的精度，保证了新网格与初始网格间的最大误差满足要求。更多还原

【Abstract】 Triangle mesh models have been established as the most general and flexible schemes to represent complex surface models in the area of reverse engineering (RE), rapid prototyping manufacturing (RPM), numerical control (NC) programming, 3D animation, etc. But the models reconstructed from real-world data may contain unavoidable noise and many narrow triangles, so the models must be optimized and modulated under given tolerances. The techniques of smoothing, feature enhancing and optimization of triangle facet’s shape are investigated systematically in this paper.Based on modification of Laplacian operator and mean curvature technique, an adaptive regularizing and smoothing mesh algorithm is put forward. With the algorithm, fairing and uniform meshes are obtained by moving each vertex in normal direction and tangent plane simultaneously.An algorithm of feature enhancing and mesh smoothing is studied. The algorithm is based on iterative use of diffusion of normals and vertices. Fairing meshes are obtained by moving each vertex in the modified normal direction.An optimization algorithm of triangle meshes is researched. The optimized triangles with locally minimized discrete curvature, are obtained by swapping edges sequentially.Many meshes live with narrow triangles, which could affect the following operations. A narrow triangle elimination algorithm is presented. All narrow triangles can be elimated by adaptive subdivision and edge collapsing schemes.An adaptive remeshing algorithm is presented. In the algorithm, the original mesh is resampled and the base mesh is recursively refined. By properly programming the resampling procedure, the algorithm can automatically resample more points in the region with higher curvature.更多还原