南京航空航天大学 硕士学位论文 基于隐式曲面的离散网格过渡技术研究及应用 姓名：段轶豪 申请学位级别：硕士 专业：航空宇航制造工程 指导教师：程筱胜 2011-03 南京航空航天大学硕士学位论文 i 摘 要摘 要 随着计算机图形学的飞速发展和相关产业的快速增长，人们对三维几何造型的要求越来越 高，如何提供更加灵活、高效且易于操作的几何造型工具，一直是相关技术人员研究、探索的 热点问题。本文在对离散网格曲面技术深入研究的基础上，提出一种基于变分隐式曲面的离散 网格过渡新方法，论文的主要工作如下： （1） 提出了一种新的待过渡网格模型自动定位方法， 通过分别选取待过渡网格模型上的一 个标记点，输入距离参数，利用特征值分解对边界点拟合平面的方法计算定位基准轴，从而构 建待过渡网格模型的定位基准，自动匹配这些定位基准并进行相关的三维几何变换即可实现模 型的自动定位，提高了网格过渡的效率。 （2）通过对待过渡网格边界点三角剖分，实现待过渡网格之间的拓扑融合。首先对待过渡 网格不规整边界进行预处理，使其平整以利于下一步的三角剖分处理；然后利用边界搭桥的方 式，通过设定相关的权值，使得剖分三角片沿边界桥以双向自生长的方式将待过渡网格无缝的 连接起来，并对剖分过程中可能出现的“盲区”进行了专门的讨论。最后，根据边界点拓扑信 息对剖分网格进行细分及优化， 使得其粒度和待过渡网格保持一致， 并具有较好的网格规整性。 （3） 采用一个光滑变分隐式曲面作为中间过渡曲面， 使用变分插值的方法插值边界点位置 约束和法矢约束，生成一个光滑连接待过渡网格边界的变分隐式曲面，通过牛顿迭代将细分优 化后的剖分网格顶点向该隐式曲面上投影，从而实现待过渡网格的几何融合。 关键词关键词：网格自动定位，平面拟合，网格过渡，三角剖分，变分隐式曲面 基于隐式曲面的离散网格过渡技术研究及应用 ii ABSTRACT Along with the rapid development of the computer graphics and the rapid expansion of relevant industries, the strong demand of the tools with high performance for the three- dimensional (3D) geometrical modeling is higher and higher. It is always being a hot topic, of the technical personnel research and exploration, that how to provide the more flexible, efficient and easy to operate tools for 3D geometrical modeling. Based on the thoughts of modeling by example, this paper put forward a new method for discrete mesh blending using variational implicit surface. The main work of this paper is as follows: (1)A new method is proposed for mesh automatic positioning in the mesh blending system. We select the mark points of the two mesh respectively, and then input the parameter of mesh distance. The locating datum axis is calculated by fitting plane on eigenvalue decomposition theory using the boundary points of the mesh. Form the above work ,we are able to get all the positioning datum. So, the mesh automatic positioning can be completed expediently by automatic matching of the locating datum using the relative corresponding 3d geometry transforms. This method of mesh automatic positioning can improve the efficiency of the mesh blending system greatly. (2)We propose a novel algorithm to complete the topology fusion of the bending meshes by triangulation to the boundary points. Firstly, a pretreatment is implemented for the irregular boundary, so that the boundary is flat and favors the next triangulations processing. Secondly, the triangulation processing of boundary points is implemented here. Through the boundary bridging and related weights setting, the new triangles are generated border with both side of the bridge. Consequently, the two boundary of blending meshes are connected seamlessly. Thirdly, we will give a special discussion of the “blind area” during the triangulations process. Finally, the result coarse mesh is refined and optimized, to keep its triangle size consistent with the original blending meshes, and to have good mesh regularity. (3)This paper adopted a smooth variational implicit surface as intermediate blending surface to realize the geometrical fusion of the blending meshes. Using the variational interpolation method of interpolation boundary point position constraints and normal constraints, we can get the smooth variational implicit surface. Then, the vertexes of the refined and optimized mesh will be projected on the variational implicit surface. So that, we complete the geometrical fusion of the blending meshes. Key words: mesh automatic positioning, plane fit, mesh blending, triangulation, variational implicit surfaces 南京航空航天大学硕士学位论文 vii 图表清单 图表清单 图 1.1 基于样例模型的实例（来自互联网） .1 图 1.2 基于样例思想的应用.2 图 1.3 样例造型的实例.5 图 1.4 本文离散网格过渡框架示意 . 10 图 2.1 三角网格细分策略 . 15 图 2.2 不同几何体的属性值 . 16 图 3.1 牙齿模型不同的定位对应产生不同的过渡效果 . 23 图 3.2 待过渡模型定位算法流程图 . 25 图 3.3 模型自动定位流程框架实例图示. 26 图 3.4 牙模预备体定位基准轴拟合 . 30 图 3.5 犰狳兽和马模型过渡自动定位分解图示 . 34 图 3.6 小鹿和人像模型过渡自动定位分解图示 . 36 图 4.1 同向和对向双半球模型过渡效果图 . 38 图 4.2 过渡网格生成流程图. 40 图 4.3 边界预处理示意 .