【作者】 李奇敏；

【导师】 柯映林；

【作者基本信息】 浙江大学 ， 机械制造及其自动化， 2006， 博士

【摘要】 在基于特征的反求工程中，基于截面数据的曲面重建技术和基于特征曲面逼近的曲面重建技术已经有相当广泛和深入的研究，形成了比较完整的反求工程CAD建模理论。进一步的研究主要集中在如何把新的数学工具引入到反求工程中，提高重建过程中各个算法的稳定性和效率；如何利用新的工具拓展已有的功能，方便产品的再设计。在此背景下本文对小波技术在反求工程中的应用进行了研究。 对小波技术在基于截面曲线的反求工程中的应用进行了研究。提出了形状尺度因子和波动程度等概念，结合去除细节重建的小波变换对截面线的形状进行分析，提取截面线的主要曲率分布情况，在此基础上给出了基于均值坐标流的截面线光顺算法，以及基于小波的特征点提取方法。最后给出了基于变截面轮廓的管道曲面重建方法。 提出了一种基于几何图像分割实现网格分割的方法。在网格参数化的基础上，改进了几何图像的生成方法。基于去除逼近项小波重建和基于梯度图像两种方法分割法矢图像，基于阈值法分割曲率图像。最后把几何图像的分割结果映射回到原始网格，实现网格的分割。 提出了基于图的三角网格分割方法。在实现上述基于几何图像的网格分割方法过程中还找到了另一条利用图论方法直接实现三角网格数据分割的途径，首先分别以网格中的顶点和三角面片作为图中的元素生成两种未定向加权全连通图的表达，然后对所建立的图用图论的方法进行分割，进而实现网格的分割。另外对三角网格上颜色信号的滤波和增强也作了一些研究，提出了基于直方图均衡化的网格数据颜色信号增强方法和基于均值滤波、中值滤波的去噪方法。 提出了基于非均匀B样条小波分解实现NURBS(非均匀有理B样条)曲线、曲面光顺的方法。利用不同的节点选取方法实现曲线的局部光顺和全局光顺，通过添加边界约束，保持了曲线的和相邻曲线之间的连接关系。用基于小波分解的最小区域算法来实现曲面局部光顺。对于由用户通过交互选择等参数曲线圈定的区域，利用小波分解实现曲面在该区域内部的光顺。曲面的整体光顺首先通过全局光顺度量决定光顺方向，然后再用小波分解实现曲面的光顺。曲面光顺时，也可以像曲线光顺时一样通过添加约束保持边界的连续性不变。在曲面光顺之后，本文还对曲面的光顺性分析进行了研究。从裁剪曲面三角化到曲面的曲率、反射线、高亮线、等照度线的生成等方面出发，改进了基于离散模型的曲面光顺性分析的算法。更多还原

【Abstract】 In feature based reverse engineering, surface reconstruction based on sectional curves and surface approximation has been broadly and deeply investigated. A feature based reverse engineering CAD modeling theory has been formed. How to introduce new mathematical methods into reverse engineering to improve the robustness and efficiency of algorithms, and how to use new methods extend existed function to facilitate product redesigning are becoming more and more attractive. Under this situation, the wavelets application in reverse engineering was studied in this thesis.Wavelets application in sectional curve based reverse engineering was studied. The concept scale factor and fluctuation were proposed to analyze sectional curve combined with detail-removed wavelet reconstruction. Based on the analysis, a fairing method of sectional curve-mean coordinate flow was proposed. Wavelets based feature point extraction method of sectional curve was presented. Finally a pipeline surface reconstruction method based on sectional contour was given out.A geometry image based mesh segmentation method was proposed. The parametrization of mesh that homeomorphic to a disk was presented firstly. The formation of geometry image based on geometry information was improved. Two segmentation methods of normal image were proposed. One is based on wavelets reconstruction that the approximation term was removed when wavelet reconstruction. Another one is based on gradient image segmentation method. The threshold segmentation method of curvature image was also studied. All these methods are combined with morphological methods to realize geometry image segmentation.A graph based mesh segmentation method was proposed. Two kinds of undirected, weighted graph were constructed to represent mesh. Vertices and triangles of mesh were taken as elements of graph respectively. The constructed graph was segmented by a disjoint-set forest, so the mesh. The filtering and enhancement of color information on mesh were researched too.A non-uniform B-spline wavelets decomposition fairing method of B-spline curves and surface was proposed. A fairing method of NURBS curve was given out. Different kinds of knot selection methods were used to realize local and global fairing.更多还原