【作者】 张丽娜；

【导师】 顾耀林；

【作者基本信息】 江南大学 ， 计算机应用， 2007， 硕士

【摘要】 计算机图形学中一个重要的研究对象就是三维空间对象。凭借着良好的视觉效果和广泛的应用领域,无论是科学研究还是经济需要,三维空间的拓扑可视化和多面体变形一直是该领域的研究焦点,越来越受到大家的青睐。本文在分析可视化和变形的基本技术的基础上逐步延伸,讨论了一种新的拓扑可视化方法,并提出一种基于连通性转换的多面体快速变形方法。在可视化部分,本文研究了基于莫尔斯理论的离散梯度向量域的构建方法,并尝试性的将其应用于拓扑可视化。用该方法和流形可视化方法分别演示了Moebius带和海螺,并做了分析和对比。从论文最终研究目的角度出发,结合实践,介绍了相关理论和离散梯度向量域构造过程,并完成向量域的可视化。实验结果表明了该方法的有效性。对于三维多面体变形,提高变形速度一直是一个关键问题。本文研究了连通性转换方法,并将其应用于三维多面体的快速变形。采用优先权控制函数控制模型特征,实现点和边的同步处理。通过预先安排连通性转换提高了变形速度,通过解一个稀疏线性方程组缩短变形片的嵌入时间。之后,通过矫正特征点以及边界处理得到平滑的变形序列。本文用该方法和传统变形方法分别演示了三维多面体模型的变形实例,并对实验结果和相关数据进行了分析比较。实验结果表明,该变形方法可快速实现平滑变形。更多还原

【Abstract】 The 3D object is an important aspect in the computer graphics. For the preferable vision purpose and the broad application purpose, whether for science research or economic requirement, the technology of visualizing and morphing of 3D object is always the focus in this domain,and it is becoming a favorite focus.In this article, we have analyzed the basic technologies of visualization and metamorphosis. This thesis discussed a new method of visualization, and then presented a fast metamorphosis technology based on the connectivity transformation.During the processing of 3D visualizing, the discrete gradient vector filed based on the Morse theory is presented, and is applied to visualization of topologies. This method and another flow-visualization way are respectively demonstrated with the Moebius strap and the trumpet shell, the analysis and the compare are presented. Considering our ultimate research purpose and practicality, the correlative theories are introduced first and then to construct the discrete gradient vector field. Finally the vector filed is visualized, and experiments show the availability of the result.As for the fast metamorphosis of 3D polyhedral models, advancing the speed of metamorphosis is always a key issue. The connectivity transformations were presented, and were applied to the fast metamorphosis of polyhedral. In order to controls the both models’features in the process of metamorphosis, the priority control function was used to handle both vertex and edge at the same time. The scheduling connectivity transformations operation advanced the speed of morphing. A sparse linear system decreased the time of embedding patches. In addition, it took advantages of shape smooth by using rectifying feature points and boundary handling in the morphing sequence. This fast morphing method and the former morphing measure were respectively demonstrated with the metamorphosis of 3D polyhedral models. Furthermore, the result analysis was given. The experiment results show that this method can implement fast and smooth metamorphosis.更多还原