Delaunay方法三维建模
摘要
3维建模技术在建筑，地质地形勘测，医学图像建模，动画设计等各方面都有广泛的应用. 1个3维模型的建立过程包括3维原始数据的获取、去除噪声、曲面拼接、修补“洞”，最终得到1个可以在计算机上显示的具有3维特征的网格. 3维可视化技术包括表面绘制技术和体绘制技术。由于将已有的3维模型显示在计算机上的技术已经很成熟，所以可视化技术的主要问题在于3维建模.
使用Delaunay方法来建模，由于Delaunay3角是尽量接近于等边3角形的，所以用这种方法建的网格会比较均匀，显示图像的时候视觉效果就是整个图像很匀称，不会出现粗细不均或者漏洞百出的情况。
本文的内容分5章。第1章引言，主要介绍研究背景和目前的发展状况以及可能的应用。第2章的第2部分就大概介绍了在2维空间建3角网的思路。在第3章里面，详细的说明了建立4面体网格的每1个步骤，其中附有说明图和流程图。第4章列出了实验结果（1系列图），验证算法的正确性。这里要说明的是，在实验中只选了9个点，但这9个点建网的过程中出现了Tsung-Pao Fang所列出的所有需要特殊处理的情况，也就是说，如果用再多的点来做这个实验，也不过就是这几种情况的重复。后面的4幅图是后来所作的工作，得到了1个正方体4顶点以及其中心点的建网结果，从这里能清楚地看到4面体网格的结构，还有对贝壳数据点云的部分建网结果，之所以没有完成整个贝壳数据的建网是因为数据中存在较多的5点或5点以上共球的情况，这种情况下Delaunay准则不再适用，建网会中断，所以只完成了1个部分。第5章针对程序中存在的问题和我在毕业设计过程中遇到的困难进行了讨论.
关键词：Delaunay ；3维建模；4面体网格；局部搜索。
Abstract
Three-dimension modeling technology is widely applied in the fields of architecture, geology and topography survey, medicine picture modeling, and cartoon design etc. The process of three-dimension modeling includes the following steps: first, obtaining three-dimension original data; second, removing yawp; third, putting curve surface together; fourth, mending “hole”; at last, reseau characterized by three-dimension will appear in PC. Three-dimension videotechnology consists of surface protracting technology and body protracting technology.Since the technology that making three-dimension model show in PC is proficient, the main problem of videotechnology lies in three-dimension modeling
Because Delaunay triangle is nearly equilateral triangle, modeling reseau with the method of Delaunay will be relatively well-proportioned. The whole image will looks shapely, not snatchy and inaccurate.
This paper includes five chapters. First chapter is Introduction, which introduce the background , recent development and the potential development.Chapter two gives a brief introduction of establishing triangle meshwork in two-dimension space. Chapter three explains every step to establish four-dimension reseau specifically, including demonstration and flow chart. Chapter Four lists the results with series of charts to test the method. Furthermore, nine dots are chosen. In the process of establishing meshwork with those nine dots, some special problems arise from Tsung-Pao Fang. That is to say , even if more dots are chosen, there are only the repetition of the above problems. The meshwork results are obtained from the later pictures. They clearly show the structure of four-dimension reseau and some meshwork results of shell data. The reason why the whole results are not achieved is that there are too many circumstances in which five or more dots share the same orb. In this case, the principle Delaunay is not in point any more, then the process of establishing meshwork will be intermitted. Chapter Five discusses some problems arising from the program and some difficulties in my thesis.
Keywords: Delaunay;three-dimension modeling; four-dimension reseau;partly search;
目录
1 前言................................................................................................................................................... 1
2 Delaunay 3角剖分的基本原理...................................................................................................... 2
2.1 相关知识…….......................................................................…………….……………………….... 2
2.1.1 Voronoi 图............................................................................................................................... 2
