可三角剖分的

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

Constrained triangulation plays an important part in finite element analysis and information visualization,also it is a hotspot problem of computational geometry and computer aided geometric design.

约束三角剖分在有限元分析和信息可视化等工程领域具有重要的应用背景，同时是计算几何和计算机辅助几何设计的一个热点问题。

Testing in terrain relief, and the algorithms can optimize the structure of TIN nicely.(2) According to the smoothness of the terrain and correlation between adjacency data points, the paper studied the possibility of smooth surface constructing of DEM based on TIN. Then based on Tayor fomula, vertical normal vector, triangular decomposition, continuous and smooth of surface and so on, a new kind of interpolate model of DEM was proposed based on TIN.

2分析原始地形起伏变化的连续光滑性以及邻近数据点之间的相关性，探讨了基于TIN的DEM光滑曲面构造的可行性，并基于二元泰勒公式、三角面剖分、曲面的连续光滑性等，提出了一种TIN上的DEM表面光滑插值模型，并通过构造数学曲面进行精度评估，并对模型进行了可视化分析。

The main results in this paper as follows: First, a prototype of a shape-based image database retrieval system is completed, it can receive the query mode both by giving an example image and by sketching the desired object on the screen, Second, five shape-based image retrieval methods are realized; Third, an algorithm based on triangulation for shape-based image retrieval is brought forward. In this algorithm, firstly, the edge of the original image is followed and the candidate corners in the original image are detected. Then the counterpoints of the candidate corners in the result of edge follow are found, and the boundary corners whose counterpoints have been found are queued in the order of their counterpoints in edge follow. After these steps, the boundary corners are triangulated and triangles are obtained which can show the true shape of the original image. Finally, shape feature is obtained by calculating the angle histogram of the triangles.

同时本文中主要完成了以下三方面的工作：完成了一个基于形状特征的图象检索的原型系统，可实现例子图象或徒手绘草图两种查询方式；实现了五种利用形状特征进行图象检索的具体方法，并对其进行了分析比较；并且在继承将三角剖分引入形状检索的思想基础上提出了利用三角剖分进行形状检索的一种新算法：先对原图象进行边界跟踪和角点检测；然后寻找初始角点在边界跟踪中的对应点，并对找到对应点的角点按其对应点在边界跟踪中的顺序进行排序；再对排序后的角点进行德洛内三角剖分，得到能表示目标真实形状的三角形序列；最后计算三角形序列的角度直方图作为形状特征，并进行相似性匹配。

In chapter 7, the constrained Delaunay triangulation is applied to visualization of oil geological data and griding of mechanical part. Data field is displayed by color map, contour map and section.

第七章将约束Delaunay三角网格应用于石油地质勘探数据场的可视化和机械零件的网格剖分，用三维立体图、渐变色图、区域填充图、等值线图、剖面图显示数据场。

The wing-edge and wing-patch data structure and fast searching method which combines the index rectangle with compass based normal vector are designed to speed the triangulation algorithm. Application in visualization of oil geological data and griding of mechanical part, the algorithm is efficient, steady and broad-spectrum. It can provide Delaunay triangular mesh for scientific computing and engineering analysis.

算法中采用了翼边、翼面型数据结构和自行设计的索引矩形与基于法矢的指南针法相结合的快速查询法，在石油地质勘探数据场可视化和机械零件网格剖分中的应用表明本文三角化算法具有高效、稳定、适用范围广的特点，能够为科学计算和工程分析提供边界一致的Delaunay三角网格。

A testing triangulation experiment for a polygon with 100 inside islets was done with this algorithm, and the result showed that this algorithm is efficient and robust for triangulating complex polygons with large numbers of inside islets. This algorithm has been successfully applied to the three- dimensional ore-body modeling and visualization system, in which it is used to triangulate the sectional polygons with inside islets, e.g., the inside stones or holes in ore-body, and its high efficiency has been proved.

实验表明，该算法在含有大量岛屿的带岛屿多边形三角剖分中具有很高的时间效率和很强的鲁棒性，并成功将其应用到基于剖面的三维矿体建模与可视化系统中，解决了含有夹石或孔洞的矿体剖面多边形三角剖分问题，具有一定的实际应用价值。

In the establishment process of three dimensional visualization model, we proposed the contour line drill hole - multi-layer face mold method.This method which improves Delaunay triangulation, is suitable for the random polygon triangulation and is easy for computer to realize. It makes three dimensional stratum visualization model of picking area realized under the limited condition.

在三维地层可视化模型的建立过程中，提出了基于等高线的钻孔—多层面模型方法，这是一种对现有的Delaunay三角剖分方法进行了改进，该方法适用于任意多边形的三角剖分，且易于计算机实现，使采区的三维地层可视化模型在有限条件下也能够实现。

This method uses all noisy datapoints directly to implement triangulation and dispenses with smoothing and datareduction process, which may lead to loss of geometric character. Moreover, thismethod is of lower complexity than other triangulation and the amount of vertexes inmesh can also be calculated, so we can control the size of mesh in advance. At last, apractical example is given to prove its effectiveness.

这种方法利用全部数据点信息进行网格剖分，无需对数据进行平滑、精简等预处理，避免了因平滑或精简而丢失重要的几何信息的可能，这种方法不仅比现有三角网格剖分算法降低了算法复杂度，而且具有可以直接处理带有噪声的数据，网格规模可控，生成的三角网格形状较好等优点。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失