二维Delaunay三角网的任意点插入算法研究

针对目前各种点插入算法的不足,提出一种二维Delaunay三角网任意点插入算法。首先基于凸壳区分点的位置,并利用三角形面积坐标、重心和点与有向线段关系三者构建的融和算法搜索插入点所在三角形,然后通过构建和优化新三角形完成点的插入,且满足Delaunay法则。通过测试证明了算法的可靠性和高效性。     

二维Delaunay三角网局部更新:点插入与点删除

二维Delaunay三角网的局部更新在地学分析、道路CAD、城市规划等领域有着广泛的用途,点插入和点删除则是其中最重要、最基本的操作。该文针对原有逐点插入法和凸耳权值点删除算法存在的不足,利用动态包围三角形和特征三角形分别对其进行改进,在设计的具有拓扑关系Delaunay的三角网数据结构基础上,实现Delaunay三角网的快速局部更新,且使之满足Delaunay特性。最后通过模拟实验验证了算法的正确性和高效性。     

基于线性和岛屿约束的Delaunay三角网构建算法研究

针对基于线性和岛屿约束的Delaunay三角网构建算法的不足,从减少算法计算机实现步骤出发,研究改进了线段相交判断、首三角形确定等影响域多边形搜索相关算法;在分析当前存在的多边形三角剖分算法基础上,给出了存在重复点(悬边)的多边形三角剖分算法;在影响域多边形搜索阶段充分利用多边形间的拓扑关系信息,消除了岛屿约束内部三角形删除时需遍历三角形数据的不足.算法涵盖线性和岛屿约束的构建,综合性强,效率高且易于实现.     

Delaunay三角网约束的Harris-SURF图像匹配算法

Harris算法提取的角点定位精度高,但不具尺度不变性,SURF算法虽具有尺度不变性和旋转不变性,但提取的特征点并非视觉角点。针对此问题,该文提出一种Delaunay三角网约束下的Harris-SURF图像匹配方法。首先,采取阈值评估策略对图像进行SURF粗匹配,利用RANSAC算法进行粗差剔除,得到的匹配点用于构建Delaunay三角网;然后以相似三角形作为约束,将其作为Harris特征点精匹配的限制区域,提高Harris点匹配的可靠性。实验表明,该算法具有匹配准确率高、鲁棒性较好等特点,对无人机影像的匹配效果明显优于其他算法。     

三角网的生成与简化算法

在三维地理信息系统的开发与研究中 ,要求三角网模型的支持 ,而高效的三角网生成算法是三角网模型的基础。该文综述各类三角网的生成算法 ,对以往被人忽视但简明高效的算法———径向扫描算法进行阐释 ,并对它的实现进行改进 ;对地形数据的简化及建立地形层次对象模型是实现高效的三维地理信息系统的关键 ,而三角网的简化是地形数据简化的基石之一 ,文中提供三种简化三角网的算法供同行讨论 ;并在微机上实现上述算法。     

基于拓扑追踪的不规则三角网裁剪算法

针对地质建模中常见的空间曲线(如断层线、断层多边形、等值线等)提出一种较为通用的空间曲线裁剪三角网算法,并给出合理的空间裁剪曲线定义。利用依附于三角网上的空间曲线,沿着三角网进行拓扑追踪,并沿追踪轨迹进行分离,最终实现三角网的裁剪。该算法对开曲面、闭曲面、复杂地质曲面裁剪效果都很好,算法复杂度低,易于编程,适用于绝大多数的地质曲线对不规则三角网的裁剪。     

约束Delaunay三角网点删除的一体化凸耳消元法(IEE)

对Delaunay三角网(CD—TIN)点删除算法——凸耳消元法(EE)进行剖析,提出约束Delaunay三角网的点删除算法——体化凸耳消元法(IEE)。该算法将CD-TIN的点删除转化为点的影响域重构,并保证重构后的CD—TIN满足CD—TIN的可视性与空圆法则,确保了CD—TIN的拓扑完备性,实现了CD—TIN中约束点与非约束点删除的一体化操作和局部更新,并得到实验验证。     

一种高准确度的约束Delaunay三角网生成算法研究

约束线段的嵌入是CDT两步法的关键步骤之一,目前该方面的研究还不够完善,主要忽视了影响区域是凹多边形和影响区域内包含悬挂点的情况.该文研究带有约束条件的Delaunay三角网的生成问题,考虑了约束线段影响区域的特殊情况,采用递归割耳法嵌入约束线段,先将影响区域调整为简单多边形,再递归寻找并割去多边形的耳,最终将影响区域重新三角剖分.该方法可有效提高约束DIelaunay三角网的质量.     

基于SRTM DEM数据的全国地表面积计算研究

对山区表面积的估算方法为准确估算复杂地形条件下的陆地生态系统固碳特征提供了基础条件。投影面积与实际表面积在山区有相当大的差异,这些差异对于估算陆表覆被面积、碳水循环有较大的影响。该文通过地形特征点提取算法和不规则三角网构建算法,以省域为单位提取地形特征点,并在此基础上构建了不规则三角网,求算区域表面积。根据表面积与投影面积的比较,得出以下结论:1)不同分辨率的DEM数据对计算结果是有影响的,分辨率越大,表面积越大;2)在SRTM DEM尺度(90m)下,我国陆地范围的表面积为1 003.36万km2,比投影面积多出约43万km2。     

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.     

基于四叉树索引构建TIN的高效合成算法

不规则三角网(TIN)可以逼真的模拟地形表面,因此被广泛应用于地学领域。Delaunay三角剖分算法是构建TIN网的最优算法,该文对传统Delaunay三角网构建算法进行分析,提出了一种针对大规模离散数据点生成TIN的高效合成算法。该算法首先根据离散点的分布位置和密度对其进行四叉树区域划分;然后以每个叶子节点的边界四边形为凸包,采用逐点插入法构建三角网;最后采用顶点合并法自底向上合并具有相同父节点的4个子节点,生成Delaunay三角网。实验结果表明,该算法时间复杂度较低,有效提高了TIN网的构建效率。     

A comparison of neighbourhood relations based on ordinary Delaunay diagrams and area Delaunay diagrams: an application to define the neighbourhood relations of buildings

ABSTRACT

The aim of this article is to describe a convenient but robust method for defining neighbourhood relations among buildings based on ordinary Delaunay diagrams (ODDs) and area Delaunay diagrams (ADDs). ODDs and ADDs are defined as a set of edges connecting the generators of adjacent ordinary Voronoi cells (points representing centroids of building polygons) and a set of edges connecting two centroids of building polygons, which are the generators of adjacent area Voronoi cells, respectively. Although ADDs are more robust than ODDs, computation time of ODDs is shorter than that of ADDs (the order of their computation time complexity is O(nlogn)). If ODDs can approximate ADDs with a certain degree of accuracy, the former can be used as an alternative. Therefore, we computed the ratio of the number of ADD edges to that of ODD edges overlapping ADDs at building and regional scales. The results indicate that: (1) for approximately 60% of all buildings, ODDs can exactly overlap ADDs with extra ODD edges; (2) at a regional scale, ODDs can overlap approximately 90% of ADDs with 10% extra ODD edges; and (3) focusing on judging errors, although ADDs are more accurate than ODDs, the difference is only approximately 1%.     

SPLITAREA: an algorithm for weighted splitting of faces in the context of a planar partition

Geographic data themes modelled as planar partitions are found in many GIS applications (e.g. topographic data, land cover, zoning plans, etc.). When generalizing this kind of 2D map, this specific nature has to be respected and generalization operations should be carefully designed. This paper presents a design and implementation of an algorithm to perform a split operation of faces (polygonal areas).

The result of the split operation has to fit in with the topological data structure supporting variable-scale data. The algorithm, termed SPLITAREA, obtains the skeleton of a face using a constrained Delaunay triangulation. The new split operator is especially relevant in urban areas with many infrastructural objects such as roads. The contribution of this work is twofold: (1) the quality of the split operation is formally assessed by comparing the results on actual test data sets with a goal/metric we defined beforehand for the ‘balanced’ split and (2) the algorithm allows a weighted split, where different neighbours have different weights due to different compatibility. With the weighted split, the special case of unmovable boundaries is also explicitly addressed.

The developed split algorithm can also be used outside the generalization context in other settings. For example, to make two cross-border data sets fit, the algorithm could be applied to allow splitting of slivers.     

基于尺度转折点的空间分析方法研究

对景观生态学中有关空间分析和尺度转换的方法及基于直方变差图的尺度转换方法进行对比,分析其优缺点;在直方变差图的基础上,结合分形理论引入了尺度转折点这一概念。确定尺度转折点是研究重点,通过各个尺度转折点可以确定遥感图像上的各个尺度域,从而为不同尺度的地表时空多变要素提供一种尺度转换的依据。采用互联网上的IKONOS天安门地区图像数据进行验证。     

多尺度地理空间点群目标相似关系的计算研究

研究多尺度地理空间点群目标相似关系的计算问题.基于4类点群信息,将点群目标包含的信息重新分成统计信息、专题信息、拓扑信息、几何信息和度量信息,这5类信息是影响点群相似性程度的主要因子.根据这5类信息描述参数的特点,给出了各个因子的相似度计算公式,建立了多尺度地理空间点群目标相似关系的计算模型,并通过算例验证了该模型的可行性与有效性,为地图综合质量的评价提供了一种新方法.     

多边形主骨架线提取算法的设计与实现

在Delaunay三角网的基础上对骨架线节点进行了分类,通过确定主骨架线的两个端点,运用回溯法提取了多边形的主骨架线,同时给出了详细的算法步骤,并在Visual C++2003环境下实现了该算法。较之其他算法,该算法思路简捷,易于编程,生成的主骨架线形态优良,较好地反映了多边形的主体形状特征和主延伸方向。