基于地图代数的最小生成树实现方法

本文介绍了最小生成树及其常见的算法,对比栅格算法分析了基于矢量的最小生成树算法的缺点,介绍了地图代数的距离变换和基于地图代数的距离变换图生成Voronoi图、Delaunay三角网,然后根据最小生成树MST是Delaunay三角剖分的一个子集,逐次删掉Delaunay三角网中每个三角形的最长边,从而得到最小生成树,该方法不仅适用于欧氏非障碍空间,同样也适用于障碍空间的情况,解决了以往最小生成树在障碍空间下(尤其是当障碍空间中的障碍是全形态的条件下)难以求解的问题,具有一定的理论意义。     

欧氏障碍空间的最短路径问题解法

提出了利用地图代数栅格路径距离变换原理求解欧氏障碍空间最短路径问题的方法(MA-ESPO),实现了二维障碍空间最短路径的一个栅格解法,并且把障碍物、源、汇图形都扩大到任意形态图形。给出了基于地图代数的障碍空间下距离变换方法(MA-DTO),其简便地生成了整个障碍空间所有点的趋源距离,从而成为E2生成所定义障碍空间下各任意形态图形的Voronoi图的实际方法。     

基于栅格距离变换的扩展对象空间聚类方法

空间聚类是空间分析和空间数据挖掘的重要方法和研究内容。在地图代数中,通过建立栅格坐标与距离平方对应的栅格平方平面!计算栅格空间的最短距离,实现栅格距离变换。以栅格空间距离变换为基础,通过提取特征等距线,揭示简单的空间点集聚类过程,并将这种算法扩展到点$线$面实体混合分布空间!以及加权距离以及障碍空间的空间聚类,算法分析表明该算法简单、合理。     

百度地图API路网搜索功能在职住分离研究中的应用

通过调用百度地图路网搜索API函数直接求解不同交通方式下的通勤距离,为武汉市居民的职住分离状况研究提供可靠的数据;同时探讨了计算过程中GPS坐标与百度地图坐标的转换以及在通勤距离求解过程中调用回调函数必须注意的问题。     

基于三维空间的地理要素表达新形式

为避免大区域地形图测绘产生地图投影变形问题,增强工作中的直观性与便捷性,借助大地测量学中大地线的理论特性,编写了基于参考椭球面两点大地坐标进行等间距内插空间大地直角坐标的解算程序,在三维模拟空间构建了参考椭球,绘制了大地线与DLG;并将其转换至GIS平台下,实现了图形与属性的挂接、编辑与查询.结果表明,这种空间地理要素...     

基于CORS的高精度实时坐标转换方法探究

通过区域坐标转换将GPS测量成果转化为1980年国家大地坐标系或CGCS2000国家大地坐标系下的平面直角坐标,在测量中尤为重要。CORS系统的坐标转换虽存在诸多不足,但基于CORS能够实现双向数据通信。文章根据狄洛尼(Delaunay)三角形构建基准站网络的特点,提出了通过实时获取坐标转换参数而获得高精度平面坐标的方法,从数据分析和理论的角度进行了可行性探究。     

DTW算法支持下的线状要素连续地图综合方法

面向线状地图要素连续尺度变换问题,本文提出了一种DTW算法支持下的连续综合方法。该方法基于尺度融合的思想,将同一地理实体在大小两种比例尺下以不同的几何表达作为输入,首先基于DTW算法建立两种几何表达坐标顶点之间的对应关系;然后采用线性内插方法动态派生任意中间尺度上几何数据,从而实现连续地图综合。顶点之间对应关系的正确性,直接决定了线性内插的结果,而同一实体在不同比例尺下的几何表达往往具有不同的坐标点数,顶点之间具有一对多的对应关系。为寻求最优顶点匹配方案,以顶点距离作为匹配代价,以整体最小距离作为目标函数,采用DTW算法求解最优匹配。试验结果表明,基于DTW的顶点匹配方法可适应不同的地图综合场景,该方法支持下的地图综合效果可实现连续、光滑的渐变,符合地图表达规则和人类空间认知。     

一种利用数字线划图快速生产数字栅格地图的方法

讨论快速生产数字栅格地图(DRG)的方法,阐述如何在已有数字线划图的基础上,转换成栅格图,编程实现自动对栅格图像进行分析,根据图号计算内图廓对应的大地坐标及像素坐标,进而快速批量地生成数字栅格地图。     

空间直角坐标计算大地坐标的抛物线逼近法

采用抛物线逼近法求解大地纬度和大地高,先计算空间点在椭球面上的子午面坐标,然后求解点的大地纬度和大地高。     

广州2000坐标与1980西安坐标高精度转换关系的建立

结合生产实际需求,在充分考虑广州2000坐标系特点的基础上,研究了一种顾及椭球膨胀后椭球面不平行但不考虑大地高的,利用不同坐标系公共点四参数确定广州2000坐标与1980西安坐标高精度转换关系的实用方法;开发了坐标转换软件,并通过算例证明了该方法的可行性和可靠性。该方法的转换精度在±2cm以内。     

椭球面三角形外接大地圆圆心测地坐标的另一种解法

为了在测地坐标系中确定外接大地圆圆心,采用了解非线性方程组的牛顿迭代法,解法简便,易于理解.数据验证表明,由该数值法求解的结果与由解析公式获得的结果完全一致.由此亦表明,一些繁难的大地测量计算也可改用数值法来进行.     

基于O-QTM的球面VORONOI图的生成算法

提出了基于“Q－QTM”（Octahedral Quaternary Triangular Mesh）剖分的球面Voronoi图的格网生成算法；首先介绍了球面的QTM格网划发和编码方法，并根据地址码进行邻近球面三角形的探索；然后，参照数学形态学原理，重新定义了球面三角网的膨胀操作和膨胀算子，利用球面实体的递归膨胀来生成球面Voronoi图。应用VC^ 语言在OpenGL3维平台上开发了相应的实验程序，实验结果表明：利用此算法可生成球面上任意实体的Voronoi图，且生成点、弧和曲面Voronoi图的时间复杂度是一样的；而其误差受球面距离的影响较小，主要与球面实体的位置有关。最后给出了本文研究的结论及进一步的工作。     

数字地面模型LOD算法的实现

利用点的三角形化构建一个3维地面模型，设计了一个基于三角形折叠的LOD算法，该算法不需任何计算即可达到快速实现模型的渐进式还原，大大提高了3维显示速度，最后调用OpenGL函数有效地显示3维地形模型。     

Height datum unification between Shenzhen and Hong Kong using the solution of the linearized fixed-gravimetric boundary value problem

The paper proposes a new algorithm to unify height datums in different regions, which is based on the solution of the linearized fixed-gravimetric boundary value problem. Compared with traditional methods, this method uses GPS ellipsoidal height and gravity disturbances on the surface of the earth to obtain a quasigeoid, which is not related to any local vertical datums. As an example, we calculate the height datum difference between Shenzhen and Hong Kong by applying this new method. The result shows that the height difference obtained by this new method is consistent with the ground leveling result to a few centimeters.     

散乱点云数据空间三角网构建方法的研究

点云数据三维建模主要是对目标物体的表面进行网格建模。三角形作为三维建模的基本表示元素,不仅性质简单,而且可以有效地表示物体表面复杂的几何属性。Delaunay三角网是当前使用最广泛的三角剖分方法,它能够最大限度地避免狭长三角形的产生,并且无论从何处开始建网都能保持网型的唯一性。本文在已有生长算法研究的基础上提出了一个新的算法:即在二维生长算法的基础上,利用空间三角形的法向量来进行第三点的搜索构建空间三角网。该算法的优点是:适合大量点云数据构建空间三角网、构建的空间三角网可以很好地反映出物体的表面特征。     

Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points

A terrestrial laser scanner measures the distance to an object surface with a precision in the order of millimeters. The quality of the individual points in a point cloud, although directly affecting standard processing steps like point cloud registration and segmentation, is still not well understood. The quality of a scan point is influenced by four major factors: instrument mechanism, atmospheric conditions, object surface properties and scan geometry. In this paper, the influence of the scan geometry on the individual point precision or local measurement noise is considered. The local scan geometry depends on the distance and the orientation of the scanned surface, relative to the position of the scanner. The local scan geometry is parameterized by two main parameters, the range, i.e. the distance from the object to the scanner and the incidence angle, i.e. the angle between incoming laser beam and the local surface normal. In this paper, it is shown that by studying the influence of the local scan geometry on the signal to noise ratio, the dependence of the measurement noise on range and incidence angle can be successfully modeled if planar surfaces are observed. The implications of this model is demonstrated further by comparing two point clouds of a small room, obtained from two different scanner positions: a center position and a corner position. The influence of incidence angle on the noise level is quantified on scans of this room, and by moving the scanner by 2 m, it is reduced by 20%. The improvement of the standard deviation is significant, going from 3.23 to 2.55 mm. It is possible to optimize measurement setups in such a way that the measurement noise due to bad scanning geometry is minimized and therefore contribute to a more efficient acquisition of point clouds of better quality.     

基于二叉树思想的任意多边形三角剖分递归算法

提出了一种基于二叉树思想的任意多边形三角剖分递归算法。该算法采用二叉树思想，确定剖分三角形的二叉树状结构，并采用递归算法实现。这算法可适用于任意形状的凹或凸多边形，也适用于包含岛屿的多边形。此外，在考虑边界点高程的基础上，可充分顾及地形特征。该算法完全适用于长距离河流流域的三维面状表达。     

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {,,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10^–8 m²/s² for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10^–4m²/s². Since 1.5× 10^–4 m²/s² is equivalent to 1.5×10^–5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.Acknowledgments. This research has been financially supported by the University of Tehran based on grant number 621/4/859. This support is gratefully acknowledged. The authors are also grateful for the comments and corrections made to the initial version of the paper by Dr. S. Petrovic from GFZ Potsdam and the other two anonymous reviewers. Their comments helped to improve the structure of the paper significantly.     

A comparison of the tesseroid,prism and point-mass approaches for mass reductions in gravity field modelling

The calculation of topographic (and iso- static) reductions is one of the most time-consuming operations in gravity field modelling. For this calculation, the topographic surface of the Earth is often divided with respect to geographical or map-grid lines, and the topographic heights are averaged over the respective grid elements. The bodies bounded by surfaces of constant (ellipsoidal) heights and geographical grid lines are denoted as tesseroids. Usually these ellipsoidal (or spherical) tesseroids are replaced by “equivalent” vertical rectangular prisms of the same mass. This approximation is motivated by the fact that the volume integrals for the calculation of the potential and its derivatives can be exactly solved for rectangular prisms, but not for the tesseroids. In this paper, an approximate solution of the spherical tesseroid integrals is provided based on series expansions including third-order terms. By choosing the geometrical centre of the tesseroid as the Taylor expansion point, the number of non-vanishing series terms can be greatly reduced. The zero-order term is equivalent to the point-mass formula. Test computations show the high numerical efficiency of the tesseroid method versus the prism approach, both regarding computation time and accuracy. Since the approximation errors due to the truncation of the Taylor series decrease very quickly with increasing distance of the tesseroid from the computation point, only the elements in the direct vicinity of the computation point have to be separately evaluated, e.g. by the prism formulas. The results are also compared with the point-mass formula. Further potential refinements of the tesseroid approach, such as considering ellipsoidal tesseroids, are indicated.