基于极球面投影的极区格网等角航线

针对传统极区航行通常采用格网导航执行大圆航线,大圆航线上格网航向角不同不利于航行控制以及大圆航线在极区投影图上不完全投影为直线引起固有原理性误差的问题,借鉴中低纬度地区等角航线上地理航向角相等以及在墨卡托投影图上为直线便于航行控制和绘算的思想,提出了一种在极球面投影图中表现为直线的"等角航线"——格网等角航线。在研究双重投影的极球面投影以及格网导航方法的基础上,提出了格网等角航线的定义,推导了航线方程,并根据该航线的航程和航向角计算方法进行航线仿真设计。理论分析和仿真验证表明:航线上格网航向角处处相等,在极区投影图上表现为直线;格网等角航线与大圆航线、大椭圆航线相近,航程较短。因此,极区格网等角航线可以与格网导航方法、极球面投影精确配合应用,适合于极区航行。     

Optimal orientations of discrete global grids and the Poles of Inaccessibility

ABSTRACT

Spatial analyses involving binning often require that every bin have the same area, but this is impossible using a rectangular grid laid over the Earth or over any projection of the Earth. Discrete global grids use hexagons, triangles, and diamonds to overcome this issue, overlaying the Earth with equally-sized bins. Such discrete global grids are formed by tiling the faces of a polyhedron. Previously, the orientations of these polyhedra have been chosen to satisfy only simple criteria such as equatorial symmetry or minimizing the number of vertices intersecting landmasses. However, projection distortion and singularities in discrete global grids mean that such simple orientations may not be sufficient for all use cases. Here, I present an algorithm for finding suitable orientations; this involves solving a nonconvex optimization problem. As a side-effect of this study I show that Fuller's Dymaxion map corresponds closely to one of the optimal orientations I find. I also give new high-accuracy calculations of the Poles of Inaccessibility, which show that Point Nemo, the Oceanic Pole of Inaccessibility, is 15?km farther from land than previously recognized.     

基于车载激光扫描数据的电线杆自动识别与定位

本文对车载激光扫描数据进行了研究,将投影点密度(DoPP)与电线杆的几何特点相结合,提出了一种基于激光扫描数据的电线杆自动识别和定位的方法。首先,将车载测量系统获取的激光点云投影到水平面,建立水平格网,设置投影点密度阈值分类出杆状地物所在的格网区域;然后将分类得到的杆状数据拟合成为一条空间直线,以电线杆的几何特性作为期望值和方差,自动识别电线杆;最后,该空间直线与地面网格相交确定电线杆的定位位置。本文算法与T3D Analyst商用软件提取的电线杆进行比较,实验结果表明本文方法行之有效。     

基于QTM的线状图形自动化简算法探讨

全球网格是由形成地球表面剖分的一系列区域所组成,八面体四分三角网(QTM)是其中一种具有层次性的网格。本文依据数据点在规则网格中的分布规律,提出了一种在QTM数据结构支持下的线状图形化简算法。该算法以经过每级QTM网格的数据点的平均值为标准,能自动地对比较平缓的线段进行较粗选点,而对相对复杂的线段进行较密选点。本文以及Dutton算法都能克服DouglasPeucker算法中难以客观和合理确定阈值的困难,但是本算法比Dutton算法简单,且具有更高的化简率,能更好地保留了线状图形的弯曲特征。     

THE CAPE BAR “A” AND THE METRE-FOOT RELATION

Abstract

The Cape Bar A has two sets of end marks. One set is represented by small dots in embedded surfaces of gold, and the other by finely engraved lines near the dots. The distance between the dots was measured in British units by Sir George Airy in 1839, and at the Ordnance Survey in. 1844; and the lines were standardised in international metres by M. Benoit at Paris in 1886. By lueasuring the small distances between the dots and the lines, and using the data of the original standardisations, it has been possible to obtain a value of the metre-foot relation. The ratio thus obtained agrees with the determinations of Benoit (1896) and Sears (1928).     

利用数值投影变换构建全球六边形离散格网

本文针对全球离散格网构建过程中从平面格网到球面格网的关键步骤进行讨论,提出了一种新型的评价球面离散格网几何属性最优化的目标函数,使用遗传算法优化,得到了球面上有限层次内最优化条件下的直接剖分格网。利用有限层次内最优化格网提供的控制点数据,结合数值投影变换理论,成功地构建了几何属性更加均匀的全球六边形离散格网系统。实验表明,相对于现有Snyder等积投影建立的全球格网,在格网单元的均匀度上更优;在运算效率方面,速度大约是Snyder投影的2.5-3倍。     

一种通用球面等积离散网格生成算法

球面离散网格模型是管理海量数据的有效途径,如何构建球面网格是这类模型的基础问题.文中利用Snyder等积多面体投影建立了平面与球面的对应关系,设计了球面等积三角形和四边形离散网格的生成算法.结合实验分析了两种网格的最大/最小边长比和单元周长均方差两项指标,结果表明全部网格的指标均收敛,适合用作多分辨率地理空间信息的管理.     

Geodetic grids in authoritative maps – new findings about the origin of the UTM Grid

ABSTRACT

Recent discoveries of Wehrmacht Maps in the Military Archive of the Federal Archive of Germany in Freiburg im Breisgau raised the motivation for further investigations into the history of the internationally employed Universal Transverse Mercator (UTM) projection which actually represents a prerequisite for the global use of Global Positioning System (GPS) – and thus of any type of navigation – instruments. In contrast to the frequently stated opinion that this map projection was first operationally used by U.S. Americans it turned out that presumably the first operational maps with indication of the orthogonal UTM grid were produced by German Wehrmacht officers prior to the post World War (WW) II triumph of this projection. Based on the authors´ recent discoveries this article reveals some hitherto hardly known facts concerning the history of cartography of the 1940s.     

一种面向虚拟地球的海面动态可视化优化方法

现有的虚拟地球中的海面可视化方法主要采用投影网格的方式组织海面格网,这种特殊的网格组织方式,导致其在反映不同海域差异性特征时存在缺陷。基于全球离散格网的海面可视化方法由于能够与虚拟地球离散的空间剖分相匹配,有效弥补了投影网格法的缺陷,因此更符合虚拟地球海面仿真应用的需要。然而现有的离散格网法存在绘制效率差、场景加载慢、需要修补格网缝隙等问题,限制了其应用发展。对此,本文在现有离散格网法基础上进行优化:首先,在数据结构上对传统等经纬度离散格网进行扩展,设计了一种面向GPU绘制的多尺度海面网格模型来组织管理海面格网;其次,为了实现风场驱动下的海浪动态绘制,在多尺度海面网格模型的基础上提出了一种支持实时风场更新的海浪动态绘制方法;同时,考虑到格网缝隙修补对系统效率的影响,本文针对海面格网特点并结合GPU技术提出了一种高效的海面格网缝隙修补方法。最后通过对比试验验证了本文方法的可行性和有效性。试验结果表明,本文方法绘制效率稳定,加载速度快,且能弥补现有方法在功能上的缺失,因此应用范围更加广泛。     

MARGINAL SCALES OF LATITUDE AND LONGITUDE ON TRANSVERSE MERCATOR MAPS

Abstract

The problem of computing marginal scales of latitude and longitude on a rectangular map on the Transverse Mercator projection, where the sheet boundaries are projection co-ordinate lines, may be solved in various ways. A simple method is to compute the latitudes and longitudes of the four corners of the sheet, and then, assuming a constant scale, to interpolate the parallels and meridians between these corner values. Although it is probably sufficiently accurate for practical purposes, this method is not precise. It is not difficult to adapt the fundamental formulce of the projection to give a direct solution of the problem.     

基于DEM和水箱理论识别流域河网方法研究

本文应用水箱原理处理流域DEM数据中存在的洼地问题,提出流域河网识别及编码的新方法。首先,确定洼地网格,搜索洼地区域,计算洼地容量,根据水箱原理确定洼地出口,判断洼地的流向;然后,逐层合并消减洼地,修正洼地水流方向;最后,计算网格集水面积,进行河网识别和编码。本文结合云南东川蒋家沟流域的DEM资料进行河网识别,得到了完整的流域河网,结果与实际勘测的河网完全吻合,这表明应用该方法提取流域河网是可行的,能够为进一步的分布式水文、泥石流、环境模型提供条件。     

Interactive Design of 3D Maps with Progressive Projection

Abstract

The progressive projection is by origin a manual cartographic technique, traditionally used by panoramic landscape painters; however, it is rarely encountered in digitally created three-dimensional (3D) maps. In this article, the advantages of this specific projection when designing 3D maps are presented, the processes involved in its manual construction, as well as the existing and potential digital implementation approaches, are reviewed. A new algorithmic solution is described, allowing for user-friendly interactive bending of a terrain model into a progressive view, with options to add a curved horizon, to vertically exaggerate the terrain, and to create a 360° strip panorama. The resulting software, Terrain Bender, is freely available for download.     

Contemporary American cartographic research: a review and prospective

ABSTRACT

We review recent developments in cartographic research in North America, in the context of informing the 29th International Cartographic Conference, and 18th General Assembly in 2019. The titles of papers published since 2015 in four leading cartographic journals yielded a corpus of 245 documents containing 1109 unique terms. These terms were analyzed using Latent Dirichlet Allocation and by visual analytics to produce 14 topic groups that mapped onto five classes. These classes were named as information visualization, cartographic data, spatial analysis and applications, methods and models, and GIScience. The classes were then used as themes to discuss the recent cartographic literature more broadly, first, to review recent trends in the research and to identify research gaps, and second, to examine prospects for new research over the next 20 years. A conclusion draws some broad findings from the review, suggesting that cartographic research in the future will be aimed less at dealing with data, and more at generating insight and knowledge to better inform society about global challenges.     

正六边形规则格网表达的DEM谷地线提取

基于规则格网DEM谷地线提取受格网的几何形态、空间剖分和网格布局影响较大.传统的四边形格网D8 算法中,四边形网格的角邻域与边邻域存在的距离度量差异,影响了其计算结果对于地形变化的表达在两方向上的均衡性,从而影响了谷地线提取结果.六边形格网具有邻域一致、各向同性、紧凑、采样率高等优点,在空间场建模中越来越得到重用.本文旨在探求六边形格网结构在DEM谷地线提取中的性能特征,发现其与四边形格网比较的突出优势.基于六邻域处理单元,对六边形格网DEM谷地线提取过程中填洼、流向计算及平地区域流向判定作预处理,然后对流向线作拓扑连通组织,从而实现基于六边形DEM的谷地线提取.本文比较发现六边形方法在谷地线形状特征保持方面能力强,随着分辨率减小,六边形DEM所提取的谷地线与实测数据吻合程度高,弯曲特征继承性强.同时,在相同数据存储量条件下,六边形DEM数据精度更高,且其提取的谷地线网络的形状特征更为精细.     

The isotropic organization of DEM structure and extraction of valley lines using hexagonal grid

The automatic extraction of valley lines (VLs) from digital elevation models (DEMs) has had a long history in the GIS and hydrology fields. The quality of the extracted results relies on the geometrical shape, spatial tessellation, and placement of the grids in the DEM structure. The traditional DEM structure consists of square grids with an eight‐neighborhood relationship, where there is an inconsistent distance measurement between orthogonal neighborhoods and diagonal neighborhoods. The directional difference results in the extracted VLs by the D8 algorithm not guaranteeing isotropy characteristics. Alternatively, hexagonal grids have been proved to be advantageous over square grids due to their consistent connectivity, isotropy of local neighborhoods, higher symmetry, increased compactness, and more. Considering the merits above, this study develops an approach to VL extraction from DEMs based on hexagonal grids. First, the pre‐process phase contains the depression filling, flow direction calculation, and flow accumulation calculation based on the six‐neighborhood relationship. Then, the flow arcs are connected, followed by estimating the flow direction. Finally, the connected paths are organized into a tree structure. To explore the effectiveness of hexagonal grids, comparative experiments are implemented against traditional DEMs with square grids using three sample regions. By analyzing the results between these two grid structures via visual and quantitative comparison, we conclude that the hexagonal grid structure has an outstanding ability in maintaining the location accuracy and bending characteristics of extracted valley networks. That is to say, the DEM‐derived VLs based on hexagonal grids have better spatial agreement with mapped river systems and lower shape diversion under the same resolution representation. Therefore, the DEMs with hexagonal grids can extract finer valley networks with the same data volume relative to traditional DEM.     

THE MERCATOR PROJECTION AND THE RHUMB LINE

Abstract

Introductory Remarks.—A line of constant bearing was known as a Rhumb line. Later Snel invented the name Loxodrome for the same line. The drawing of this line on a curvilinear graticule was naturally difficult and attempts at graphical working in the chart-house were not very successfuL Consequently, according to Germain, in 1318 Petrus Vesconte de Janua devised the Plate Carree projection (“Plane” Chart). This had a rectilinear graticule and parallel meridians, and distances on the meridians were made true. The projection gave a rectilinear rhumb line; but the bearing of this rhumb line was in general far from true and the representation of the earth's surface was greatly distorted in high latitudes. For the former reason it offered no real solution of the problem of the navigator, who required a chart on which any straight line would be a line not alone of constant bearing but also of true bearing; the first condition necessarily postulated a chart with rectilinear meridians, since a meridian is itself a rhumb line, and for the same reason it postulated rectilinear parallels. It follows, therefore, that the meridians also must be parallel inter se, like the parallels of latitude. The remaining desideratum—that for a true bearing—was attained in I569 by Gerhard Kramer, usually known by his Latin name of Mercator, in early life a pupil of Gemma Frisius of Louvain, who was the first to teach triangulation as a means for surveying a country. Let us consider, then, that a chart is required to show a straight line as a rhumb line of true bearing and let us consider the Mercator projection from this point of view.     

Recent literature in cartography and geographic information science

Tissot's Indicatrix and regular grids have been used for assessing map projection accuracies. Despite their broad applicability for accuracy assessment, they have limitations in quantifying resampling errors caused by map projections. This is due to the structural uncertainty with regard to the placement and pattern of grids. It is also difficult to calculate the absolute amount of resampling error in each projection. As an alternative to traditional testing methods, the use of random points was investigated. Specifically, random point generation, resampling with spherical block search algorithms, resampling accuracy with a perfect grid, and resampling accuracy with eight projections were investigated and are discussed here. Eight global referencing methods were tested: the equal-area cylindrical, sinusoidal, Mollweide, Eckert IV, Hammer-Aitoff, interrupted Goode homolosine, integerized sinusoidal projections, and the equal area global gridding with a fixed latitudinal metric distance. The resampling accuracy with a perfect grid is about 75 percent. Results showed the sinusoidal and the integerized sinusoidal projections and equal-area global gridding to achieve the highest accuracies.     

THE NOMENCLATURE OF MAP PROJECTIONS

Abstract

Map Projections.—A matter that should have been mentioned in the original article under this title (E.S.R., vii, 51, 190) is the definition of a map projection. In the list of carefully worded “Definitions of Terms used in Surveying and Mapping” prepared by the American Society of Photogrammetry (Photogrammetrie Engineering, vol. 8,1942, pp. 247–283), a map projection is defined as “a systematic drawing of lines on a plane surface to represent the parallels of latitude and the meridians of longitude of the earth or a section of the earth”, and most other published works in which a definition appears employ a somewhat similar wording. This, however, is an unnecessary limitation of the term. Many projections are (and all projections can be) plotted from rectangular grid co-ordinates, and meridians and parallels need not be drawn at all; but a map is still on a projection even when a graticule is not shown. Objection could be raised also to the limitation to “plane surface”, since we may speak of the projection of the spheroid upon a sphere, or of the sphere upon a hemisphere. Hence, it is suggested that “any systematic method of representing the whole or a part of the curved surface of the Earth upon another (usually plane) surface” is an adequate definition of a map projection.     

Exploiting Illusory Grid Lines for Object-Location Memory Performance in Urban Topographic Maps

In order to be successful in spatial orientation tasks, people need to recall locations and configurations of spatial objects from their memory. This understanding of geographic space often arises from experience with cartographic media representing topographic and topological information by graphic symbols. Learning spatial information from graphic media is influenced by different perception-based grouping effects distorting the accuracy of spatial object-positions and their relations. Such geometric inaccuracies can be softened by adding a grid layer, which regionalizes the map and can be used as an additional orientation pattern. This grid layer usually consists of solid lines and overlays semantic information. The present paper reports the results of two empirical studies on object-location memory (OLM) performance. In these studies, the amount of visual detail of the grid layer was reduced. By positioning the grid layer below specific urban topographic objects (study 1), the grid pattern was graphically interrupted. These interrupted grid lines were completed by cognitive completion mechanisms (illusory grid lines) described in the Gestalt principles of closure and continuation. The second experiment examined the maximum grid line gap that is closed by cognitive line completion and keeps an advantage for OLM (study 2).     

Line generalisation by repeated elimination of points

Abstract

This paper presents a new approach to line generalisation which uses the concept of 'effective area' for progressive simplification of a line by point elimination. Two coastlines are used to compare the performance of this, with that of the widely used Douglas-Peucker, algorithm. The results from the area-based algorithm compare favourably with manual generalisation of the same lines. It is capable of achieving both imperceptible minimal simplifications and caricatural generalisations. By careful selection of cut-off values, it is possible to use the same algorithm for scale-dependent and scale-independent generalisations. More importantly, it offers scope for modelling cartographic lines as consisting of features within features so that their geometric manipulation may be modified by application- and/or user-defined rules and weights. The paper examines the merits and limitations of the algorithm and the opportunities it offers for further research and progress in the field of line generalisation.