The Equal Earth map projection

The Equal Earth map projection is a new equal-area pseudocylindrical projection for world maps. It is inspired by the widely used Robinson projection, but unlike the Robinson projection, retains the relative size of areas. The projection equations are simple to implement and fast to evaluate. Continental outlines are shown in a visually pleasing and balanced way.     

A compromise aspect-adaptive cylindrical projection for world maps

There are two problems with current cylindrical projections for world maps. First, existing cylindrical map projections have a static height-to-width aspect ratio and do not automatically adjust their aspect ratio in order to optimally use available canvas space. Second, many of the commonly used cylindrical compromise projections show areas and shapes at higher latitudes with considerable distortion. This article introduces a new compromise cylindrical map projection that adjusts the distribution of parallels to the aspect ratio of a canvas. The goal of designing this projection was to show land masses at central latitudes with a visually balanced appearance similar to how they appear on a globe. The projection was constructed using a visual design procedure where a series of graphically optimized projections was defined for a select number of aspect ratios. The visually designed projections were approximated by polynomial expressions that define a cylindrical projection for any height-to-width ratio between 0.3:1 and 1:1. The resulting equations for converting spherical to Cartesian coordinates require a small number of coefficients and are fast to execute. The presented aspect-adaptive cylindrical projection is well suited for digital maps embedded in web pages with responsive web design, as well as GIS applications where the size of the map canvas is unknown a priori. We highlight the projection with a height-to-width ratio of 0.6:1, which we call the Compact Miller projection because it is inspired by the Miller Cylindrical projection. Unlike the Miller Cylindrical projection, the Compact Miller projection has a smaller height-to-width ratio and shows the world with less areal distortion at higher latitudes. A user study with 448 participants verified that the Compact Miller – together with the Plate Carrée projection – is the most preferred cylindrical compromise projection.     

Graphical design of world map projections

The design of new map projections has up until now required mathematical and cartographic expertise that has limited this activity to a small group of specialists. This article introduces the background mathematics for a software-based method that enables cartographers to easily design new small-scale world map projections. The software is usable even by those without mathematical expertise. A new projection is designed interactively in an iterative process that allows the designer to graphically and numerically assess the graticule, the representation of the continents, and the distortion properties of the new projection. The method has been implemented in Flex Projector, a free and open-source application enabling users to quickly create new map projections and modify existing projections. We also introduce new tools that help evaluate the distortion properties of projections, namely a configurable acceptance index to assess areal and angular distortion, a derived acceptance visualization, and interactive profiles through the distortion space of a projection. To illustrate the proposed method, a new projection, the Cropped Ginzburg VIII projection, is presented.     

地图投影与地缘政治理论构建——以麦金德地缘政治思想为例

地缘政治理论的提出和发展深刻烙印了地图的影响。在地缘政治发展史中,不同地图投影既服务于各思想家的理论提出,也深入到各思想家在不同时期对自身理论的动态修正。地图投影到底是如何参与到地缘政治理论构建过程中的?本文在既有地缘政治地图研究的基础上,从空间性和文本性两大地图基本属性出发,通过阐释并沟通地图的空间分析与话语分析功能,探讨地图投影与地缘政治理论构建间的关系。一方面,地图投影变形抽象后的心象地图框架为构建地缘政治理论提供了空间依托;另一方面,地图投影通过地图变形在复杂情境中聚集了丰富的文本性含义。在地图投影各层次文本性的互文（互补性叙事）下,新的地图话语得以产生并渗透进心象地图,具象式推动了地缘政治理论核心概念的生成和逻辑关系的构建。综合考虑麦金德的地图观影响,本文对麦金德“心脏地带”地缘政治思想变迁各阶段（1904年、1919年、1943年）地图投影透视的分析验证了该关系框架的解释力。这启示该分析框架在其他地缘政治理论研究中的潜在适用性,更期待在百年变局和复兴全局等交织下的复杂情境中,基于地图投影创新互文下的中国地缘政治理论构建。     

二战期间美国地缘战略空间观念变迁 ——基于地图投影的视角

在地图投影变换影响下,得益于多样化的地图服务,二战期间美国地缘战略空间观念经历了从孤立主义向干涉主义的转变,推动了美国的参战与具体战略展开。这一空间逻辑在战时地图投影的选择上表现为从圆柱投影下的二维“矩形世界”向等距方位投影下的“圆形世界”和正射投影下的三维“球体世界”“鸟瞰世界”转变,折射出空中时代下的全球一体观。通过不同投影下“地图空间”的调整,二战期间美国地缘战略空间观念逐渐接近现实地球空间,这无疑增强了美国参战的合理性和战略决策的正确性。作为认知话语和实践话语的统一,地图投影通过地图服务反映并参与到了二战的地缘政治发展进程。伴随着美国地缘战略空间观念的变迁,美国也由此从世界舞台的边缘走向国际体系的中心。在当前中国和平崛起和全球地缘调整的大背景下,地图投影创新也为今后的地缘关系研究提供了诸多启示。     

多投影间地图投影变换实现的途径与优化

针对多种地图投影间自由变换的需求 ,综合对比地图投影变换的主要方法及其特点 ,该文认为反解变换是解决多种投影间投影变换的最佳途径。以此为基础 ,具体探讨了地图投影变换计算机实现的主要过程 ,讨论了地图投影体系、投影参数、算法优化和误差控制等投影变换计算机实现中的关键问题     

海洋小比例尺地图精确测量及计算方法

针对传统的欧式测量方法在海洋小比例尺地图长度、面积等计算时存在精度差的问题,通过对WGS1984投影、墨卡托投影、兰勃托投影和阿尔伯斯投影等特性的研究,利用ArcEngine技术实现海洋小比例尺地图投影的精确测量及计算,论述在不规则地球椭球体下如何精确量算海洋距离、面积等信息,为我国海洋资源探测和军事战略方面提供基础服务.     

Computation and visualisation of the accuracy of old maps using differential distortion analysis

The accuracy of old maps can hold interesting historical information, and is therefore studied using distortion analysis methods. These methods start from a set of ground control points that are identified both on the old map and on a modern reference map or globe, and conclude with techniques that compute and visualise distortion. Such techniques have advanced over the years, but leave room for improvement, as the current ones result in approximate values and a coarse spatial resolution. We propose a more elegant and more accurate way to compute distortion of old maps by translating the technique of differential distortion analysis, used in map projection theory, to the setting where an old map and a reference map are directly compared. This enables the application of various useful distortion metrics to the study of old maps, such as the area scale factor, the maximum angular distortion and the Tissot indicatrices. As such a technique is always embedded in a full distortion analysis method we start by putting forward an optimal analysis method for a general-purpose study, which then serves as the foundation for the development of our technique. Thereto, we discuss the structure of distortion analysis methods and the various options available for every step of the process, including the different settings in which the old map can be compared to its modern counterpart, the techniques that can be used to interpolate between both, and the techniques available to compute and visualise the distortion. We conclude by applying our general-purpose method, including the differential distortion analysis technique, to an example map also used in other literature.     

Quasi indicatrix approach for distortion visualization and analysis for map projections

Tissot’s indicatrix or ellipse of distortion is a diagram that is the projection of an infinitesimal circle on the original surface. It is normally an ellipse of which elongation depends on the amount of distortion caused by map projection. It provides a medium for analyzing existing projections and developing new ones. The ellipse can be scaled and depicted on the map for visualization purposes. This paper presents an alternative approach, in which the projection of a finite small circle on the sphere is used. Its projection is normally an ellipse that can be very close to Tissot’s indicatrix, and is called quasi indicatrix, here. Its parameters can be derived from the forward projection equations without using partial derivatives. Therefore, it is a useful and practical approach from a programmer’s point of view. The quasi indicatrix approach is also numerically tested on Aitoff–Hammer projection with a set of points. The indicatrix parameters obtained by using this approach deviate 0.5% from the ground truths at most, being the average less than 0.2%.     

一种适用于极区的横轴墨卡托海图

极区位于高纬度地区,极区航海图投影采用墨卡托投影时,图上极区附近变形较大,在极点处变形达到无穷大;采用极球面投影时,图上恒向线不是直线;心射切面投影不是正形投影,不能直接在图上量取方位和距离;兰伯特正形投影图上,经度是由角度表示,而不是真的经度;采用横轴墨卡托投影时,几乎所有的经线以及纬线在图上为曲线。以上常用的海图投影不利于船舶在极区安全航行,也不利于航海人员进行海图作业。针对此问题,将构建的伪经纬线网与经纬线网进行转换,通过Matlab得到基于伪经纬线网的横轴墨卡托投影图,此图具有类似于墨卡托海图的特点,图上极区变形失真小,图上伪经纬线的特点可方便极区海图作业。     

南极地区常用地图投影及其应用

南极地区常用的地图投影方式有 :极方位立体投影、横轴墨卡托投影、兰伯特正形圆锥投影等三种等角投影。本文在介绍了所有等角投影应满足的一般条件的基础上 ,分别详述了上述三种投影在南极地区的具体应用。并对卫星影像的投影作了探讨。     

基于面向对象的地图投影转换模块设计

以基于面向对象的方法实现地图投影转换模块设计,探讨该方法在地图投影转换中以及具体投影转换模块的设计及实现,在VC6.0平台下通过相关接口的建立以及地理坐标系和投影坐标系两大主要类的设计和扩充,实现地理坐标系间、投影坐标系间或两者间的投影转换.该模块有利于快速、高效编程的实现,并具有扩展性强和易于维护等优势.     

Volume 111 Index

Abstract

Concepts related to alternative map projections can be difficult to explain to students given the diversity and complexity of available projections. Students frequently have trouble understanding how distortions caused by the choice of a projection can affect map readability and comprehension. Programs available for personal computers now provide geography and cartography instructors with a method for interactively educating students concerning the distortions associated with alternative map projections. Such software can be incorporated into laboratory assignments in introductory geography courses or in more advanced courses that deal with map design or thematic cartography.     

Four World Maps for Use in Biology and Geophysics

Even nowadays one frequently sees distributional data plotted on world maps on the Mercator projection, the only advantage of which is that loxodromes (rhumb lines) appear as straight lines, but which is grotesquely misleading for comparison of area and distance. Equal-area projections are, however, more and more used, the uncertainty mainly being which of the numerous kinds should be the most suitable one.     

Automation and evaluation of graduated dot maps

Dot mapping is a traditional method for visualizing quantitative data, but current automated dot mapping techniques are limited. The most common automated method places dots pseudo-randomly within enumeration areas, which can result in overlapping dots and very dense dot clusters for areas with large values. These issues affect users’ ability to estimate values. Graduated dot maps use dots with different sizes that represent different values. With graduated dot maps the number of dots on a map is smaller, reducing the likelihood of overlapping dots. This research introduces an automated method of generating graduated dot maps that arranges dots with blue-noise patterns to avoid overlap and uses clustering algorithms to replace densely packed dots with those of larger sizes. A user study comparing graduated dot maps, pseudo-random dot maps, blue-noise dot maps and proportional circle maps with almost 300 participants was conducted. Results indicate that map users can more accurately extract values from graduated dot maps than from the other map types. This is likely due to the smaller number of dots per enumeration area in graduated dot maps. Map users also appear to prefer graduated dot maps over other map types.     

Land cover dynamic changes in northern China: 1989?2003

The 13 provinces (autonomous regions and municipalities) in northern China are located in latitude 31°–54°N and longitude 73°–136°E including Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia, Jilin, Liaoning, Heilongjiang, Shaanxi, Gansu, Ningxia, Qinghai, and Xinjiang, where environments are fragile. In recent years, the eco-environmental problems such as vegetation destruction, desertification and soil erosion etc. become serious because of climate change and unreasonable human activities. In this paper, landscape pattern and its evolution in northern China from 1989 to 2003 was investigated by the combined use of RS and GIS based on the basic theory and method of landscape ecology. Land use/cover maps of the study area in 1989, 1999 and 2003 were produced by using 1 km monthly NOAA Ad-vanced Very High Resolution Radiometer (AVHRR) and SPOT/VGT Normalized Difference Vegetation Index (NDVI) dataset from national climate bureau of China which were geo-registered to Lambert azimuthal equal-area map projection and were used in the paper. Landscape evolution in the area over the study period was investigated by two methods: (a) the changes of various landscape metrics were analyzed using the landscape structure analysis program FRAGSTATS; (b) the transition matrix of landscape patch types was cal-culated with the help of the RS and GIS software. The results showed that from 1989 to 2003, the landscape within the study area had undertaken a complicated evolution in landscape structure and composition. The diversity index and evenness index increased during the pe-riod, which means that the landscape pattern tended to be diversified and even. The fragmentation index of grassland, forestland and water areas also increased significantly. This showed that the distribution and structure of forestland, grassland and water areas had been changed greatly during the period, especially grassland which became more and more fragmentized, and its fragmentation index increased from 19.23% to 88.72%. The transitions of the landscape types were mainly shown by the changes among forestland, grassland and farmland, and grassland changing into unable land. Over the study period, grassland and water areas had decreased remarkably, accounting for 15% and 37% from 1989 to 1999 and 24.79% and 49.25% from 1999 to 2003 respectively. The grassland and water resources play an important role in the eco-environment and economic development of the region. So, they must be protected carefully. According to the analysis, we can conclude that the eco-environment in the study area is obviously degenerated due to unreasonable human activities and climate changes and some measures should be taken to combat the environ-mental degradation.     

基于地图方里网的全球剖分系统

针对现有剖分模型的不足,提出了一种基于地图方里网的全球剖分系统,有效避免了传统经纬度格网模型在高纬度地区的形状退化和正多面体格网模型的面片形状不规则问题。制定了相应的编码,实现了面片编码与传统地理坐标之间的转换和邻接关系的计算,最后对方里网在地球椭球面上的变形规律进行了研究。研究结果表明:基于地图方里网的剖分系统不仅具有科学的数据组织形式,而且面片单元的变形面积小、变形规律稳定。     

Book Reviews

Regular grid sampling structures in the plane are a common spatial framework for many studies. Constructing grids with desirable properties such as equality of area and shape is more difficult on a sphere. We studied the distortion characteristics of recursive partitions of the surface of the globe starting with the octahedron and icosahedron polyhedral models. We used five different methods for mapping from the polyhedral model to the surface of the sphere: the Gnomonic projection, Fuller's Dymaxion projection, Snyder's equal area polyhedral projection, direct spherical subdivision, and a recursive polyhedral projection. We increased partition density using both a 4-fold and a 9-fold ratio at each level of recursive subdivision by subdividing to the 8th level with the 4-fold density ratio (65 536 cells per polyhedral face) and to the fifth level with the 9-fold density ratio (59 049 cells per polyhedral face). We measured the area and perimeter of each cell at each level of recursion for each method on each model using each density ratio. From these basic measurements we calculated the range and standard deviation of the area measurement, and the mean, range, and standard deviation of a compactness measurement defined as the ratio of (the ratio of the perimeter to the area of the cell) to (the ratio of the perimeter to the area of a spherical circle with the same area). We looked at these basic measurements and their statistics using graphs of variation with recursion level, sums of squares analyses of variation, histograms of the distributions, maps of the spatial variation, and correlograms. The Snyder projection performed best in area distortion and the Gnomonic projection performed best in compactness distortion. The Fuller projection and the Sphere method had moderate distortion in both area and compactness relative to the worst methods. There was little difference in distortion performance between partitions using the 4-fold density ratio and those using the 9-fold density ratio. Partitions based on the icosahedron performed better for all statistics than those based on the octahedron.     

1989-2003年中国北方土地覆被变化

The 13 provinces （autonomous regions and municipalities） in northern China are located in latitude 31°-54°N and longitude 73°-136°E including Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia, Jilin, Liaoning, Heilongjiang, Shaanxi, Gansu, Ningxia, Qinghai, and Xinjiang, where environments are fragile. In recent years, the eco-environmental problems such as vegetation destruction, desertification and soil erosion etc. become serious because of climate change and unreasonable human activities. In this paper, landscape pattern and its evolution in northern China from 1989 to 2003 was investigated by the combined use of RS and GIS based on the basic theory and method of landscape ecology. Land use/cover maps of the study area in 1989, 1999 and 2003 were produced by using 1 km monthly NOAA Advanced Very High Resolution Radiometer （AVHRR） and SPOTNGT Normalized Difference Vegetation Index （NDVI） dataset from national climate bureau of China which were geo-registered to Lambert azimuthal equal-area map projection and were used in the paper. Landscape evolution in the area over the study period was investigated by two methods： （a） the changes of various landscape metrics were analyzed using the landscape structure analysis program FRAGSTATS; （b） the transition matrix of landscape patch types was calculated with the help of the RS and GIS software. The results showed that from 1989 to 2003, the landscape within the study area had undertaken a complicated evolution in landscape structure and composition. The diversity index and evenness index increased during the period, which means that the landscape pattern tended to be diversified and even. The fragmentation index of grassland, forestland and water areas also increased significantly. This showed that the distribution and structure of forestland, grassland and water areas had been changed greatly during the period, especially grassland which became more and more fragmentized, and its fragmentation index increased from 19.23% to 88.72%. The transi     

南大洋海冰影像地图投影变换与瓦片切割应用研究

南大洋海冰分布是南极考察过程中影响破冰船航行的重要因素,也是南极研究的重要内容之一。目前国际上不同机构发布的南大洋海冰分布图,大多是球面投影,不能直接用于主流的瓦片地图发布。将极方位立体投影海冰图转换为目前主流的网络墨卡托投影地图,并利用合适的图像重采样方法,按照不同级别比例尺进行瓦片切割和编号存储,最终实现海冰影像地图的发布共享是本文的主要研究内容。笔者对不同的图像重采样方法进行了比较,分析了最邻近点采样方法、双线性内插和双三次卷积重采样方法的优劣,针对本文的研究优选双线性内插方法进行影像地图瓦片的切割,并最终叠加融合在Google地图上,实现了Google底图、准实时海冰影像图与破冰船走航位置的集成显示,为雪龙船的冰区航行提供了重要的数据支撑。