基于QTM的海平面上升分析与模拟

针对海平面上升影响范围分析与模拟这一国际前沿问题,通过研究基于球面四元三角网(QTM)的关键技术问题,包括复杂拓扑关系计算、LOD剖分、球面水淹分析、基于QTM的多分辨率的DEM数据组织方法和分析精度的相关性评定等,以.Net和Direct3D为开发工具,设计开发了基于QTM的海平面上升影响范围评估模型。该研究结果可为全球海平面上升影响的防灾减灾决策提供有效支撑,并推动了球面数据模型和球面格网拓扑分析的理论成果在全球变化预测相关领域的应用进展。     

平面影像到QTM像元的转换算法及精度分析

平面影像数据到四元三角网(Quaternary Triangular Mesh,QTM)像元的转换是实现全球QTM格网影像无缝建模的首要任务。提出基于面积权的数据转换方法,给出不同类型的权重及格网值的计算,并利用ArcGIS中256级灰度的Wsiearth.tif图像数据分析了转换精度。结果表明:将4 km分辨率的影像数据转换到12层的QTM像元时,转换误差在0~2灰度内占96.27%,对一般应用的影响可以忽略不计。     

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.     

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.     

A new pseudocylindrical equal-area projection for adaptive composite map projections

The recently introduced adaptive composite map projection technique changes the projection to the geographic area shown on a map. It is meant as a replacement for the commonly used web Mercator projection, which grossly distorts areas when representing the entire world. The original equal-area version of the adaptive composite map projection technique uses the Lambert azimuthal projection for regional maps and three alternative projections for world maps. Adaptive composite map projections can include a variety of other equal-area projections when the transformation between the Lambert azimuthal and the world projections uses Wagner’s method. To select the most suitable pseudocylindrical projection, the distortion characteristics of a pseudocylindrical projection family are analyzed, and a user study among experts in the area of map projections is carried out. Based on the results of the distortion analysis and the user study, a new pseudocylindrical projection is recommended for extending adaptive composite map projections. The new projection is equal-area throughout the transformation to the Lambert azimuthal projection and has better distortion characteristics then small-scale projections currently included in the adaptive composite map projection technique.     

球面似均匀格网的剖分方法及特征分析

给出球面"似均匀格网"概念的内涵,并介绍3种常用的球面似均匀格网(三角形格网、菱形格网和六边形格网)的剖分方法.从几何上分析3种格网的单元特征及不同格网在不同领域的应用优势.通过对比得出3种格网的特征对照表及相互关系,即:三角形格网是最基本的球面剖分格网,球面六边形格网和菱形格网可以通过球面三角格网来生成,且这3种剖分格网各有优缺点并在一定条件下可以相互转换.     

基于球面DQG的数字高程建模算法与可视化表达

为有效解决经纬度格网与四元三角网(Quaternary Triangular Mesh,QTM)在全球地形建模方面存在的不足,根据球面DQG(Degenerate Quadtree Grid)的几何结构特点,选择双线性多项式内插方法进行格网点高程内插,给出基于球面DQG的DEM建模算法与效率分析,并应用美国地质调查局提供的GTOPO30全球地形数据进行相关实验。结果表明:全球DEM建模时,DQG所需的格网数是经纬度格网或QTM的2/3左右,且可视化操作(图形放大、缩小及漫游等)时画面平滑、流畅,没有抖动。     

High-performance three-horizon composition algorithm for large-scale terrains

This work presents a high-performance algorithm to compute the horizon in very large high-resolution DEMs. We used Stewart's algorithm as the core of our implementation and considered that the horizon has three components: the ground, near, and far horizons. To eliminate the edge-effect, we introduced a multi-resolution halo method. Moreover, we used a new data partition approach, to substantially increase the parallelism in the algorithm. In addition, several optimizations have been applied to considerably reduce the number of arithmetical operations in the core of the algorithm. The experimental results have demonstrated that by applying the above-described contributions, the proposed algorithm is more than twice faster than Stewart's algorithm while maintaining the same accuracy.     

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%.     

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。     

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two‐dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area‐preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.     

基于TIN数据三维地质体的折剖面切割算法

为有效分析地质模型的内部结构,研究直接利用折切面对模型数据进行几何切割的算法。该算法面向基于TIN数据表达的三维地质体,包括"折剖面的生成"和"被切割地质体的拆分"两大关键步骤;采用向二维平面投影的策略,将复杂的切割转化为交线的快速连接、三角形重新剖分和点与多边形的包含测试等简单操作。对不同复杂程度的三维地质模型进行切割实验,发现化繁为简和二维投影策略极大地提高了算法效率。     

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.     

Comments to a polar bear population model

Larsen, T. & Ugland, K. I. (Polar Research 2 n.s., 117–118) note correctly that a Leslie matrix model treats cubs and females as independent units which is not the case lor polar bears. Population projections using the Leslie model with hunting mortalities added are instructive first approximations in evaluations of field data, however, and are recommended as exercises also for polar bear biologists. An APL programme for such projections is available.     

中国沙漠旅游资源空间结构与主体功能分区

基于中国沙漠旅游资源的赋存条件,分析了中国沙漠旅游资源空间结构特征;通过主要旅游景区（点）的统计,基于GPS定位和ArcGIS软件,建立了中国沙漠旅游资源空间数据库,实现了沙漠旅游资源的空间可视化表达;基于沙漠旅游资源空间结构特征和旅游发展的景观主体功能分区需要,进行了中国沙漠旅游资源主体功能分区。结论表明：中国北方沙漠旅游资源地域广、类型丰富,主要分布在沙漠（地）的边缘和少数腹地,呈现出个别地域较为集中分布的特征;沙漠景区（点）以主要交通线为轴,呈集群串珠状分布;沙漠旅游资源功能分区划分为：一大沙漠旅游带、三大沙漠旅游区、七大沙漠旅游圈。最后讨论了中国沙漠旅游资源的开发对策。     

The latest trend tracing model for projection of mineral demand

A new method for short- and long-term forecasting of mineral commodities based upon historical data is developed. The method, referred to as the latest trend tracing (LTT) model, is constructed as a weighting and adaptive approach based on a general linear model. The LTT model considers the functions of data location and statistical behavior. The newest data receive the largest weights, whereas the older data are given smaller weights. The LTT model is performed by an iterative algorithm. The data set is successively partitioned into training and testing subsets. Each LTT model is estimated and tested for each partition. The updated estimates are then synthesized to produce the final estimates based upon the data locations and estimation variances. The LTT model is demonstrated on two real case studies, one on the projection of U.S. aluminum consumption and the other on the forecasting of U.S. copper consumption.     

The Demographic Constraints on Future Population Growth in Regional Australia

Concern about rapid population growth in Australia's large cities and slower growth in many non-metropolitan areas has stimulated a range of government policies attempting to lift non-metropolitan growth rates. However, there is relatively little research on which to base these policies. It would be helpful to understand more about the consequences of current demographic trends continuing and the effects of alternative migration patterns. This paper presents sub-national population projections for Australia over the horizon 2011–2041, basing the projections on more socially meaningful Remoteness Areas instead of common statistical geographies. Three sets of projections were generated: a Current Direction scenario in which recent demographic trends are maintained, a Regional Immigration scenario in which more immigrants settle in regional and remote areas, and a Metro Exodus scenario in which there is increased internal migration from metropolitan to non-metropolitan areas. The future of Australia's population geography is shown to be one of spatially varying growth and population ageing, and continued metropolitanisation. In regional areas rapid population ageing will lower natural increase rates and thus reduce overall growth, resulting in a falling share of the national population. Policy measures attempting to increase the share of growth in regional areas will struggle against natural demographic forces operating in the opposite direction.     

The Sinusoidal Projection: A New Importance in Relation to Global Image Data

The reprojection of image data causes the loss or duplication of original pixel values. This research investigated the feasibility of using the sinusoidal projection for global image database construction. Specifically, reprojection accuracies were tested with geographic latitude and longitude coordinates, and the Hammer‐Aitoff, Eckert IV, Mollweide, and sinusoidal projections. Reprojections between these five global projections and the Universal Transverse Mercator (UTM) projection and referencing system were performed using fifty‐four sample datasets. A statistical analysis of categorical accuracy, a measure describing the omission of pixel values during reprojection, was conducted. Geographic coordinates and the sinusoidal projection both showed very high accuracy rates (100.0 percent and 99.5 percent respectively) when sample datasets were reprojected from UTM. The geographic coordinates, however, showed very low accuracy (65.3 percent) when sample datasets were reprojected to the UTM projection, while the sinusoidal projection showed the highest accuracy (98.4 percent). The results strongly suggest that the sinusoidal projection is very accurate and efficient for building global image databases.     

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.