Delaunay Triangulations and Stereographic Projections

After describing Delaunay triangulations of vertices on a sphere and in a plane, we prove that every Delaunay triangulation of vertices on a sphere corresponds to the Delaunay triangulation in the plane of any stereographic projection of the spherical triangle vertices. We then exploit this correspondence to build robust algorithms for Delaunay triangulations in the plane or on the sphere. We also describe a collection of "fisheye" conformal transformations of the sphere that are the composition of one stereographic projection with the inverse of another stereographic projection.     

The Generalized Conic Projection

The Equidistant Cylindric and the Equidistant Conic projections are reviewed as foundations for a series of new projections. The new projections are introduced as the Patchwork Conic, an amalgamation of Equidistant Conic projections; the Generalized Equidistant Cylindric, with a standard path, or conformal path of correct scale, that is definable by the projection designer; and the Generalized Equidistant Conic, having two definable standard paths. Several potential uses are mentioned. Maps, formulae, and computation examples are provided. It is concluded that the projection is unique in allowing tailoring without compromising desirable mathematical properties.     

Symbolization of Map Projection Distortion: A Review

One of the most fundamental steps in map creation is the transformation of information from the surface of a globe onto a flat map. Mapmakers have developed and used hundreds of different map projections over the past 2,000 years, yet there is no perfect choice because every map projection uniquely alters some aspect of space during the transformation process. Detailed information about the type, amount, and distribution of distortion is essential for choosing the best projection for a particular map or data set. The distortion inherent in projections can be measured and symbolized much like any other map variable. Methods for symbolizing map projection distortion are reviewed, with each method described and illustrated in graphical form. The symbolization methods are collected under ten separate headings organized from simple to more complex in terms of interpretation. Most of these methods are highly effective at communicating distortion, yet they are rarely used beyond textbooks and technical documentation. Map projections and the distortions they carry need to be better understood by spatial data developers, distributors, and users. Map distortion should be carried along with map data as confidence layers, and the easily accessible distortion displays should be available to help in the selection of map projections. There is a suitably wide array of symbolization methods to match any need from basic education to research.     

The Exploratory Essays Initiative: Background and Overview

We define as Positional Accuracy Improvement the problem of putting together maps A and B of the same area, with B of higher planimetric accuracy. To do so, all objects in A might have to be slightly moved according to a mathematical transformation. Such transformation might ideally be of a specific type, like analytical or conformal functions. We have developed a theory to find a suitable analytical transformation despite it is not well defined because the only data available is the displacement vectors at a limited number of homologue control points. There exists a similar problem in fluid mechanics devoted on estimating the complete velocity field given just values at a limited number of points. We borrowed some ideas from there and introduced them into the positional accuracy improvement problem. We shall demonstrate that it is possible to numerically estimate an analytic function that resembles the given displacement at control points. As a byproduct, an uncertainty estimation is produced, which might help to detect regions of different lineage. The theory has been applied to rural 1:50.000 cartography of Uruguay while trying to diminish the discrepancies against GNSS readings. After the analytic transformation, the RMSE error diminished from 116 m to 48 m. Other problems with similar math requirements are the transformation between geodetic control networks.     

Joint Leadership for Spatial Data Standards

The Defense Mapping Agency, the National Ocean Service, and the U.S. Geological Survey each has earned a reputation among respective user communities as a leader in producing quality data and map products that meet the highest standards. With the increased use of GIS, user communities are rapidly expanding and have now begun to overlap. With adoption of SDTS as a Federal Information Processing Standard, all federal agencies are required to use the SDTS domestically. There is additionally an emerging need to unify efforts in the development of international standards. Existing standards need to be harmonized and future standards activities need to be linked more closely. This paper reviews the roles of each agency in developing spatial data and standards for exchange and outlines leadership activities in standards development that are currently underway.     

Combining Usability Techniques to Design Geovisualization Tools for Epidemiology

Designing usable geovisualization tools is an emerging problem in GIScience software development. We are often satisfied that a new method provides an innovative window on our data, but functionality alone is insufficient assurance that a tool is applicable to a problem in situ. As extensions of the static methods they evolved from, geovisualization tools are bound to enable new knowledge creation. We have yet to learn how to adapt techniques from interaction designers and usability experts toward our tools in order to maximize this ability. This is especially challenging because there is limited existing guidance for the design of usable geovisualization tools. Their design requires knowledge about the context of work within which they will be used, and should involve user input at all stages, as is the practice in any human-centered design effort. Toward that goal, we have employed a wide range of techniques in the design of ESTAT, an exploratory geovisualization toolkit for epidemiology. These techniques include; verbal protocol analysis, card-sorting, focus groups, and an in-depth case study. This paper reports the design process and evaluation results from our experience with the ESTAT toolkit.     

Establishing Classification and Hierarchy in Populated Place Labeling for Multiscale Mapping for The National Map

Current standards for federal mapping call for use of the Geographic Names Information System (GNIS) point layer for placement of United States populated place labels. However, this point layer contains limited classification information and hierarchy information, resulting in problems of map quality for database-driven, multi-scale, reference mapping, such as maps served by The National Map Viewer from USGS. Database-driven mapping often relies simply on what labels fit best in the map frame. Our research investigates alternative sources for labeling populated places, including polygons defined by the U.S. Census Bureau, such as incorporated place, census designated place (CDP), and economic place. Within each of these polygon layers we investigate relevant attributes from the decennial and economic censuses, such as population for incorporated places and CDPs, and the number of employees for economic places. The data selected are available for the entire country to serve national mapping requirements. This combination of data allows a more refined classification of populated places on maps that better represents relative importance. Visual importance on maps through scale should derive from more than simply residential population, but also economic importance, though comparison is made to this simpler case. We differentiate a fourth category of GNIS populated place points, essentially “neighborhoods” and related features—which are not incorporated places, CDPs, nor economic places. Populated places in this fourth class do not have federally defined boundaries, necessitating an alternative method for determining hierarchy in label presentation through scale.     

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.     

Multivariate Analysis and Geovisualization with an Integrated Geographic Knowledge Discovery Approach

The discovery, interpretation, and presentation of multivariate spatial patterns are important for scientific understanding of complex geographic problems. This research integrates computational, visual, and cartographic methods together to detect and visualize multivariate spatial patterns. The integrated approach is able to: (1) perform multivariate analysis, dimensional reduction, and data reduction (summarizing a large number of input data items in a moderate number of clusters) with the Self-Organizing Map (SOM); (2) encode the SOM result with a systematically designed color scheme; (3) visualize the multivariate patterns with a modified Parallel Coordinate Plot (PCP) display and a geographic map (GeoMap); and (4) support human interactions to explore and examine patterns. The research shows that such "mixed initiative" methods (computational and visual) can mitigate each other's weakness and collaboratively discover complex patterns in large geographic datasets, in an effective and efficient way.     

Design and Implementation of a Model,Web-based,GIS-Enabled Cancer Atlas

Abstract

The design and development of a highly interactive web-based, GIS-enabled atlas is reported. The atlas is a prototype, designed as a model for implementation of atlases to support government cancer-control activities. This model integrates symbolisation and design principles from print cartography, interaction strategies from exploratory geovisualisation, and web-map/web-feature service advances from GIS. The atlas has been implemented using a client-server architecture. It makes use of two open-source GIS tools, PostGIS (as the system database) and GeoServer (to connect the database to the client mapping application). The client mapping application has been built in Macromedia Flash. The entire client-server architecture is described, then direct primary emphasis is focused on the client mapping application. For this component of the system, the interface design strategy is detailed, the approach taken to implement this strategy in Flash is documented, and the mechanisms developed to build dynamic links from the client to the underlying database through the server are outlined. Features of the atlas are presented through a prototypical use scenario for a target user.     

Opponent Process Theory and Syntax for Qualitative Relationships in Quantitative Series

Opponent Process theory is a model of human color perception that predicts that there are four unique hues, with all others appearing as mixtures. An experiment was conducted to evaluate this model for its ability to predict the perception of qualitative relationships in single-variable quantitative series. Two such series were tested—“Balance” schemes where the categories represent varying mixtures of two distinctly different phenomena, and “Bipolar” schemes where the series divides into halves of differing interpretation. The results indicate that Balance schemes were most often associated with part-spectral hue progressions that fell between unique hues, while Bipolar schemes were associated with hue progressions that crossed a unique hue. This effect however is apparent only when value relationships are “double-ended” within the series.     

倾斜相机式投影的几何解法及其与外心投影的比较

本文根据透视投影的基本原理,给出了关于倾斜相机式投影的几何解法,在此基础上分析了倾斜相机式投影与外心投影的异同,提出了二者比较的一致性条件,并给出了实例验证。     

Qibla,and Related,Map Projections

The qibla problem—determination of the direction to Mecca—has given rise to retro-azimuthal map projections, an interesting, albeit unusual and little known, class of map projections. Principal contributors to this subject were Craig and Hammer, both writing in 1910. A property of retro-azimuthal projections is that the parallels are bent downwards towards the equator. The resulting maps, when extended to the entire world, thus must overlap themselves. An unusual recent discovery from Iran suggests that Muslims might have been prior inventors of a similar projection, by at least several centuries. A later corollary by Schoy leads to a new "cylindrical" azimuthal map projection with parallels bending away from the equator, here illustrated for the first time.     

海图、谷歌地图的投影选择

由于因特网的普及,各种影像数据在现代制图中已成为一种不可或缺的手段。如何能更好地利用现有的我们能掌控的技术资源,让它为我们的海图制作服务呢?本文从投影的选择进行了探讨,希望能给大家带来有益的思考。     

等角投影理论和方法综述

等角投影与其它性质投影比较之，其研究尤为深刻，应用也最为广泛。本文对等角投影的历史发展作了简单回顾，重点对等角投影的数学基础、等角投影的一般公式、等角投影变形量度、具有极值特性的等角投影和探求等角投影的方法进行了综述。最后提出需要继续研究的若干问题作为等角投影研究展望。     

等角投影理论和方法综述

等角投影比其它性质投影之研究更为深刻，应用也最为广泛。本文对等角投影的历史发展作了简单回顾，重点对等角投影的数学基础、等角投影的一般公式、等角投影变形量度［８］、具有极值特性的等角投影和探求等角投影的方法等进行了综述。最后提出需要继续研究的若干问题作为等角投影研究展望。     

The Roles of Web Feature and Web Map Services in Real-time Geospatial Data Sharing for Time-critical Applications

Many time-critical applications such as emergency response, location-based services, and real time traffic management need instant access to diverse data to make quick decisions and take instantaneous actions. However, two issues block time-critical applications to quickly acquire and integrate spatial data over the web: (1) the heterogeneity of existing GIS systems, and (2) the file-level data sharing systems over the web. This research examines current open standards, protocols, and technologies capable of solving the two issues for real-time spatial data sharing over the web. Focusing on investigating the role of Web Feature Services (WFS) and Web Map Services (WMS), this research has developed a solution for real-time geospatial data sharing at the feature level over the web. A prototype has been implemented to query, extract, create, delete, update, and map geographic features stored in web-accessible OGC (Open Geospatial Consortium) simple feature datastores for transportation emergency applications. The prototype results show that the OGC WFS and WMS play important roles in real-time geospatial data sharing and exchange from heterogeneous sources at the feature level for time-critical applications. The WFS and WMS eliminate time-consuming data translation and facilitate reuse of existing geospatial data over the web. Several issues related to the solution are also discussed in the paper.     

计算机兵棋棋盘中投影变形及坐标转换问题研究

兵棋是对作战过程进行逻辑推演研究和评估的军事科学工具,其三大组成要素包括棋盘、棋子和规则。棋盘的经典样式就是六角格兵棋棋盘,计算机兵棋中也常采用六角格棋盘描述战场地形环境,而棋盘的投影变形和坐标转换分别是制约兵棋推演可信度和推演效率的重要因素。首先分析了棋盘所用投影方式的变形规律,提出了个体值法和平均值法对变形进行修正;然后针对经纬度坐标和六角格编码的转换,提出了直接转换和间接转换两种方法,分析其基本转换原理,并给出了坐标转换公式;最后通过实验对所述方法进行验证,结果证实平均值法对于修正投影变形具有很好的实用性,且间接坐标转换法具有更高的转换效率。     

An Empirical Analysis of the Design Principles for Quantitative and Qualitative Area Symbols

To test the appropriateness of area symbol design principles, this study examined eye fixations on maps that varied in three areas: quantitative or qualitative information, conventional or unconventional design, and chromatic or achromatic presentation. The conventional design of associating darker symbols with greater magnitudes on quantitative maps led to shorter fixation on the map legend, and better performance on the overall map-distribution questions from a memory questionnaire given after the maps were viewed. In contrast, the convention of using pattern or hue symbols on qualitative maps resulted in longer fixation on the map body, and poor performance on the overall map-distribution questions. Some evidence of sex difference was also reported.     

极地海区等距离正圆柱投影平面上等角航线的展绘方法

墨卡托投影由于其纬度渐长的特性导致在极地海区投影存在严重的长度变形,无法在南北纬80°以外高纬度海区航海图中较好地应用。将长度变形程度明显低于墨卡托投影的等距离正圆柱投影作为极地海区的海图投影,研究了该投影平面中等角航线在极地海区的展绘方法。建立了等距离正圆柱投影平面上等角航线方程并对其曲率进行了分析,推导了绘制一般曲线形态的"以直代曲"公式;最后提出了一种可满足给定精度要求的等角航线展绘算法。实验结果表明:该算法简单易行,可在海图编绘规范规定的误差范围内,实现等角航线的精确展绘。