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.     

New Equal-Area Map Projections For Noncircular Regions

A series of new equal-area map projections has been devised. Called Oblated Equal-Area, its lines of constant distortion follow approximately oval or rectangular paths instead of the circles of the Lambert Azimuthal Equal-Area projection or the straight lines of the Cylindrical Equal-Area projection. The projection series permits design of equal-area maps of oblong regions with less overall distortion of shape and scale than equal-area maps on other projections.     

Variations of the Gringorten Square Equal-area Map Projection

Gringonen's square equal-area map projection has been forgotten since its appearance in 1972. I describe a modern implementation, including details of how to arrange, in different ways, the fundamental Gringonen projection of a sexadecant (one sixteenth of the surface of the sphere) onto a triangle. The Gringorten Mark I projection is an arrangement in which one hemisphere forms a square, with the other hemisphere disposed around it so that the whole sphere projects as a diamond, which may then be rotated to appear as a square. I introduce an alternative arrangement, the Gringorten Mark II, which is twice as high as it is wide, with one hemisphere on top of the other. These variants are compared with some other square map projections. Maps that fill a rectangular space completely can be very useful where, as on computer screens, space is limited and must be used efficiently.     

Cartographic Consequences of a Planned Economy—50 Years of Soviet Cartography

For half a century all cartography in the Soviet Union has been under centralized control. It was recognized early that mapmaking was an activity of prime importance. All phases of the activity—from cartographic education and the preparation of topographic and thematic maps to the development of regional atlases and school maps—have been managed by and for the benefit of the state in accordance with its economic and social objectives. This has had a significant effect on the development of cartography, the degree of its standardization, and the relative emphasis placed on its various aspects.     

Numerical Evaluation of the Robinson Projection

The Robinson projection is one of the most preferred projections for world reference maps in atlas cartography. The projection is constructed from Robinson's look-up table since there are no analytical formulas. This deficiency has led to a number of requests for the plotting formulas to which cartographers have responded by deriving analytical equations using different interpolation algorithms applied to Robinson's table values. The Robinson projection was examined with regard to its deformations calculated by four different algorithms, including the multiquadratic method. The numerical evaluations were then used to compare the algorithms. Solutions have been presented including some criticisms about this projection. The latitudes along which the scale is true and on which the maximum angular distortion equals zero have been determined.     

An Implementation of the Robinson Map Projection Based on Cubic Splines

The Robinson world map projection has been in existence since 1963. Mapping equations for the projection are based on table interpolation. Cubic splines with the choice of appropriate boundary conditions are shown to possess favorable characteristics as interpolative functions. The evaluation of cubic splines for given latitudes provides a basis for efficient forward mapping equations. Inverse mapping equations are based on an efficient inversion of the cubic spline functions utilizing Newton's method. Derivatives of the cubic spline functions lead to formulas for scale factors along projected meridians and parallels and for areal scale factors. Details for a computer implementation of the mapping equations and the computation of scale factors are given.     

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.     

A Geodesic Map Projection for Quadrilaterals

Part of a cuboctahedron-based geodesic map projection by Buckminster Fuller is expanded to spherical quadrilaterals with opposite sides equal. Points on such a quadrilateral can be described by intersections of geodesics, which provide parameterized coordinate values in a Geodesic Coordinate System. Through a linear transform of the geodesic coordinates, a spherical quadrilateral maps to a parallelogram. The resulting map has the same constant scale on all four sides. Within the map, all lines parallel to the sides correspond to geodesics on the globe. Spherical rectangles, spherical squares, and diamonds (spherical rhombi) are specifically examined; various tiling sets of diamonds can be used to cover the globe. Non-projection applications in geometry, astronomy, and computer graphics are described.     

The Miller Oblated Stereographic Projection for Africa,Europe, Asia and Australasia

The Miller Oblated Stereographic Projection, implemented by both the American Geographical Society and the Defense Mapping Agency in small-scale mapping of Africa, Europe, Asia and Australasia, is conformal for most land masses, reducing overall scale and area distortion by using a double projection. “Fill-in” sections are not conformal. Developed in 1953–1955 by O. M. Miller, the projection is implemented via tables for map construction. With the advent of computer-assisted intelligence and operations systems that use this projection to provide electronic images, the computation of rectangular projection coordinates from geographic locations via table look-up is no longer adequate. This paper presents an algorithm, based upon the original Miller work, which performs this transformation in a form applicable to scientific programming languages.     

Designing Effective Bivariate Symbols: The Influence of Perceptual Grouping Processes

The purpose of this research was to empirically assess perceptual groupings of various combinations of symbol dimensions (e.g., graphic variables) used in designing bivariate map symbols. Perceptual grouping ability was assessed using the theory of selective attention, a construct first proposed in psychological research. Selective attention theory contends that one's ability to analyze a symbol's dimensions—such as color or size—is affected by other dimensions present in the same symbol. Symbol dimensions are described as either separable (capable of being attended to independently of other dimensions), integral (cannot be processed without interference from other dimensions), or configural (i.e., show characteristics of both integrality and separability, which may also form new, emergent properties). Without empirical evidence describing such interactions for various combinations of symbol dimensions, cartographers cannot truly evaluate the functionality of the symbols they use on maps. The symbol dimensions or graphic combinations chosen for this study were selected to incorporate a wide range of traditional cartographic symbolization, including line and lettering symbolization, areal shading, dot patterns, and point symbols. Combinations were examined in an abstract setting using a speeded classification task, which is the traditional means of studying selective attention. Subject reaction times provided an assessment of the levels of integrality, separability, and configurality. Results suggest that most symbol dimension combinations are either separable or exhibit evidence of asymmetrical dimensional interactions. Findings from this study will be integrated into subsequent experiments, the results of which will assist cartographers in the design of complex map symbols.     

An atlas of Northamptonshire the medieval and early-modern landscape

National Geographic Society (NGS) has made several changes throughout the years in their choice of map projection for their world reference maps. The Van der Crinten I map projection was used from 1922 to 1988. Then, in 1988, it was replaced by the Robinson projection. Beginning in 1998, the Winkel Tripel became the map projection of choice for NCS' world maps. Given this change, cartographers and others who make maps may be interested in using the Winkel Tripel for custom applications. The goal of this paper is to show how Winkel Tripel's complex projection equations can be programmed using Visual Basic. Those who use other languages such as C++ can use this programming example to help them create a similar algorithm in their language of choice.     

World Maps With Natural Boundaries

The graticule of meridians and parallels is a largely artificial type of map boundary that can detract from the display of irregular features such as oceans. Such natural boundaries as shorelines may be used instead as the boundary of world maps. The principle of natural boundaries has been applied to several examples of equal-area or conformal world ocean maps with single or multiple lobes. By careful selection of the poles and centers, these maps can show both oceans and continents in their entirety on a single map.     

采用双重投影法的椭球面日晷投影

研究了从地球椭球面描写到海图平面的采用双重投影法的日晷投影方程式,并阐明了椭球面日晷投影的 3个重要特性及其应用。     

地图投影系统进一步补充的可能性——关于多圆柱投影

本文指出了地图投影分类系统中还有若干\     

空间Gauss—Kruger投影研究

研究了适合于星下点轨迹是某一经线的卫星图像数据投影选择的空间Gauss—Kruger投影，推导了空间Gauss—Kruger投影公式及其变形情况，并证明了该投影是等角空间投影，最后给出了算例。     

GPS网投影变形及消去投影变形的方法

利用GPS技术进行测量可以不受通视、气候等条件的限制,不仅大大提高了测量工作的效率,而且大大降低了劳动强度。GPS技术虽然是一种全新的技术,但是其基本的理论仍然脱离不了传统测绘理论基础。本文对坐标系统转换进行了介绍,并重点针对高斯投影变形和高程面异常引起的控制网误差进行分析,并通过实例提出了工程测量中变形的简易解决方法。     

基于AutoCAD二次开发的高斯投影转等积割圆锥投影

目前测制地形图使用的高斯坐标是等角投影,存在面积变形,而在利用地形图进行大面积土地量算时要求应用等积投影地形图。本文针对如何在CASS成图软件中实现高斯投影转换为等积割圆锥投影进行阐述,开发了投影转换功能菜单并进行了转换有效性验证,摈弃了传统的借助其他GIS软件进行投影转换再求积的工作程序。     

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。     

日照正射方位投影的实现

日照投影是将地球被阳光照射的状态绘制在平面上,使得地图和时间建立了联系。日照正射方位投影保持了地球的圆弧轮廓,逼真地表现出了昼、夜半球。基于坐标系的变换,给出了实现日照正射方位投影的原理,并推导出了投影方程。     

抵偿投影最大适用范围及最大投影变形最小参数确定方法

为了满足相关规范对测区最大投影变形的控制要求,需要采取措施抑制测区投影变形,无论是抵偿投影面高斯正形投影或者任意带高斯正形投影,或者以上两种方式的结合,都有必要确定该投影方法满足最大投影变形限差条件的最大可适用范围,还有必要根据项目确定的范围对投影最大投影变形进行判定,并进行投影参数的科学选择.研究了满足最大投影变形限...