Adaptive Composite Map Projections
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5–21 5.5 Miscellaneous Projections GMT Supports 6 Common
GMT TECHNICAL REFERENCE & COOKBOOK 5–21 5.5 Miscellaneous Projections GMT supports 6 common projections for global presentation of data or models. These are the Hammer, Mollweide, Winkel Tripel, Robinson, Eckert VI, and Sinusoidal projections. Due to the small scale used for global maps these projections all use the spherical approximation rather than more elaborate elliptical formulae. 5.5.1 Hammer Projection (–Jh or –JH) The equal-area Hammer projection, first presented by Ernst von Hammer in 1892, is also known as Hammer-Aitoff (the Aitoff projection looks similar, but is not equal-area). The border is an ellipse, equator and central meridian are straight lines, while other parallels and meridians are complex curves. The projection is defined by selecting • The central meridian • Scale along equator in inch/degree or 1:xxxxx (–Jh), or map width (–JH) A view of the Pacific ocean using the Dateline as central meridian is accomplished by running the command pscoast -R0/360/-90/90 -JH180/5 -Bg30/g15 -Dc -A10000 -G0 -P -X0.1 -Y0.1 > hammer.ps 5.5.2 Mollweide Projection (–Jw or –JW) This pseudo-cylindrical, equal-area projection was developed by Mollweide in 1805. Parallels are unequally spaced straight lines with the meridians being equally spaced elliptical arcs. The scale is only true along latitudes 40˚ 44' north and south. The projection is used mainly for global maps showing data distributions. It is occasionally referenced under the name homalographic projection. Like the Hammer projection, outlined above, we need to specify only -
A Pipeline for Producing a Scientifically Accurate Visualisation of the Milky
A pipeline for producing a scientifically accurate visualisation of the Milky Way M´arciaBarros1;2, Francisco M. Couto2, H´elderSavietto3, Carlos Barata1, Miguel Domingos1, Alberto Krone-Martins1, and Andr´eMoitinho1 1 CENTRA, Faculdade de Ci^encias,Universidade de Lisboa, Portugal 2 LaSIGE, Faculdade de Ci^encias,Universidade de Lisboa, Portugal 3 Fork Research, R. Cruzado Osberno, 1, 9 Esq, Lisboa, Portugal [email protected] Abstract. This contribution presents the design and implementation of a pipeline for producing scientifically accurate visualisations of Big Data. As a case study, we address the data archive produced by the European Space Agency's (ESA) Gaia mission. The satellite was launched in Dec 19 2013 and is repeatedly monitoring almost two billion (2000 million) astronomical sources during five years. By the end of the mission, Gaia will have produced a data archive of almost a Petabyte. Producing visually intelligible representations of such large quantities of data meets several challenges. Situations such as cluttering, overplot- ting and overabundance of features must be dealt with. This requires careful choices of colourmaps, transparencies, glyph sizes and shapes, overlays, data aggregation and feature selection or extraction. In addi- tion, best practices in information visualisation are sought. These include simplicity, avoidance of superfluous elements and the goal of producing esthetical pleasing representations. Another type of challenge comes from the large physical size of the archive, which makes it unworkable (or even impossible) to transfer and process the data in the user's hardware. This requires systems that are deployed at the archive infrastructure and non-brute force approaches. Because the Gaia first data release will only happen in September 2016, we present the results of visualising two related data sets: the Gaia Uni- verse Model Snapshot (Gums), which is a simulation of Gaia-like data; the Initial Gaia Source List (IGSL) which provides initial positions of stars for the satellite's data processing algorithms. -
A Bevy of Area Preserving Transforms for Map Projection Designers.Pdf
Cartography and Geographic Information Science ISSN: 1523-0406 (Print) 1545-0465 (Online) Journal homepage: http://www.tandfonline.com/loi/tcag20 A bevy of area-preserving transforms for map projection designers Daniel “daan” Strebe To cite this article: Daniel “daan” Strebe (2018): A bevy of area-preserving transforms for map projection designers, Cartography and Geographic Information Science, DOI: 10.1080/15230406.2018.1452632 To link to this article: https://doi.org/10.1080/15230406.2018.1452632 Published online: 05 Apr 2018. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tcag20 CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE, 2018 https://doi.org/10.1080/15230406.2018.1452632 A bevy of area-preserving transforms for map projection designers Daniel “daan” Strebe Mapthematics LLC, Seattle, WA, USA ABSTRACT ARTICLE HISTORY Sometimes map projection designers need to create equal-area projections to best fill the Received 1 January 2018 projections’ purposes. However, unlike for conformal projections, few transformations have Accepted 12 March 2018 been described that can be applied to equal-area projections to develop new equal-area projec- KEYWORDS tions. Here, I survey area-preserving transformations, giving examples of their applications and Map projection; equal-area proposing an efficient way of deploying an equal-area system for raster-based Web mapping. projection; area-preserving Together, these transformations provide a toolbox for the map projection designer working in transformation; the area-preserving domain. area-preserving homotopy; Strebe 1995 projection 1. Introduction two categories: plane-to-plane transformations and “sphere-to-sphere” transformations – but in quotes It is easy to construct a new conformal projection: Find because the manifold need not be a sphere at all. -
View Preprint
1 Remaining gaps in open source software 2 for Big Spatial Data 1 3 Lu´ısM. de Sousa 1ISRIC - World Soil Information, 4 Droevendaalsesteeg 3, Building 101 6708 PB Wageningen, The Netherlands 5 Corresponding author: 1 6 Lu´ıs M. de Sousa 7 Email address: [email protected] 8 ABSTRACT 9 The volume and coverage of spatial data has increased dramatically in recent years, with Earth observa- 10 tion programmes producing dozens of GB of data on a daily basis. The term Big Spatial Data is now 11 applied to data sets that impose real challenges to researchers and practitioners alike. As rule, these 12 data are provided in highly irregular geodesic grids, defined along equal intervals of latitude and longitude, 13 a vastly inefficient and burdensome topology. Compounding the problem, users of such data end up 14 taking geodesic coordinates in these grids as a Cartesian system, implicitly applying Marinus of Tyre’s 15 projection. 16 A first approach towards the compactness of global geo-spatial data is to work in a Cartesian system 17 produced by an equal-area projection. There are a good number to choose from, but those supported 18 by common GIS software invariably relate to the sinusoidal or pseudo-cylindrical families, that impose 19 important distortions of shape and distance. The land masses of Antarctica, Alaska, Canada, Greenland 20 and Russia are particularly distorted with such projections. A more effective approach is to store and 21 work with data in modern cartographic projections, in particular those defined with the Platonic and 22 Archimedean solids. -
Portraying Earth
A map says to you, 'Read me carefully, follow me closely, doubt me not.' It says, 'I am the Earth in the palm of your hand. Without me, you are alone and lost.’ Beryl Markham (West With the Night, 1946 ) • Map Projections • Families of Projections • Computer Cartography Students often have trouble with geographic names and terms. If you need/want to know how to pronounce something, try this link. Audio Pronunciation Guide The site doesn’t list everything but it does have the words with which you’re most likely to have trouble. • Methods for representing part of the surface of the earth on a flat surface • Systematic representations of all or part of the three-dimensional Earth’s surface in a two- dimensional model • Transform spherical surfaces into flat maps. • Affect how maps are used. The problem: Imagine a large transparent globe with drawings. You carefully cover the globe with a sheet of paper. You turn on a light bulb at the center of the globe and trace all of the things drawn on the globe onto the paper. You carefully remove the paper and flatten it on the table. How likely is it that the flattened image will be an exact copy of the globe? The different map projections are the different methods geographers have used attempting to transform an image of the spherical surface of the Earth into flat maps with as little distortion as possible. No matter which map projection method you use, it is impossible to show the curved earth on a flat surface without some distortion. -
Maps and Cartography: Map Projections a Tutorial Created by the GIS Research & Map Collection
Maps and Cartography: Map Projections A Tutorial Created by the GIS Research & Map Collection Ball State University Libraries A destination for research, learning, and friends What is a map projection? Map makers attempt to transfer the earth—a round, spherical globe—to flat paper. Map projections are the different techniques used by cartographers for presenting a round globe on a flat surface. Angles, areas, directions, shapes, and distances can become distorted when transformed from a curved surface to a plane. Different projections have been designed where the distortion in one property is minimized, while other properties become more distorted. So map projections are chosen based on the purposes of the map. Keywords •azimuthal: projections with the property that all directions (azimuths) from a central point are accurate •conformal: projections where angles and small areas’ shapes are preserved accurately •equal area: projections where area is accurate •equidistant: projections where distance from a standard point or line is preserved; true to scale in all directions •oblique: slanting, not perpendicular or straight •rhumb lines: lines shown on a map as crossing all meridians at the same angle; paths of constant bearing •tangent: touching at a single point in relation to a curve or surface •transverse: at right angles to the earth’s axis Models of Map Projections There are two models for creating different map projections: projections by presentation of a metric property and projections created from different surfaces. • Projections by presentation of a metric property would include equidistant, conformal, gnomonic, equal area, and compromise projections. These projections account for area, shape, direction, bearing, distance, and scale. -
Map Projections
MAP PROJECTIONS Methods of presenting the curved surface of the Earth on a flat map. MAP PROJECTIONS On your notebook paper, create a graphic organizer as illustrated below…Title it MAP PROJECTIONS Map Name Illustration Strength Weakness Used For?? Are all Maps created equally? Imagine trying to flatten out a globe; you would have to stretch it here, compress it there. Because of this, it is quite common for sizes, shapes, and even distances to be misrepresented in the transition from three dimensions to two. Large distortion if you are looking at a hemisphere or the entire world. Smaller distortion/inaccuracies - At the scale of a city or even a small country, Mercator Projection Cylinder shape Meridians stretched apart & parallel to each other instead of meeting at the poles. Landmasses at high latitudes appears LARGER Landmasses at lower latitudes appears relatively SMALLER. Conic Projection Designed as if a cone had been placed over the globe. Arctic regions portrayed accurately. Further you get from the top of the cone, the more distorted sizes and distances become. Great for aeronautical plotting - latitudes are more accurate. Flat Plane/Azumithal Projection Distances measured from the center are accurate. Distortion increases as you get further away from the center point. Used by airline pilots & ship navigators to find the shortest distance between 2 places. Equal Area Map Projection An interrupted view of the globe. Land masses are proportional - giving the correct perspective of size. Not usable for navigation - longitude & latitude are stretched apart in order to conform to sizes. Gall-Peters Projection Landmasses in this projection are kept accurate and in proportion. -
Cylindrical Projections 27
MAP PROJECTION PROPERTIES: CONSIDERATIONS FOR SMALL-SCALE GIS APPLICATIONS by Eric M. Delmelle A project submitted to the Faculty of the Graduate School of State University of New York at Buffalo in partial fulfillments of the requirements for the degree of Master of Arts Geographical Information Systems and Computer Cartography Department of Geography May 2001 Master Advisory Committee: David M. Mark Douglas M. Flewelling Abstract Since Ptolemeus established that the Earth was round, the number of map projections has increased considerably. Cartographers have at present an impressive number of projections, but often lack a suitable classification and selection scheme for them, which significantly slows down the mapping process. Although a projection portrays a part of the Earth on a flat surface, projections generate distortion from the original shape. On world maps, continental areas may severely be distorted, increasingly away from the center of the projection. Over the years, map projections have been devised to preserve selected geometric properties (e.g. conformality, equivalence, and equidistance) and special properties (e.g. shape of the parallels and meridians, the representation of the Pole as a line or a point and the ratio of the axes). Unfortunately, Tissot proved that the perfect projection does not exist since it is not possible to combine all geometric properties together in a single projection. In the twentieth century however, cartographers have not given up their creativity, which has resulted in the appearance of new projections better matching specific needs. This paper will review how some of the most popular world projections may be suited for particular purposes and not for others, in order to enhance the message the map aims to communicate. -
Gaia Data Release 1: the Archive Visualisation Service A
Astronomy & Astrophysics manuscript no. arxiv c ESO 2017 August 2, 2017 Gaia Data Release 1: The archive visualisation service A. Moitinho1, A. Krone-Martins1, H. Savietto2, M. Barros1, C. Barata1, A.J. Falcão3, T. Fernandes3, J. Alves4, A.F. Silva1, M. Gomes1, J. Bakker5, A.G.A. Brown6, J. González-Núñez7; 8, G. Gracia-Abril9; 10, R. Gutiérrez-Sánchez11, J. Hernández12, S. Jordan13, X. Luri10, B. Merin5, F. Mignard14, A. Mora15, V. Navarro5, W. O’Mullane12, T. Sagristà Sellés13, J. Salgado16, J.C. Segovia7, E. Utrilla15, F. Arenou17, J.H.J. de Bruijne18, F. Jansen19, M. McCaughrean20, K.S. O’Flaherty21, M.B. Taylor22, and A. Vallenari23 (Affiliations can be found after the references) Received date / Accepted date ABSTRACT Context. The first Gaia data release (DR1) delivered a catalogue of astrometry and photometry for over a billion astronomical sources. Within the panoply of methods used for data exploration, visualisation is often the starting point and even the guiding reference for scientific thought. However, this is a volume of data that cannot be efficiently explored using traditional tools, techniques, and habits. Aims. We aim to provide a global visual exploration service for the Gaia archive, something that is not possible out of the box for most people. The service has two main goals. The first is to provide a software platform for interactive visual exploration of the archive contents, using common personal computers and mobile devices available to most users. The second aim is to produce intelligible and appealing visual representations of the enormous information content of the archive. Methods. The interactive exploration service follows a client-server design. -
The Mercator Projection: Its Uses, Misuses, and Its Association with Scientific Information and the Rise of Scientific Societies
ABEE, MICHELE D., Ph.D. The Mercator Projection: Its Uses, Misuses, and Its Association with Scientific Information and the Rise of Scientific Societies. (2019) Directed by Dr. Jeff Patton and Dr. Linda Rupert. 309 pp. This study examines the uses and misuses of the Mercator Projection for the past 400 years. In 1569, Dutch cartographer Gerard Mercator published a projection that revolutionized maritime navigation. The Mercator Projection is a rectangular projection with great areal exaggeration, particularly of areas beyond 50 degrees north or south, and is ill-suited for displaying most reference and thematic world maps. The current literature notes the significance of Gerard Mercator, the Mercator Projection, the general failings of the projection, and the twentieth century controversies that arose as a consequence of its misuse. This dissertation illustrates the path of the institutionalization of the Mercator Projection in western cartography and the roles played by navigators, scientific societies and agencies, and by the producers of popular reference and thematic maps and atlases. The data are pulled from the publication record of world maps and world maps in atlases for content analysis. The maps ranged in date from 1569 to 1900 and displayed global or near global coverage. The results revealed that the misuses of the Mercator Projection began after 1700, when it was connected to scientists working with navigators and the creation of thematic cartography. During the eighteenth century, the Mercator Projection was published in journals and reports for geographic societies that detailed state-sponsored explorations. In the nineteenth century, the influence of well- known scientists using the Mercator Projection filtered into the publications for the general public. -
Types of Projections
Types of Projections Conic Cylindrical Planar Pseudocylindrical Conic Projection In flattened form a conic projection produces a roughly semicircular map with the area below the apex of the cone at its center. When the central point is either of Earth's poles, parallels appear as concentric arcs and meridians as straight lines radiating from the center. Usually used for maps of countries or continents in the middle latitudes (30-60 degrees) Cylindrical Projection A cylindrical projection is a type of map in which a cylinder is wrapped around a sphere (the globe), and the details of the globe are projected onto the cylindrical surface. Then, the cylinder is unwrapped into a flat surface, yielding a rectangular-shaped map. Generally used for navigation, but this map is very distorted at the poles. Very Northern Hemisphere oriented. Planar (Azimuthal) Projection Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional projection plane. Generally used for polar maps. Focused on a central point. Outside edge is distorted Oval / Pseudo-cylindrical Projection Pseudo-cylindrical maps combine many cylindrical maps together. This reduces distortion. Each cylinder is focused on a particular latitude line. Generally used to show world phenomenon or movement – quite accurate because it is computer generated. Famous Map Projections Mercator Winkel-Tripel Sinusoidal Goode’s Interrupted Homolosine Robinson Mollweide Mercator The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. this map accurately shows the true distance and the shapes of landmasses, but as you move away from the equator the size and distance is distorted. -
GCTP General Cartographic Transformation Package
National Mapping Program Technical Instructions GCTP General Cartographic Transformation Package Software Documentation U.S. Department of the Interior U.S. Geological Survey National Mapping Division Software Documentation for the General Cartographic Transformation Package CONTENTS Page 1. General information. 1 1.1 Summary . 1 1.2 Environment . 1 1.3 References. 1 2. Package description. 3 2.1 System description. 3 2.2 Subroutine GTPZ0, primary access routine to the package . 5 2.3 Function ADJLZ0, adjusts longitude to range -180° to +180°. 11 2.4 Function ASINZ0, checks arc sin argument before calling DASIN . 12 2.5 Function DMSPZ0, converts an angle to +DDDMMMSSS.SSS format . 13 2.6 Function E0FNZ0, computes constant "e0" for distance along meridian . 14 2.7 Function E1FNZ0, computes constant "e1" for distance along meridian . 15 2.8 Function E2FNZ0, computes constant "e2" for distance along meridian . 16 2.9 Function E3FNZ0, computes constant "e3" for distance along meridian . 17 2.10 Function E4FNZ0, computes constant "e4" for Polar Stereographic . 18 2.11 Function MLFNZ0, computes "M," distance Equator to PHI. 19 2.12 Function MSFNZ0, computes "m," radius of parallel of latitude divided by semimajor axis . 20 2.13 Function PAKCZ0, converts +DDDMMSS.SSS to +DDDMMMSSS.SSS. 21 2.14 Function PAKDZ0, converts +DDDMMMSSS.SSS to degrees, minutes, seconds. 22 2.15 Function PAKRZ0, converts +DDDMMMSSS.SSS angle format to radians. 23 2.16 Function PAKSZ0, converts +DDDMMMSSS.SSS angle format to seconds. 24 2.17 Function PHI1Z0, computes latitude in inverse of Albers Equal-Area 25 2.18 Function PHI2Z0, computes latitude in inverses in Lambert Conformal Conic and Polar Stereographic.