Estimation of an Unknown Cartographic Projection and Its Parameters from the Map
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Unusual Map Projections Tobler 1999
Unusual Map Projections Waldo Tobler Professor Emeritus Geography department University of California Santa Barbara, CA 93106-4060 http://www.geog.ucsb.edu/~tobler 1 Based on an invited presentation at the 1999 meeting of the Association of American Geographers in Hawaii. Copyright Waldo Tobler 2000 2 Subjects To Be Covered Partial List The earth’s surface Area cartograms Mercator’s projection Combined projections The earth on a globe Azimuthal enlargements Satellite tracking Special projections Mapping distances And some new ones 3 The Mapping Process Common Surfaces Used in cartography 4 The surface of the earth is two dimensional, which is why only (but also both) latitude and longitude are needed to pin down a location. Many authors refer to it as three dimensional. This is incorrect. All map projections preserve the two dimensionality of the surface. The Byte magazine cover from May 1979 shows how the graticule rides up and down over hill and dale. Yes, it is embedded in three dimensions, but the surface is a curved, closed, and bumpy, two dimensional surface. Map projections convert this to a flat two dimensional surface. 5 The Surface of the Earth Is Two-Dimensional 6 The easy way to demonstrate that Mercator’s projection cannot be obtained as a perspective transformation is to draw lines from the latitudes on the projection to their occurrence on a sphere, here represented by an adjoining circle. The rays will not intersect in a point. 7 Mercator’s Projection Is Not Perspective 8 It is sometimes asserted that one disadvantage of a globe is that one cannot see all of the entire earth at one time. -
Map Projections Paper 4 (Th.) UNIT : I ; TOPIC : 3 …Introduction
FOR SEMESTER 3 GE Students , Geography Map Projections Paper 4 (Th.) UNIT : I ; TOPIC : 3 …Introduction Prepared and Compiled By Dr. Rajashree Dasgupta Assistant Professor Dept. of Geography Government Girls’ General Degree College 3/23/2020 1 Map Projections … The method by which we transform the earth’s spheroid (real world) to a flat surface (abstraction), either on paper or digitally Define the spatial relationship between locations on earth and their relative locations on a flat map Think about projecting a see- through globe onto a wall Dept. of Geography, GGGDC, 3/23/2020 Kolkata 2 Spatial Reference = Datum + Projection + Coordinate system Two basic locational systems: geometric or Cartesian (x, y, z) and geographic or gravitational (f, l, z) Mean sea level surface or geoid is approximated by an ellipsoid to define an earth datum which gives (f, l) and distance above geoid gives (z) 3/23/2020 Dept. of Geography, GGGDC, Kolkata 3 3/23/2020 Dept. of Geography, GGGDC, Kolkata 4 Classifications of Map Projections Criteria Parameter Classes/ Subclasses Extrinsic Datum Direct / Double/ Spherical Triple Surface Spheroidal Plane or Ist Order 2nd Order 3rd Order surface of I. Planar a. Tangent i. Normal projection II. Conical b. Secant ii. Transverse III. Cylindric c. Polysuperficial iii. Oblique al Method of Perspective Semi-perspective Non- Convention Projection perspective al Intrinsic Properties Azimuthal Equidistant Othomorphic Homologra phic Appearance Both parallels and meridians straight of parallels Parallels straight, meridians curve and Parallels curves, meridians straight meridians Both parallels and meridians curves Parallels concentric circles , meridians radiating st. lines Parallels concentric circles, meridians curves Geometric Rectangular Circular Elliptical Parabolic Shape 3/23/2020 Dept. -
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. -
Bibliography of Map Projections
AVAILABILITY OF BOOKS AND MAPS OF THE U.S. GEOlOGICAL SURVEY Instructions on ordering publications of the U.S. Geological Survey, along with prices of the last offerings, are given in the cur rent-year issues of the monthly catalog "New Publications of the U.S. Geological Survey." Prices of available U.S. Geological Sur vey publications released prior to the current year are listed in the most recent annual "Price and Availability List" Publications that are listed in various U.S. Geological Survey catalogs (see back inside cover) but not listed in the most recent annual "Price and Availability List" are no longer available. Prices of reports released to the open files are given in the listing "U.S. Geological Survey Open-File Reports," updated month ly, which is for sale in microfiche from the U.S. Geological Survey, Books and Open-File Reports Section, Federal Center, Box 25425, Denver, CO 80225. Reports released through the NTIS may be obtained by writing to the National Technical Information Service, U.S. Department of Commerce, Springfield, VA 22161; please include NTIS report number with inquiry. Order U.S. Geological Survey publications by mail or over the counter from the offices given below. BY MAIL OVER THE COUNTER Books Books Professional Papers, Bulletins, Water-Supply Papers, Techniques of Water-Resources Investigations, Circulars, publications of general in Books of the U.S. Geological Survey are available over the terest (such as leaflets, pamphlets, booklets), single copies of Earthquakes counter at the following Geological Survey Public Inquiries Offices, all & Volcanoes, Preliminary Determination of Epicenters, and some mis of which are authorized agents of the Superintendent of Documents: cellaneous reports, including some of the foregoing series that have gone out of print at the Superintendent of Documents, are obtainable by mail from • WASHINGTON, D.C.--Main Interior Bldg., 2600 corridor, 18th and C Sts., NW. -
Representations of Celestial Coordinates in FITS
A&A 395, 1077–1122 (2002) Astronomy DOI: 10.1051/0004-6361:20021327 & c ESO 2002 Astrophysics Representations of celestial coordinates in FITS M. R. Calabretta1 and E. W. Greisen2 1 Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia 2 National Radio Astronomy Observatory, PO Box O, Socorro, NM 87801-0387, USA Received 24 July 2002 / Accepted 9 September 2002 Abstract. In Paper I, Greisen & Calabretta (2002) describe a generalized method for assigning physical coordinates to FITS image pixels. This paper implements this method for all spherical map projections likely to be of interest in astronomy. The new methods encompass existing informal FITS spherical coordinate conventions and translations from them are described. Detailed examples of header interpretation and construction are given. Key words. methods: data analysis – techniques: image processing – astronomical data bases: miscellaneous – astrometry 1. Introduction PIXEL p COORDINATES j This paper is the second in a series which establishes conven- linear transformation: CRPIXja r j tions by which world coordinates may be associated with FITS translation, rotation, PCi_ja mij (Hanisch et al. 2001) image, random groups, and table data. skewness, scale CDELTia si Paper I (Greisen & Calabretta 2002) lays the groundwork by developing general constructs and related FITS header key- PROJECTION PLANE x words and the rules for their usage in recording coordinate in- COORDINATES ( ,y) formation. In Paper III, Greisen et al. (2002) apply these meth- spherical CTYPEia (φ0,θ0) ods to spectral coordinates. Paper IV (Calabretta et al. 2002) projection PVi_ma Table 13 extends the formalism to deal with general distortions of the co- ordinate grid. -
Mapping the Drowned World by Tracey Clement
Mapping The Drowned World by Tracey Clement A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Sydney College of The Arts The University of Sydney 2017 Statement This volume is presented as a record of the work undertaken for the degree of Doctor of Philosophy at Sydney College of the Arts, University of Sydney. Table of Contents Acknowledgments iii List of images iv Abstract x Introduction: In the beginning, The End 1 Chapter One: The ABCs of The Drowned World 6 Chapter Two: Mapping The Drowned World 64 Chapter Three: It's all about Eve 97 Chapter Four: Soon it would be too hot 119 Chapter Five: The ruined city 154 Conclusion: At the end, new beginnings 205 Bibliography 210 Appendix A: Timeline for The Drowned World 226 Appendix B: Mapping The Drowned World artist interviews 227 Appendix C: Experiment and process documentation 263 Work presented for examination 310 ii Acknowledgments I wish to acknowledge the support of my partner Peter Burgess. He provided installation expertise, help in wrangling images down to size, hard-copies of multiple drafts, many hot dinners, and much, much more. Thanks also to my supervisor Professor Bradford Buckley for his steady guidance. In addition, the technical staff at SCA deserve a mention. Thanks also to all my friends, particularly those who let themselves be coerced into assisting with installation: you know who you are. And last, but certainly not least, thank you so much to the librarians at all of the University of Sydney libraries, and especially at SCA. -
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. -
Download Ebook ^ Cartography Introduction
NKAXDCBELVYX // eBook < Cartography Introduction Cartography Introduction Filesize: 5.46 MB Reviews Basically no words to clarify. Of course, it is perform, still an amazing and interesting literature. Its been printed in an exceptionally basic way which is only soon after i finished reading through this ebook where actually altered me, change the way i really believe. (Newton Runolfsson) DISCLAIMER | DMCA M5NRJO9YEFUZ ^ Book « Cartography Introduction CARTOGRAPHY INTRODUCTION Reference Series Books LLC Dez 2011, 2011. Taschenbuch. Book Condition: Neu. 244x190x3 mm. This item is printed on demand - Print on Demand Neuware - Source: Wikipedia. Pages: 66. Chapters: Cylindrical equal-area projection, Waymarking, Pacific Railroad Surveys, Raised-relief map, Babylonian Map of the World, Cartography of Asia, GeoComputation, SAGA GIS, MapGuide Open Source, Robert Erskine, Great Trigonometric Survey, Leo Belgicus, Baseline, United States National Grid, Esri grid, 45X90 points, Willem Blaeu, Cartography of Africa, Decimal degrees, Charles F. Homann, Pieter van der Aa, NearMap, Principal Triangulation of Great Britain, David Rumsey, Raleigh Ashlin Skelton, George Dow, Goode homolosine projection, Fantasy map, Rafael Palacios, Dual naming, General Perspective projection, Rumpsville, Geographia Map Company, Serra de Collserola, National mapping agency, Geographical pole, Globe of Peace, Ergograph, Bonne projection, United States and Mexican Boundary Survey, Principal meridian, ArcMap, Digital raster graphic, Lambert cylindrical equal-area projection, -
Between the Sinusoidal Projection and the Werner: an Alternative to the Bonne
CyberGeo, No. 241, 13/06/2003 Between the Sinusoidal projection and the Werner: an alternative to the Bonne. Une alternative à la projection cartographique de Bonne. Henry Bottomley Abstract The Sinusoidal projection and the Werner projection are equal area projections of the world. There are intermediate projections with similar properties, of which the best known is the Bonne projection. This note describes an alternative intermediate projection. Mots-clés : projection cartographique, projection équivalente, projection sinusoïdale, Werner, Bonne Résumé La projection sinusoïdale et la projection de Werner sont des projections équivalentes du monde: elles conservent les surfaces. Entre les deux, il existe des projections avec des propriétés similaires, parmi lesquelles la plus connue est la projection de Bonne. Cette article represente une autre projection entre la projection sinusoïdale et celle de Werner. Key-words : map projection, equal area projection, sinusoidal projection, Werner, Bonne ---------------------------------------------------------------------------------------------------- Both the Sinusoidal projection and the Werner provide simple equal area map projections, and have been used for many centuries. Unlike cylindrical equal area projections, they both reflect the fact that lines of latitude are shorter nearer the poles than those near the equator. To achieve this, they keep the central meridian straight and preserve distances along it, while transforming other meridians into curves; this has the effect of distorting shapes, in particular those towards the sides of the map, but helps remind the viewer of the curvature of the earth’s surface. There are intermediate projections with similar properties, of which the best known is the Bonne projection used extensively in the 19th century. This note describes an alternative intermediate projection. -
Guidance Note 7 Part 2
IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – September 2019 To facilitate improvement, this document is subject to revision. The current version is available at www.epsg.org. Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas Revised - September 2019 Page 1 of 162 IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – September 2019 To facilitate improvement, this document is subject to revision. The current version is available at www.epsg.org. Table of Contents Preface ............................................................................................................................................................5 1 IMPLEMENTATION NOTES ................................................................................................................. 6 1.1 ELLIPSOID PARAMETERS ......................................................................................................................... 6 1.2 ARCTANGENT FUNCTION ......................................................................................................................... 6 1.3 ANGULAR UNITS ....................................................................................................................................... 7 1.4 LONGITUDE 'WRAP-AROUND' .................................................................................................................. 7 1.5 OFFSETS ................................................................................................................................................... -
Map Projection Article on Wikipedia
Map Projection Article on Wikipedia Miljenko Lapaine a, * a University of Zagreb, Faculty of Geodesy, [email protected] * Corresponding author Abstract: People often look up information on Wikipedia and generally consider that information credible. The present paper investigates the article Map projection in the English Wikipedia. In essence, map projections are based on mathematical formulas, which is why the author proposes a mathematical approach to them. Weaknesses in the Wikipedia article Map projection are indicated, hoping it is going to be improved in the near future. Keywords: map projection, Wikipedia 1. Introduction 2. Map Projection Article on Wikipedia Not so long ago, if we were to find a definition of a term, The contents of the article Map projection at the English- we would have left the table with a matching dictionary, a language edition of Wikipedia reads: lexicon or an encyclopaedia, and in that book asked for 1 Background the term. However, things have changed. There is no 2 Metric properties of maps need to get up, it is enough with some search engine to 2.1 Distortion search that term on the internet. On the monitor screen, the search term will appear with the indication that there 3 Construction of a map projection are thousands or even more of them. One of the most 3.1 Choosing a projection surface famous encyclopaedias on the internet is certainly 3.2 Aspect of the projection Wikipedia. Wikipedia is a free online encyclopaedia, 3.3 Notable lines created and edited by volunteers around the world. 3.4 Scale According to Wikipedia (2018a) “The reliability of 3.5 Choosing a model for the shape of the body Wikipedia (predominantly of the English-language 4 Classification edition) has been frequently questioned and often assessed. -
COMMUNICATIONS of the DUBLIN INSTITUTE for ADVANCED STUDIES Series D, Geophysical Bulletin No
COMMUNICATIONS OF THE DUBLIN INSTITUTE FOR ADVANCED STUDIES Series D, Geophysical Bulletin No. 39 NOTES ON THE SIX INCH AND ONE INCH SHEET MAPS OF IRELAND and Methods for deducing Rectangular and Geographical Coordinates for points thereon by THOMAS MURPHY DUBLIN THE DUBLIN INSTITUTE FOR ADVANCED STUDIES 1988 Price £6.00 COMMUNICATIONS OF THE DUBLIN INSTITUTE FOR ADVANCED STUDIES Series D, Geophysical Bulletin No. 39 NOTES ON THE SIX INCH AND ONE INCH SHEET MAPS OF IRELAND and Methods for deducing Rectangular and Geographi cal Coordinates for points thereon by THOMAS MURPHY DUBLIN THE DUBLIN INSTITUTE FOR ADVANCED STUDIES 1988 Price £.6 . 00 ISBN 185500-983-8 NOTES ON THE SIX INCH AND ONE INCH SHEET MAPS OF IRELAND and Methods for deducing Rectangular and Geographical Coordinates for points thereon Sununary The coordinate systems employed in the production of the sheet maps of Ireland are described briefly . The transformation of coordinates from one to the other has been deduced from a study of historical docum~~ts. Introduction A point ~n Ireland is usually specified by one or more of five different coordinate systems namely:- County Grid Coordinates (feet) . National Grid Coordinates (metres). Latitude and Longitude on AIRY spheroid. Latitude and Longitude on INTERNATIONAL spheroid. European Datum 1950. Universal Transverse Mercator Coordinates, Zone 29. For geophysical studies in Ireland positional data are usually obtained from the. large scale maps of the Ordnance Survey, and given in National Grid Coordinates and/or Latitude and Longitude on the AIRY ellipsoid. The series which covers the complete country and the one still in use is at the scale of 1: 10 560, the so- called Six Inch series .