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Map Projections--A Working Manual
This is a reproduction of a library book that was digitized by Google as part of an ongoing effort to preserve the information in books and make it universally accessible. https://books.google.com 7 I- , t 7 < ?1 > I Map Projections — A Working Manual By JOHN P. SNYDER U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1395 _ i UNITED STATES GOVERNMENT PRINTING OFFIGE, WASHINGTON: 1987 no U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary U.S. GEOLOGICAL SURVEY Gordon P. Eaton, Director First printing 1987 Second printing 1989 Third printing 1994 Library of Congress Cataloging in Publication Data Snyder, John Parr, 1926— Map projections — a working manual. (U.S. Geological Survey professional paper ; 1395) Bibliography: p. Supt. of Docs. No.: I 19.16:1395 1. Map-projection — Handbooks, manuals, etc. I. Title. II. Series: Geological Survey professional paper : 1395. GA110.S577 1987 526.8 87-600250 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, DC 20402 PREFACE This publication is a major revision of USGS Bulletin 1532, which is titled Map Projections Used by the U.S. Geological Survey. Although several portions are essentially unchanged except for corrections and clarification, there is consider able revision in the early general discussion, and the scope of the book, originally limited to map projections used by the U.S. Geological Survey, now extends to include several other popular or useful projections. These and dozens of other projections are described with less detail in the forthcoming USGS publication An Album of Map Projections. As before, this study of map projections is intended to be useful to both the reader interested in the philosophy or history of the projections and the reader desiring the mathematics. -
An Efficient Technique for Creating a Continuum of Equal-Area Map Projections
Cartography and Geographic Information Science ISSN: 1523-0406 (Print) 1545-0465 (Online) Journal homepage: http://www.tandfonline.com/loi/tcag20 An efficient technique for creating a continuum of equal-area map projections Daniel “daan” Strebe To cite this article: Daniel “daan” Strebe (2017): An efficient technique for creating a continuum of equal-area map projections, Cartography and Geographic Information Science, DOI: 10.1080/15230406.2017.1405285 To link to this article: https://doi.org/10.1080/15230406.2017.1405285 View supplementary material Published online: 05 Dec 2017. 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 Download by: [4.14.242.133] Date: 05 December 2017, At: 13:13 CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE, 2017 https://doi.org/10.1080/15230406.2017.1405285 ARTICLE An efficient technique for creating a continuum of equal-area map projections Daniel “daan” Strebe Mapthematics LLC, Seattle, WA, USA ABSTRACT ARTICLE HISTORY Equivalence (the equal-area property of a map projection) is important to some categories of Received 4 July 2017 maps. However, unlike for conformal projections, completely general techniques have not been Accepted 11 November developed for creating new, computationally reasonable equal-area projections. The literature 2017 describes many specific equal-area projections and a few equal-area projections that are more or KEYWORDS less configurable, but flexibility is still sparse. This work develops a tractable technique for Map projection; dynamic generating a continuum of equal-area projections between two chosen equal-area projections. -
Arxiv:1811.01571V2 [Cs.CV] 24 Jan 2019 Many Traditional Cnns on 3D Data Simply Extend the 2D Convolutional Op- Erations to 3D, for Example, the Work of Wu Et Al
SPNet: Deep 3D Object Classification and Retrieval using Stereographic Projection Mohsen Yavartanoo1[0000−0002−0109−1202], Eu Young Kim1[0000−0003−0528−6557], and Kyoung Mu Lee1[0000−0001−7210−1036] Department of ECE, ASRI, Seoul National University, Seoul, Korea https://cv.snu.ac.kr/ fmyavartanoo, shreka116, [email protected] Abstract. We propose an efficient Stereographic Projection Neural Net- work (SPNet) for learning representations of 3D objects. We first trans- form a 3D input volume into a 2D planar image using stereographic projection. We then present a shallow 2D convolutional neural network (CNN) to estimate the object category followed by view ensemble, which combines the responses from multiple views of the object to further en- hance the predictions. Specifically, the proposed approach consists of four stages: (1) Stereographic projection of a 3D object, (2) view-specific fea- ture learning, (3) view selection and (4) view ensemble. The proposed ap- proach performs comparably to the state-of-the-art methods while having substantially lower GPU memory as well as network parameters. Despite its lightness, the experiments on 3D object classification and shape re- trievals demonstrate the high performance of the proposed method. Keywords: 3D object classification · 3D object retrieval · Stereographic Projection · Convolutional Neural Network · View Ensemble · View Se- lection. 1 Introduction In recent years, success of deep learning methods, in particular, convolutional neural network (CNN), has urged rapid development in various computer vision applications such as image classification, object detection, and super-resolution. Along with the drastic advances in 2D computer vision, understanding 3D shapes and environment have also attracted great attention. -
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. -
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 -
Geographical Analysis on the Projection and Distortion of IN¯O's
International Journal of Geo-Information Article Geographical Analysis on the Projection and Distortion of INO’s¯ Tokyo Map in 1817 Yuki Iwai 1,* and Yuji Murayama 2 1 Graduate School of Life and Environmental Science, University of Tsukuba, Tsukuba 305-8572, Japan 2 Faculty of Life and Environmental Science, University of Tsukuba, Tsukuba 305-8572, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-29-853-5696 Received: 5 July 2019; Accepted: 10 October 2019; Published: 12 October 2019 Abstract: The history of modern maps in Japan begins with the Japan maps (called INO’s¯ maps) prepared by Tadataka Ino¯ after he thoroughly surveyed the whole of Japan around 200 years ago. The purpose of this study was to investigate the precision degree of INO’s¯ Tokyo map by overlaying it with present maps and analyzing the map style (map projection, map scale, etc.). Specifically, we quantitatively examined the spatial distortion of INO’s¯ maps through comparisons with the present map using GIS (geographic information system), a spatial analysis tool. Furthermore, by examining various factors that caused the positional gap and distortion of features, we explored the actual situation of surveying in that age from a geographical viewpoint. As a result of the analysis, a particular spatial regularity was confirmed in the positional gaps with the present map. We found that INO’s¯ Tokyo map had considerably high precision. The causes of positional gaps from the present map were related not only to natural conditions, such as areas and land but also to social and cultural phenomena. -
Uon Digital Repository Home
University of Nairobi School of Engineering Building a QGIS Helper Application to Overcome the Challenges of Cassini to UTM Coordinate System Conversions in Kenya BY Ajanga Dissent Ingati F56/81982/2015 A Project submitted in partial fulfillment for the Degree of Master of Science in Geographical Information Systems, in the Department of Geospatial & Space Technology of the University of Nairobi October 2017 I Declaration I, Ajanga Dissent Ingati, hereby declare that this project is my original work. To the best of my knowledge, the work presented here has not been presented for a degree in any other Institution of Higher Learning. ……………………………………. ……………………… .……..……… Name of student Signature Date This project has been submitted for examination with my approval as university supervisor. ……………………………………. ……………………… .……..……… Name of Supervisor Signature Date I Dedication I dedicate this work to my family for their support throughout the entire process of pursuing this degree and to the completion of the project. Your encouragement has been instrumental in ensuring the success of this project; may God truly bless you. II Acknowledgement I would like to show my heartfelt appreciation to all the people who saw me through the process of preparing this report. These thanks go to all those who provided technical support, talked through the issues I studied, read, wrote, gave comments, and also those who assisted in editing and proof reading of this project report before submission. I would like to thank Steve Firsake for his technical support through Python Programing. Special thanks also go to Dr.-Ing. Musyoka for his technical advice and support for the entire project. -
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. -
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. -
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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.