The Application of the Montage Image Mosaic Engine to the Visualization of Astronomical Images
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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 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. -
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. -
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. -
Map Projections
Map Projections Map Projections A Reference Manual LEV M. BUGAYEVSKIY JOHN P. SNYDER CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Published in 1995 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 1995 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 1 International Standard Book Number-10: 0-7484-0304-3 (Softcover) International Standard Book Number-13: 978-0-7484-0304-2 (Softcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress Visit the Taylor & Francis Web site at http ://www. -
5 Orbit and Ground Track of a Satellite
5 Orbit and Ground Track of a Satellite 5.1 Position of the Satellite on its Orbit Let (O; x, y, z) be the Galilean reference frame already defined. The satellite S is in an elliptical orbit around the centre of attraction O. The orbital plane P makes a constant angle i with the equatorial plane E. However, although this plane P is considered as fixed relative to in the Keplerian motion, in a real (perturbed) motion, it will in fact rotate about the polar axis. This is precessional motion,1 occurring with angular speed Ω˙ , as calculated in the last two chapters. A schematic representation of this motion is given in Fig. 5.1. We shall describe the position of S in using the Euler angles. 5.1.1 Position of the Satellite The three Euler angles ψ, θ and χ were introduced in Sect. 2.3.2 to specify the orbit and its perigee in space. In the present case, we wish to specify S. We obtain the correspondence between the Euler angles and the orbital elements using Fig. 2.1: ψ = Ω, (5.1) θ = i, (5.2) χ = ω + v. (5.3) Although they are fixed for the Keplerian orbit, the angles Ω, ω and M − nt vary in time for a real orbit. The inclination i remains constant, however. The distance from S to the centre of attraction O is given by (1.41), expressed in terms of the true anomaly v : a(1 − e2) r = . (5.4) 1+e cos v 1 The word ‘precession’, meaning ‘the action of preceding’, was coined by Coper- nicus around 1530 (præcessio in Latin) to speak about the precession of the equinoxes, i.e., the retrograde motion of the equinoctial points. -
Understanding Map Projections
Understanding Map Projections ArcInfo™ 8 Melita Kennedy Copyright © 1994, 1997, 1999, 2000 Environmental Systems Research Institute, Inc. All Rights Reserved. Printed in the United States of America. The information contained in this document is the exclusive property of Environmental Systems Research Institute, Inc. This work is protected under United States copyright law and the copyright laws of the given countries of origin and applicable international laws, treaties, and/or conventions. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system, except as expressly permitted in writing by Environmental Systems Research Institute, Inc. All requests should be sent to Attention: Contracts Manager, Environmental Systems Research Institute, Inc., 380 New York Street, Redlands, CA 92373- 8100 USA. The information contained in this document is subject to change without notice. U.S. GOVERNMENT RESTRICTED/LIMITED RIGHTS Any software, documentation, and/or data delivered hereunder is subject to the terms of the License Agreement. In no event shall the U.S. Government acquire greater than RESTRICTED/LIMITED RIGHTS. At a minimum, use, duplication, or disclosure by the U.S. Government is subject to restrictions as set forth in FAR §52.227-14 Alternates I, II, and III (JUN 1987); FAR §52.227-19 (JUN 1987) and/or FAR §12.211/12.212 (Commercial Technical Data/Computer Software); and DFARS §252.227-7015 (NOV 1995) (Technical Data) and/or DFARS §227.7202 (Computer Software), as applicable. Contractor/Manufacturer is Environmental Systems Research Institute, Inc., 380 New York Street, Redlands, CA 92373-8100 USA. -
II: "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 on the Healpix Grid
Mon. Not. R. Astron. Soc. 000, 1–8 (2007) Printed 25 July 2007 (MN LATEX style file v2.2) Mapping on the HEALPix grid Mark R. Calabretta1 and Boudewijn F. Roukema2 1Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia 2Toru´nCentre for Astronomy, N. Copernicus University, ul. Gagarina 11, PL-87-100 Toru´n,Poland Revised draft for acceptance by MNRAS 2007 July 25 ABSTRACT The natural spherical projection associated with the Hierarchical Equal Area and isoLatitude Pixelisation, HEALPix, is described and shown to be one of a hybrid class that combines the cylindrical equal-area and Collignon projections, not previously documented in the car- tographic literature. Projection equations are derived for the class in general and are used to investigate its properties. It is shown that the HEALPix projection suggests a simple method (a) of storing, and (b) visualising data sampled on the grid of the HEALPix pixelisation, and also suggests an extension of the pixelisation that is better suited for these purposes. Poten- tially useful properties of other members of the class are described, and new triangular and hexagonal pixelisations are constructed from them. Finally, the standard formalism is defined for representing the celestial coordinate system for any member of the class in the FITS data format. Key words: astronomical data bases: miscellaneous – cosmic microwave background – cos- mology: observations – methods: data analysis, statistical – techniques: image processing 1 INTRODUCTION The Hierarchical Equal Area and isoLatitude Pixelisation, HEALPix (Gorski´ et al. 1999, 2005), offers a scheme for distribut- ing 12N2(N ∈ N) points as uniformly as possible over the surface of the unit sphere subject to the constraint that the points lie on a relatively small number (4N − 1) of parallels of latitude and are equispaced in longitude on each of these parallels. -
Mercator Projection
U.S. ~eological Survey Profes-sional-Paper 1453 .. ~ :.. ' ... Department of the Interior BRUCE BABBITT Secretary U.S. Geological Survey Gordon P. Eaton, Director First printing 1989 Second printing 1994 Any use of trade names in this publication is for descriptive purposes only and does not imply endorsement by the U.S. Geological Survey Library of Congress Cataloging in Publication Data Snyder, John Parr, 1926- An album of map projections. (U.S. Geological Survey professional paper; 1453) Bibliography: p. Includes index. Supt. of Docs. no.: 119.16:1453 1. Map-projection. I. Voxland, Philip M. II. Title. Ill. Series. GA110.S575 1989 526.8 86-600253 For sale by Superintendent of Documents, U.S. Government Printing Office Washington, DC 20401 United States Government Printing Office : 1989 CONTENTS Preface vii Introduction 1 McBryde·Thomas Flat-Polar Parabolic 72 Glossary 2 Quartic Authalic 74 Guide to selecting map projections 5 McBryde-Thomas Flat-Polar Quartic 76 Distortion diagrams 8 Putnii)S P5 78 Cylindrical projections DeNoyer Semi-Elliptical 80 Mercator 10 Robinson 82 Transverse Mercator 12 Collignon 84 Oblique Mercator 14 Eckert I 86 Lambert Cylindrical Equal-Area 16 Eckert II 88 Behrmann Cylindrical Equal-Area 19 Loximuthal 90 Plate Carree 22 Conic projections Equirectangular 24 Equidistant Conic 92 Cassini 26 Lambert Conformal Conic 95 Oblique Plate Carree 28 Bipolar Oblique Conic Conformal 99 Central Cylindrical 30 Albers Equal-Area Conic 100 Gall 33 Lambert Equal-Area Conic 102 Miller Cylindrical 35 Perspective Conic 104 Pseudocylindrical -
Nevron Diagram for .NET - Maps
Nevron Diagram for .NET - Maps Introduction Nowadays the globalization process is stronger than ever and many companies sell products and services all over the world. That’s why software applications in many areas need to provide geographical and mapping information to the end users. World’s most popular format for storing such information is the ESRI shapefile. There are hundreds of freely available ESRI maps on the web and now you can easily take advantage of them using Nevron Diagram and its integrated mapping features. All you have to do is to put our diagramming component in your project and your mapping solution is just a few lines of code away. Nevron Diagram for .NET Maps will enhance your .NET desktop or Web-based applications by adding intuitive, user-friendly and interactive Maps and geographical data, extending the Diagram to provide sophisticated graphs for your specific business needs. Visualize Your Success www.nevron.com [email protected] 1-888-201-6088 How to add a map To import maps in you diagrams just follow these simple steps: 1. Create an object of type NEsriMap that will host the geographical data. 2. Add the ESRI shapefiles you want to load one by one using the A d d method of the map. The Add method returns the created shapefile in case you want to set some of its properties: o EnableZoomInRange - Gets/Sets whether the objects from the file should only be shown if the current zoom factor is in the Min/Max Zoom factor range specified by the MinShowZoomFactor and MaxShowZoomFactor properties. -
Blending World Map Projections with Flex Projector
Cartography and Geographic Information Science, 2013 Vol. 40, No. 4, 289–296, http://dx.doi.org/10.1080/15230406.2013.795002 Blending world map projections with Flex Projector Bernhard Jennya* and Tom Pattersonb aCollege of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331-5503, USA; bUS National Park Service, Harpers Ferry Center, Harpers Ferry, West Virginia 25425-0050, USA (Received 12 October 2012; accepted 15 February 2013) The idea of designing a new map projection via combination of two projections is well established. Some of the most popular world map projections in use today were devised in this manner. One construction method is to combine two source projections along a common parallel; a second method calculates the arithmetic means of two projections. These two methods for creating new world map projections are included in the latest version of Flex Projector. Flex Projector, a freeware mapping application, offers a graphical approach for customizing existing projections and creating new projections. The Mixer is a new feature in the latest version that allows the user to blend two existing projections to create a new hybrid projection. In addition to the two established combination methods, the software includes a new method for blending projections specific to its visual design approach. With this new method, a unique trait of one projection is transferable to a second projection. Flex Projector allows for the blending of four different projection traits separately or in combination: (1) the horizontal length of parallels, (2) the vertical distance of parallels from the equator, (3) the distribution of meridians, and (4) the bending of parallels.