Nevron Diagram for .NET - Maps
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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. -
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. -
Choosing the Best Atlas for Your Classroom William Slattery, Editor
Choosing the Best Atlas for Your Classroom William Slattery, Editor (Last updated August 14, 2008) As editor of Social Studies School Service's Geography Catalog, I frequently receive plaintive phone calls from teachers and department heads who are about to spend their hard-won money on an atlas (or on dozens or even hundreds of atlases), and they need more information than the one-paragraph descriptions our print catalogs give them. Often they ask which atlas is "best," but the real question that needs to be asked is "Which atlas is best for my particular needs?" Some important questions to consider here: Who is going to use the atlas? What will they use it for? What features are most important to you? How much do you plan to spend? For instance, if you will use the atlas for intensive work on understanding latitude and longitude, you might require an atlas that uses no other location system that might distract students or be used as a crutch. On the other hand, you may prefer an atlas that includes not only latitude and longitude but also alphanumeric grids, because then one system can serve as the answer key to the other. This article provides a series of descriptions that permit point-by-point comparisons between atlases. It discusses what types of maps are included, how color is used, how much detail is shown, and how up-to-date the atlases are. Note that, throughout these descriptions, the term "sub-national political units" refers to political entities one level below the national government (such as states, departments, provinces, and republics in a federation). -
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. -
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. -
Assignment #3 Map Projection
Assignment #3 Map Projection 1.) Mapping the world For assignment 3, I have used World Winkel Tripel Projection system to project map of the world. This projection is used for world maps to minimize shape and area distortion. It has been used by the National Geographic Society since 1998 for general and thematic world maps. It is a compromise projection used for world maps that averages the coordinates from the equirectangular (equidistant cylindrical) and Aitoff projections. This was developed by Oswald Winkel in 1921. Modified azimuthal—coordinates are the average of the Aitoff and equirectangular projections. Meridians are equally spaced and concave toward the central meridian. The central meridian is a straight line. Parallels are equally spaced curves, concave toward the poles. The poles are approximately 0.4 times the length of the equator. The length of the poles depends on the standard parallel chosen. Figure 1: Mapping world map using World Winkel Tripel NGS Projection 2.) Mapping the United States In this exercise, map of the United States showing states was selected. The properties of U.S cities was modified using “Query Builder” such that the capital cities of each state is considered with population greater than 10000. Symbology was edited and each capital cities were labeled. After that, the distance between two cities was measured using “Measure” tool in toolbar and “Magnifier” option in windows tool in toolbar. Later, for the same map projection was introduced. The map was projected using USA Albert Equal Area projection. After the projection was completed, the distance between same two cities was measured. -
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. -
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. -
1. Introduction
Chapter-Introduction GIS 1. INTRODUCTION. Geography is the study of Earth’s features and patterns of their variations in spatial location and time. Many questions of agricultural production are geographic in nature as the production depends on the environment and prevailing socio economic conditions, both of which vary spatially and in time. Examples are questions related to natural resources management, precision agriculture, agro- ecological classification for land use planning, regional trends and patterns in technology adaptation, agricultural productivity and income, non-Pont source pollution from agricultural lands, etc. Answering these questions requires access to large volumes of multidimensional geographical (spatial) information of weather, soils, topography, water resources, socio economic status, etc. Further, answers to even apparently simple questions require that the data from several sources be integrated in a consistent form. Geographical Information Systems or GIS enable representation and integration of such spatial information. Geographic information systems (GIS) (also known as Geospatial information systems) are Computer Software and hardware systems that enable users to capture, store, analyze and manage spatially referenced data. GISs have transformed the way spatial (geographic) data, relationships and patterns in the world are able to be interactively queried, processed, analyzed, mapped, modelled, visualized, and displayed for an increasingly large range of users, for a multitude of purposes. In a general sense, the term describes any information system that integrates, stores, edits, analyzes, shares, and displays geographic information. GIS applications are tools that allow users to create interactive queries (user-created searches), analyze spatial information, edit data in maps, and present the results of all these operations.