The History of Cartography / Volume 1 / Review Article
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Nicolas-Auguste Tissot: a Link Between Cartography and Quasiconformal Theory
NICOLAS-AUGUSTE TISSOT: A LINK BETWEEN CARTOGRAPHY AND QUASICONFORMAL THEORY ATHANASE PAPADOPOULOS Abstract. Nicolas-Auguste Tissot (1824{1897) published a series of papers on cartography in which he introduced a tool which became known later on, among geographers, under the name of the Tissot indicatrix. This tool was broadly used during the twentieth century in the theory and in the practical aspects of the drawing of geographical maps. The Tissot indicatrix is a graph- ical representation of a field of ellipses on a map that describes its distortion. Tissot studied extensively, from a mathematical viewpoint, the distortion of mappings from the sphere onto the Euclidean plane that are used in drawing geographical maps, and more generally he developed a theory for the distor- sion of mappings between general surfaces. His ideas are at the heart of the work on quasiconformal mappings that was developed several decades after him by Gr¨otzsch, Lavrentieff, Ahlfors and Teichm¨uller.Gr¨otzsch mentions the work of Tissot and he uses the terminology related to his name (in particular, Gr¨otzsch uses the Tissot indicatrix). Teichm¨ullermentions the name of Tissot in a historical section in one of his fundamental papers where he claims that quasiconformal mappings were used by geographers, but without giving any hint about the nature of Tissot's work. The name of Tissot is also missing from all the historical surveys on quasiconformal mappings. In the present paper, we report on this work of Tissot. We shall also mention some related works on cartography, on the differential geometry of surfaces, and on the theory of quasiconformal mappings. -
Mercator-15Dec2015.Pdf
THE MERCATOR PROJECTIONS THE NORMAL AND TRANSVERSE MERCATOR PROJECTIONS ON THE SPHERE AND THE ELLIPSOID WITH FULL DERIVATIONS OF ALL FORMULAE PETER OSBORNE EDINBURGH 2013 This article describes the mathematics of the normal and transverse Mercator projections on the sphere and the ellipsoid with full deriva- tions of all formulae. The Transverse Mercator projection is the basis of many maps cov- ering individual countries, such as Australia and Great Britain, as well as the set of UTM projections covering the whole world (other than the polar regions). Such maps are invariably covered by a set of grid lines. It is important to appreciate the following two facts about the Transverse Mercator projection and the grids covering it: 1. Only one grid line runs true north–south. Thus in Britain only the grid line coincident with the central meridian at 2◦W is true: all other meridians deviate from grid lines. The UTM series is a set of 60 distinct Transverse Mercator projections each covering a width of 6◦in latitude: the grid lines run true north–south only on the central meridians at 3◦E, 9◦E, 15◦E, ... 2. The scale on the maps derived from Transverse Mercator pro- jections is not uniform: it is a function of position. For ex- ample the Landranger maps of the Ordnance Survey of Great Britain have a nominal scale of 1:50000: this value is only ex- act on two slightly curved lines almost parallel to the central meridian at 2◦W and distant approximately 180km east and west of it. The scale on the central meridian is constant but it is slightly less than the nominal value. -
General Index
General Index Italic page numbers refer to illustrations. Authors are listed in ical Index. Manuscripts, maps, and charts are usually listed by this index only when their ideas or works are discussed; full title and author; occasionally they are listed under the city and listings of works as cited in this volume are in the Bibliograph- institution in which they are held. CAbbas I, Shah, 47, 63, 65, 67, 409 on South Asian world maps, 393 and Kacba, 191 "Jahangir Embracing Shah (Abbas" Abywn (Abiyun) al-Batriq (Apion the in Kitab-i balJriye, 232-33, 278-79 (painting), 408, 410, 515 Patriarch), 26 in Kitab ~urat ai-arc!, 169 cAbd ai-Karim al-Mi~ri, 54, 65 Accuracy in Nuzhat al-mushtaq, 169 cAbd al-Rabman Efendi, 68 of Arabic measurements of length of on Piri Re)is's world map, 270, 271 cAbd al-Rabman ibn Burhan al-Maw~ili, 54 degree, 181 in Ptolemy's Geography, 169 cAbdolazlz ibn CAbdolgani el-Erzincani, 225 of Bharat Kala Bhavan globe, 397 al-Qazwlni's world maps, 144 Abdur Rahim, map by, 411, 412, 413 of al-BlrunI's calculation of Ghazna's on South Asian world maps, 393, 394, 400 Abraham ben Meir ibn Ezra, 60 longitude, 188 in view of world landmass as bird, 90-91 Abu, Mount, Rajasthan of al-BlrunI's celestial mapping, 37 in Walters Deniz atlast, pl.23 on Jain triptych, 460 of globes in paintings, 409 n.36 Agapius (Mabbub) religious map of, 482-83 of al-Idrisi's sectional maps, 163 Kitab al- ~nwan, 17 Abo al-cAbbas Abmad ibn Abi cAbdallah of Islamic celestial globes, 46-47 Agnese, Battista, 279, 280, 282, 282-83 Mu\:lammad of Kitab-i ba/Jriye, 231, 233 Agnicayana, 308-9, 309 Kitab al-durar wa-al-yawaqft fi 11m of map of north-central India, 421, 422 Agra, 378 n.145, 403, 436, 448, 476-77 al-ra~d wa-al-mawaqft (Book of of maps in Gentil's atlas of Mughal Agrawala, V. -
The History of Cartography, Volume Six: Cartography in the Twentieth Century
The AAG Review of Books ISSN: (Print) 2325-548X (Online) Journal homepage: http://www.tandfonline.com/loi/rrob20 The History of Cartography, Volume Six: Cartography in the Twentieth Century Jörn Seemann To cite this article: Jörn Seemann (2016) The History of Cartography, Volume Six: Cartography in the Twentieth Century, The AAG Review of Books, 4:3, 159-161, DOI: 10.1080/2325548X.2016.1187504 To link to this article: https://doi.org/10.1080/2325548X.2016.1187504 Published online: 07 Jul 2016. Submit your article to this journal Article views: 312 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=rrob20 The AAG Review OF BOOKS The History of Cartography, Volume Six: Cartography in the Twentieth Century Mark Monmonier, ed. Chicago, document how all cultures of all his- IL: University of Chicago Press, torical periods represented the world 2015. 1,960 pp., set of 2 using maps” (Woodward 2001, 28). volumes, 805 color plates, What started as a chat on a relaxed 119 halftones, 242 line drawings, walk by these two authors in Devon, England, in May 1977 developed into 61 tables. $500.00 cloth (ISBN a monumental historia cartographica, 978-0-226-53469-5). a cartographic counterpart of Hum- boldt’s Kosmos. The project has not Reviewed by Jörn Seemann, been finished yet, as the volumes on Department of Geography, Ball the eighteenth and nineteenth cen- State University, Muncie, IN. tury are still in preparation, and will probably need a few more years to be published. -
From the Old Ages to Mercator
14 The World Image in Maps – From the Old Ages to Mercator Mirjanka Lechthaler Institute of Geoinformation and Cartography Vienna University of Technology, Austria Abstract Studying the Australian aborigines’ ‘dreamtime’ maps or engravings from Dutch cartographers of the 16 th century, one can lose oneself in their beauty. Casually, cartography is a kind of art. Visualization techniques, precision and compliance with reality are of main interest. The centuries of great expeditions led to today’s view and mapping of the world. This chapter gives an overview on the milestones in the history of cartography, from the old ages to Mercator’s map collections. Each map presented is a work of art, which acts as a substitute for its era, allowing us to re-live the circumstances at that time. 14.1 Introduction Long before people were able to write, maps have been used to visualise reality or fantasy. Their content in \ uenced how people saw the world. From studying maps conclusions can be drawn about how visualized regions are experienced, imagined, or meant to be perceived. Often this is in \ uenced by social and political objectives. Cartography is an essential instrument in mapping and therefore preserving cultural heritage. Map contents are expressed by means of graphical language. Only techniques changed – from cuneiform writing to modern digital techniques. From the begin- nings of cartography until now, this language remained similar: clearly perceptible graphics that represented real world objects. The chapter features the brief and concise history of the appearance and develop- ment of topographic representations from Mercator’s time (1512–1594), which was an important period for the development of cartography. -
History of Cartography by Trista L
Name Date History of Cartography By Trista L. Pollard Our view of the world has changed since 1500 years ago. The maps and globes we use today are very accurate. They show more details. You can see cities and countries. They show landforms and landmarks. Our maps now have a standard coordinate or grid system. This measurement system helps us to locate places on Earth. But what about the first maps? What are they like? How were they made? Let's take a journey into the history of cartography. Cartography is the science of making maps. Today's cartographers use computers and cameras to help make maps. This is called remote sensing. Cameras are placed or mounted on airplanes. These cameras take pictures of the Earth's surface. Satellites in space are also used for cartography. Mapmakers in the past had much less technology. They used observation and stories from sailors to make maps. Most early scientists believed the Earth was flat. Imagine sailing from your country and falling over a cliff! That's what people thought. They also thought Earth was a flat disc. The center of the disc was filled with people. The outer edges of the Earth were empty. A world map made as early as 500 B.C. showed a disc with two continents. These continents were Europe and Asia. Both were surrounded by an ocean. That makes sense! Most people only knew about their surrounding or immediate area. Geographers also found early maps of the Pacific Ocean. They were made by navigators from Polynesia or the Pacific Islands. -
Map Projections
Map Projections Chapter 4 Map Projections What is map projection? Why are map projections drawn? What are the different types of projections? Which projection is most suitably used for which area? In this chapter, we will seek the answers of such essential questions. MAP PROJECTION Map projection is the method of transferring the graticule of latitude and longitude on a plane surface. It can also be defined as the transformation of spherical network of parallels and meridians on a plane surface. As you know that, the earth on which we live in is not flat. It is geoid in shape like a sphere. A globe is the best model of the earth. Due to this property of the globe, the shape and sizes of the continents and oceans are accurately shown on it. It also shows the directions and distances very accurately. The globe is divided into various segments by the lines of latitude and longitude. The horizontal lines represent the parallels of latitude and the vertical lines represent the meridians of the longitude. The network of parallels and meridians is called graticule. This network facilitates drawing of maps. Drawing of the graticule on a flat surface is called projection. But a globe has many limitations. It is expensive. It can neither be carried everywhere easily nor can a minor detail be shown on it. Besides, on the globe the meridians are semi-circles and the parallels 35 are circles. When they are transferred on a plane surface, they become intersecting straight lines or curved lines. 2021-22 Practical Work in Geography NEED FOR MAP PROJECTION The need for a map projection mainly arises to have a detailed study of a 36 region, which is not possible to do from a globe. -
How to Determine Latitude and Longitude from Topographic Maps
Oregon Department of Environmental Quality HOW TO DETERMINE LATITUDE AND LONGITUDE FROM TOPOGRAPHIC MAPS Latitude is the distance north or south of the equator. 2. For each location, construct a small rectangle around Longitude is the distance east or west of the prime the point with fine pencil lines connecting the nearest meridian (Greenwich, England). Latitude and longitude 2-1/2′ or 5′ graticules. Graticules are intersections of are measured in seconds, minutes, and degrees: latitude and longitude lines that are marked on the map edge, and appear as black crosses at four points in ″ ′ 60 (seconds) = 1 (minute) the interior of the map. 60′ (minutes) = 1° (degree) 3. Read and record the latitude and longitude for the To determine the latitude and longitude of your facility, southeast corner of the small quadrangle drawn in step you will need a topographic map from United States two. The latitude and longitude are printed at the edges Geological Survey (USGS). of the map. How to Obtain USGS Maps: 4. To determine the increment of latitude above the latitude line recorded in step 3: USGS maps used for determining latitude and longitude • Position the map so that you face its west edge; may be obtained from the USGS distribution center. These maps are available in both the 7.5 minute and l5 • Place the ruler in approximately a north-south minute series. For maps of the United States, including alignment, with the “0” on the latitude line recorded Alaska, Hawaii, American Samoa, Guam, Puerto Rico, in step 3 and the edge intersecting the point. -
Geomatics Tech (GEMT) 1
Geomatics Tech (GEMT) 1 Geomatics Tech (GEMT) Courses GEMT 4400 Essentials of Surveying: 2 semester hours. Preparation for fundamentals of surveying exam. May not be used as a technical GEMT 2231 Survey Computations: 3 semester hours. elective. May be repeated once for a total of 4 credits. PREREQ: Senior in Units of measurement and conversions, check and adjustment of raw data, Geomatics, graduate or Civil Engineering Technology, Civil Engineering, or closure and adjustment of survey figures, calculations for missing elements of a industry experience. Graded S/U. F, S figure, working coordinates and coordinate geometry (COGO), intersections of straight lines and circles, instrument specifications and introduction to adjustment GEMT 4411 Geodesy: 3 semester hours. theory. S Introduces geometry of ellipsoid, reference coordinate systems, local geodetic coordinate system, reduction of observation to other geodetic values, precise GEMT 3310 Boundary Surveying Law: 3 semester hours. leveling and orthometric height, direct and inverse geodetic position computation Concept of boundaries, ownership, transfer, boundary law principles, and gravity field of earth. PREREQ: GEMT 3311 or permission of instructor. S presumptions, easements and reversions, sequential and simultaneous conveyances, case studies, Riparian and littoral rights, state laws, rules GEMT 4413 Land Information System: 3 semester hours. for practicing surveying, ALTA survey. PREREQ: GEMT junior status or Model of land information system, reference systems, data capture, structure, permission of instructor. S quality, and implementation of land information system. Student works on a case study and writes a final report. PREREQ: GEMT 2227 and MATH 1147 or GEMT 3311 Advanced Surveying: 3 semester hours. permission of instructor. D Discuss transverse mercator projection and state plane coordinates, spherical trigonometry and astronomical observation, and coordinate geometry GEMT 4415 Survey Office Practice: 3 semester hours. -
16 · Introduction to Southeast Asian Cartography
16 · Introduction to Southeast Asian Cartography JOSEPH E. SCHWARTZBERG For this history, Southeast Asia is defined as the portion trasts markedly with the situation respecting influences of mainland Asia to the south of China and between India from China, which appear to be present in many maps and Vietnam, together with that portion of insular Asia from Burma and Thailand. Regrettably, however, I am in which Malay peoples predominate (fig. 16.1). Hence aware of nothing in the literature that makes it clear when it comprises the whole of Burma (Myanmar), Thailand, and how Chinese cartographic concepts were transmit Laos, and Cambodia, an area within which Hinayana ted. (Theravada) Buddhism is the dominant faith, and the In the rest of this chapter I shall discuss first the state Malay world-Malaysia, most of Indonesia, Brunei, and of knowledge with respect to the indigenous cartography the Philippines-within which Islam and Christianity have of Southeast Asia and then the nature of the surviving come to be the leading religions. Vietnam is excluded corpus. The next chapter relates to cosmography, and because of its cultural affinity to China, an affinity that there I will treat both the dominant cosmographic ideas is strongly reflected in its rich cartographic heritage (see and their expression in two-dimensional maps and in chap. 12). other forms, including works of architecture and the lay Southeast Asia, as here defined, shows relatively little out of cities. Chapter 18 will be devoted mainly to ter unity with regard to the surviving corpus of its premodern restrial maps: topographic maps, route maps, town plans, indigenous maps. -
Scale in GIS: What You Need to Know for GIS
Scale in GIS: What You Need To Know for GIS Y WHAT IS SCALE? CARTOGRAPHIC SCALE Scale is the scale represents the relationship of the distance on Scale in a cartographic sense (1 inch = 1 mile) is a the map/data to the actual distance on the ground. remnant of vector cartography, but still has importance • Map detail is determined by the source scale of the data: the for us in a digital world. finer the scale, the more detail. • Source scale is the scale of the data source (i.e. aerial photo Common cartographic scales: or satellite image) from which data is digitized (into boundaries, roads, landcover, etc. in a GIS). • Topographic Maps • In a GIS, zooming in on a small scale map does not o 1:24,000 7.5” quads increase its level of accuracy or detail. o 1:63,360 15” quads • Rule of thumb: Match the appropriate scale to the level of o 1:100,000 quads detail required in the project. o 1:250,000 quads 1:500 1:1200 • World Maps o 1:2,000,000 – DCW • Shoreline o 1:20,000 o 1:70,000 Above, right. Comparing fine and coarse source scales shows how the • Aerial Photography level of detail in the data is o 1:40,000 NHAP/NAPP determined by the spatial scale of the o 1:12,000 – 4,000 custom aerial photography source data. SPATIAL SCALE GUIDELINES X Spatial scale involves grain & extent: 1. Pay attention to source scale of your spatial data. Grain: the size of your pixel & the smallest resolvable unit. -
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.