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The Light Source Metaphor Revisited—Bringing an Old Concept for Teaching Map Projections to the Modern Web

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The Light Source Metaphor Revisited—Bringing an Old Concept for Teaching Map Projections to the Modern Web International Journal of Geo-Information Article The Light Source Metaphor Revisited—Bringing an Old Concept for Teaching Map Projections to the Modern Web Magnus Heitzler 1,* , Hans-Rudolf Bär 1, Roland Schenkel 2 and Lorenz Hurni 1 1 Institute of Cartography and Geoinformation, ETH Zurich, 8049 Zurich, Switzerland; [email protected] (H.-R.B.); [email protected] (L.H.) 2 ESRI Switzerland, 8005 Zurich, Switzerland; [email protected] * Correspondence: [email protected] Received: 28 February 2019; Accepted: 24 March 2019; Published: 28 March 2019 Abstract: Map projections are one of the foundations of geographic information science and cartography. An understanding of the different projection variants and properties is critical when creating maps or carrying out geospatial analyses. The common way of teaching map projections in text books makes use of the light source (or light bulb) metaphor, which draws a comparison between the construction of a map projection and the way light rays travel from the light source to the projection surface. Although conceptually plausible, such explanations were created for the static instructions in textbooks. Modern web technologies may provide a more comprehensive learning experience by allowing the student to interactively explore (in guided or unguided mode) the way map projections can be constructed following the light source metaphor. The implementation of this approach, however, is not trivial as it requires detailed knowledge of map projections and computer graphics. Therefore, this paper describes the underlying computational methods and presents a prototype as an example of how this concept can be applied in practice. The prototype will be integrated into the Geographic Information Technology Training Alliance (GITTA) platform to complement the lesson on map projections. Keywords: map projections; computer graphics; visualization; 3D; education; teaching; multimedia; open educational resources 1. Introduction Map projections are a key concept in cartography and geographic information science. Choosing an inappropriate map projection may cause severely flawed results when carrying out geospatial analyses (e.g., when buffering in an inappropriate projected coordinate system [1]) or may distort a map reader’s view on the world when exploring a thematic or topographic map. Hence, a thorough understanding of the construction process and map properties is important. Mapping software typically implements the projection process as a set of equations that can be applied to a point in geographic coordinates to obtain its projected coordinates. Examples for this approach can be found in kartograph.js [2], d3.js [3], or Flex Projector [4]. However, educational resources tend to follow a more figurative approach to explain the underlying geometrical meaning of the projection process. This construction process typically starts with a projection center that can be imagined as a light source (or light bulb) placed in the proximity of (or within) the globe and emitting light in all directions. In the simplest case, the light source has the shape of a point, but other geometries exist as well. Light rays pass through the globe, casting the colors at their intersection points on the globe’s surface onto the projection surface (usually a plane, cone or cylinder). ISPRS Int. J. Geo-Inf. 2019, 8, 162; doi:10.3390/ijgi8040162 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2019, 8, 162 2 of 10 ISPRS Int. J. Geo-Inf. 2019, 8, 162 2 of 10 Figure1 1 shows shows threethree examplesexamples ofof howhow mapmap projectionsprojections maymay bebe constructedconstructed thisthis way.way. FigureFigure1 A1A explains the construction of the gnomonic azimuthal projection by depicting light rays from the light source inin all directions (indicated(indicated byby arrows)arrows) toto hithit the projection plane.plane. The resulting map is depicted below, showingshowing distorteddistorted shapesshapes ofof landland areas.areas. Figure1 1BB depicts depictsthe theconstruction construction of ofthe thecentral centralconic conic projectionprojection byby indicatingindicating a projection conecone touchingtouching the globe with the resulting unrolled map shown below. Figure1 1CC intendsintends toto illustrateillustrate thethe didifferentfferent positionspositions ofof thethe parallels for the central cylindrical and the Mercator projection implying that an additionaladditional non-linear scaling is required to realize the desired projection.projection. ThereThere are are numerous numerous resources resources that that show show similar similar depictions, depictions, either either on the on web the (e.g.,web References(e.g., References [5,6]) [5,6]) or in printedor in printed textbooks textbooks (e.g., References(e.g., References [7,8]). [7,8]). Figure 1. ExamplesExamples for for educational educational resources resources following following the the light light source source metaphor metaphor when when explaining explaining map mapprojections: projections: (A) gnomonic (A) gnomonic azimuthal azimuthal projection ( projectionhttps://commons.wikimedia.org/wiki/File:Comparison (https://commons.wikimedia.org/wiki/File: Comparison_azimuthal_projections.svg_azimuthal_projections.svg, CC BY-SA 3.0,, CCaccessed BY-SA 15.02.2019); 3.0, accessed (B) central 15.02.2019); conic projection (B) central (Weisstein, conic projectionEric W. (Weisstein,“Conic EricProjection.” W. “Conic Projection.”From MathWorld—A From MathWorld—A Wolfram Wolfram Web Web Resource.Resource. http:http://mathworld.wolfram.com/ConicProjection.html,//mathworld.wolfram.com/ConicProjection.html ©, © 1999–20191999–2019 Wolfram Wolfram Research, Inc., accessedaccessed 15.03.2019);15.03.2019); ( C)) central central cylindrical cylindrical projection projection and and Mercator Mercator projection projection (https://commons.wikimedia.org/ (https://commons.wikimedia.org / wikiwiki/File:Mercator_and_central_cylindrical.p/File:Mercator_and_central_cylindrical.pngng, Public, Public Domain, Domain, accessed accessed 15.02.2019). 15.02.2019). These illustrations have several limitations. Firstl Firstly,y, each illustration shows only snapshots of the construction process. There is still considerableconsiderable mental work involved to understandunderstand thethe transitiontransition fromfrom thethe projectionprojection concept concept to to the the resulting resulting map. map. Secondly, Secondly, static static images images only only provide provide one one view view on theon constructionthe construction process. process. It is not It possibleis not possible to obtain dito ffobtainerent views different to get views a comprehensive to get a comprehensive understanding ofunderstanding the mapping of process. the mapping Thirdly, process. exploring Thirdly, diff erentexploring configurations different configurations of these objects of isthese not objects possible is asnot this possible would as require this would interactive require adjustments interactive ofadju thestments light source, of the projectionlight source, surface, projection basemap, surface, etc. Webasemap, argue thatetc. suchWe argue interactivity that such allows interactivity improving allows the understandingimproving the ofunderstanding how different of map how projections different relatemap projections to each other. relate The to each authors other. are The not authors aware of are any not interactive aware of any visualization interactive tool, visualization which allows tool, constructingwhich allows map constructing projections map following projections an implementation following an of theimplementation light source metaphor. of the light source metaphor.These limitations can be overcome if interactive visualization methods are provided. The computationalThese limitations concepts can be and overcome how they if caninteract be implementedive visualization to createmethods a fully are functionalprovided. webThe applicationcomputational are theconcepts main contributions and how they of this can paper. be im Theplemented concepts areto applicablecreate a fully for projections, functional which web canapplication be constructed are the by main simple contributions geometric means of this (i.e., pape mapr. The projections concepts that are can applicable be manually for constructedprojections, withwhich ruler can and be constructed compasses and by dosimple not requiregeometric the usemean ofs formulas) (i.e., map by projections using diff erentthat configurationscan be manually of theconstructed projection with surface ruler and and the compasses light source. and Furthermore, do not require the resultingthe use of map formulas) projections by using may bedifferent scaled inconfigurations a non-linear wayof the to approximateprojection surface variants and such th ase thelight Mercator source. projection.Furthermore, the resulting map projectionsIt is recommended may be scaled to tryin outa non-linear the prototype way showcasingto approximate the concepts variants described such as the in this Mercator paper directlyprojection. in the browser: https://gevian.github.io/GITTA-MP. Note that the prototype accessible at this URLIt may is recommended change in the futureto try asout new the versions prototype of theshowcasing prototype the are concepts released. described The prototype in this version paper describeddirectly in in the this browser: paper ishttps://gevian.github.io/GITTA available as a zip archive and as-MP. tag Note v1.0.0-light-source-metaphor that the prototype accessible at the at code this
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