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Journal articles on the topic 'Map projection'
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1
Panigrahi, Narayan, and Cyan Subhra Mishra. "A Generic Method for Azimuthal Map Projection." Defence Science Journal 65, no. 5 (September 11, 2015): 390. http://dx.doi.org/10.14429/dsj.65.8598.
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Map projections are mathematical methods for projecting spherical coordinates in the form of (φ, λ) to the map coordinates in the form of (X,Y) in Cartesian reference frame. Numerous methods for map projection have been derived and are being used for preparation of cartographic products. These map projections take into account specific position of the viewer on the datum surface for derivation of the map projections. A generic method for azimuthal map projection where the position of the viewer can be taken at an arbitrary point on the datum surface is derived. Using this generic method all the specific azimuthal map projections can be derived.
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Kessler, Fritz. "Map Projection Education in General Cartography Textbooks: A Content Analysis." Cartographic Perspectives, no. 90 (August 16, 2018): 6–30. http://dx.doi.org/10.14714/cp90.1449.
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As developments in the field of map projections occur (e.g., the deriving of a new map projection), it would be reasonable to expect that those developments that are important from a teaching standpoint would be included in cartography textbooks. However, researchers have not examined whether map projection material presented in cartography textbooks is keeping pace with developments in the field and whether that material is important for cartography students to learn. To provide such an assessment, I present the results of a content analysis of projection material discussed in 24 cartography textbooks published during the twentieth and early twenty-first centuries. Results suggest that some material, such as projection properties, was discussed in all textbooks across the study period. Other material, such as methods used to illustrate distortion patterns, and the importance of datums, was either inconsistently presented or rarely mentioned. Comparing recent developments in projections to the results of the content analysis, I offer three recommendations that future cartography textbooks should follow when considering what projection material is important. First, textbooks should discuss the importance that defining a coordinate system has in the digital environment. Second, textbooks should summarize the results from experimental studies that provide insights into how map readers understand projections and how to choose appropriate map projections. Third, textbooks should review the impacts of technology on projections, such as the web Mercator projection, programming languages, and the challenges of projecting raster data.
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Kerkovits, Krisztián. "Polyazimuthal Map Projections." Kartografija i geoinformacije 18, no. 32 (December 15, 2019): 18–32. http://dx.doi.org/10.32909/kg.18.32.2.
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A polyazimuthal map projection is a mapping that represents parallels as non-concentric full circles on the plane. Polyazimuthal mappings are almost never mentioned in the literature dealing with map projections. However, these projections are flexible; their distortion characteristics are highly mutable. This paper expands the theory of polyazimuthal map projections. Furthermore, this study also shows the derivation for variants of this projection family (e. g. equal-area, orthogonal). The article concludes with some practical applications in the field of low-distortion map projections to demonstrate their advantages.
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Lapaine, Miljenko. "From Conic to Cylindrical Map Projections." Geodetski vestnik 67, no. 03 (2023): 363–73. http://dx.doi.org/10.15292/geodetski-vestnik.2023.03.363-373.
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In books and textbooks on map projections, cylindrical, conic and azimuthal projections are usually considered separately. It is sometimes mentioned that cylindrical and azimuthal projections can be interpreted as limiting cases of conic, but this is rarely proven. The goal of this article is to show in a rigorous and systematic way how to generally approach solving the problem of transition from a conic to a corresponding cylindrical projection. This article points to the fact that J. H. Lambert showed as early as 1772 that a conformal cylindrical projection is created from a conformal conic projection. Following his idea, this paper shows that not only conformal, but also equal-area and equidistant cylindrical projections can be derived from corresponding conic map projections. Although it seems that the paper deals with quite well known and intuitive property of conic projections, it will also show that the transition from the conic to the corresponding cylindrical projection is not always possible.
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Okonek, Christian, and Andrei Teleman. "A wall-crossing formula for degrees of Real central projections." International Journal of Mathematics 25, no. 04 (April 2014): 1450038. http://dx.doi.org/10.1142/s0129167x14500384.
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The main result is a wall-crossing formula for central projections defined on submanifolds of a Real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to Real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a ℤ-valued degree map in a coherent way. We end the article with several examples, e.g. the pole placement map associated with a quotient, the Wronski map, and a new version of the Real subspace problem.
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Rees, W. G. "A new bipolar map projection." Polar Record 41, no. 3 (July 2005): 215–22. http://dx.doi.org/10.1017/s0032247405004614.
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This paper discusses map projections suitable for representing the whole of the Earth's surface while drawing particular attention to the polar regions, and proposes a new projection. The projection is a latitudinally distorted variant of the transverse Mollweide projection, relative to which it roughly doubles the linear scale and trebles the areal coverage of the polar regions. It was adopted by the Scott Polar Research Institute in 2005.
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Lapaine, Miljenko, and Nedjeljko Frančula. "Polar and Equatorial Aspects of Map Projections?" Proceedings of the ICA 2 (July 10, 2019): 1–6. http://dx.doi.org/10.5194/ica-proc-2-71-2019.
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<p><strong>Abstract.</strong> There is no standard or generally accepted terminology of aspect in the theory of map projections. The term is probably derived from the concept that a graticule is produced by perspective projection of the meridians and parallels on a sphere onto a developable surface. Developable surfaces are widely accepted, and it is almost impossible to find a publication that deals with map projections in general and without developable surfaces story. If found, it usually classifies projections as cylindrical, conical and azimuthal, and applies developable surfaces to define the projection aspect. This paper explains why applying developable surfaces in the interpretation of map projections is not recommended, nor defining the aspect of all projections by the position of a midpoint as polar, equatorial, or oblique. In fact, defining a projection aspect this way is invalid in general, and obscures the fact that the aspect depends on the class to which a particular map projection belongs.</p>
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Lapaine, Miljenko. "Map Projection Article on Wikipedia." Advances in Cartography and GIScience of the ICA 1 (July 3, 2019): 1–8. http://dx.doi.org/10.5194/ica-adv-1-10-2019.
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<p><strong>Abstract.</strong> People often look up information on Wikipedia and generally consider that information credible. The present paper investigates the article Map projection in the English Wikipedia. In essence, map projections are based on mathematical formulas, which is why the author proposes a mathematical approach to them. Weaknesses in the Wikipedia article Map projection are indicated, hoping it is going to be improved in the near future.</p>
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Strebe, Daniel. "Given the problem of projection, are heat maps an oxymoron?" Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-352-2019.
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<p><strong>Abstract.</strong> With the proliferation of data analysis and visualization tools, we see more and more heat maps. But should we? Are such displays meaningful? At large scales, heat maps need not be controversial (though common tools can blight even simple cases). But what about small-scale maps? Is anyone thinking about the effects of projection on heat maps? How do map projections change the semantics of heat maps? What projections permit meaningful heat maps? How should heat maps be calculated in the presence of a map projection? We explore these problems and questions in this presentation to offer critique and advice.</p><p>For the purposes of this discussion, a heat map is a representation of the density or magnitude of a spatial phenomenon on two dimensions, treating the density or magnitude as a continuous measure whether or not the underlying phenomenon is continuous. If the data are too sparse in the presentation space, then the fiction of continuity ought to be avoided; a heat map would not be an appropriate visualization. While real world examples of heat maps that violate this principle are easy to find, we take the principle for granted and do not elaborate further here.</p><p>Unfortunately, there are several other ways to construct ineffective heat maps. One of the primary offenses is to ignore the effect of map projection on the presentation of density. It should be clear that a projection whose area measure varies widely across the presentation space necessarily distorts density. If the heat map is a presentation of density &ndash; which most are &ndash; then poor choice of projection would contradict the purpose of a heat map. The result would be a blatant fiction. Surprisingly, the Mercator projection often can be found in small scale heat maps, for the reason that the projection is common, is the default in many sets of tooling, and is sometimes the only projection available with the set of map construction tools. And yet, as far as density variation goes, a worse case than Mercator cannot be found among common projections.</p><p>Even if density remains constant across the map, a poor heat map could be generated if the analysis for the heat map mixes phenomenon space, which is geographic, with projected space, which is not. Common tools commit this fallacy. The result is that a phenomenon whose density diminishes radially (for example) from a hot point might show as concentric circles of decreasing intensity on the projected map, whereas we would expect elongations of the heat field in accordance with the projection’s distortion metric.</p><p>We conclude that, while it is possible to construct responsible heat maps of geographic data, there are several pitfalls. Among these pitfalls, we find that common tools conspire to assist in the presentation of fiction instead of fact.</p>
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Yildirim, Faruk, and Fatih Kadi. "Proposed single-zone map projection system for Turkey." Reports on Geodesy and Geoinformatics 112, no. 1 (December 1, 2021): 35–45. http://dx.doi.org/10.2478/rgg-2021-0006.
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Abstract The coordinate base of the maps or sheets produced is the Universal Transversal Mercator (UTM) conformal projection, and it is not possible to work in a single coordinate system in Turkey. Therefore, a transition from UTM to other conformal projections is required. For the countries extending in an east–west UTM zone width like Turkey, composite projection (CP), a double standard paralleling Lambert Conformal Conic (LCC) and double map projections (DP) are used widely. However, this process causes increase in working load and processing errors by users. This study aims to determine a common projection system that can be used in the whole country. In this context, a composite projection from UTM and LCC projection has been defined for the first time. According to the results obtained, map projection CP with the least distortion values in both east–west and north–south directions has been chosen. With the CP selection, a single coordinate system has been determined for medium- and large-scale maps. Projection correction formulas, scale factor and false origin have been determined for map coordinates in CP. These distortions are obtained with a difference of less than 1 cm for 1 km long sides and less than 0.003″ for the azimuth value of this side, when the correction formulas are used.
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DA ROCHA, RONALDO DOS SANTOS. "Definição de um Sistema de Projeção Cartográfica para Mapeamento Urbano no Estado do Rio Grande do Sul." Pesquisas em Geociências 23, no. 1-2 (December 31, 1996): 25. http://dx.doi.org/10.22456/1807-9806.21223.
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This work studies the use of map projections in large scale mapping to provide support for a Land Information System. For this purpose, evaluations of the map projections commonly used in France, Switzerland, USA and Brazil are presented. The adequate precision to record property lines in a cadastral survey is identified and then compared to the linear distortions inherent to the map projections used in Brazil. Based upon these discrepancies, an optimum projection was developed to be used in large scale cartography in the State of Rio Grande do SuI. The expressions to transform geographic coordinates into projection coordinates are also presented. Several tests have been performed and the results are portrayed on a comparative chart showing the values of geodectics, plane distance on the UTM projection and plane distance on the above mentioned projection. The identified projection presents linear distortions lower than the established precision for property delimitation, corroborating the validity of its use in a Land Information System.
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Heitzler, Magnus, Hans-Rudolf Bär, Roland Schenkel, and Lorenz Hurni. "The Light Source Metaphor Revisited—Bringing an Old Concept for Teaching Map Projections to the Modern Web." ISPRS International Journal of Geo-Information 8, no. 4 (March 28, 2019): 162. http://dx.doi.org/10.3390/ijgi8040162.
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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.
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Lapaine, Miljenko, and Nedjeljko Frančula. "Map Projections Classification." Geographies 2, no. 2 (May 29, 2022): 274–85. http://dx.doi.org/10.3390/geographies2020019.
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Many books, textbooks and papers have been published in which the classification of map projections is based on auxiliary (developable) surfaces and projections are divided into conic, cylindrical and azimuthal projections. We argue that such a classification of map projections is unacceptable and give many reasons for that. Many authors wrote in more detail about the classification of map projections, and our intention is to give a new refined and rectified insight into the classification of map projections. Our approach can be included in map projection publications of general and thematic cartography. Doing this, misconceptions and unnecessary insistence on conceptuality instead of reality will be avoided.
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Ledermann, Florian. "Classifying Cartographic Projections Based on Dynamic Analysis of Program Code." Abstracts of the ICA 2 (October 9, 2020): 1. http://dx.doi.org/10.5194/ica-abs-2-38-2020.
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Abstract. Analyzing a given map to identify its projection and other geometrical properties has long been an important aspect of cartographic analysis. If explicit information about the projection used in a particular map is not available, the properties of the cartographic transformation can sometimes be reconstructed from the map image. However, such a process of projection analysis requires significant manual labor and oversight.For digital maps, we usually expect the projection from geographic space to map space to have been calculated by a computer program. Such a program can be expected to contain the implementation of the mathematical rules of the projection and subsequent coordinate transformations such as translation and scaling. The program code, therefore, contains information that would allow an analyst to reliably identify map projections and other geometrical transformations applied to the input data.In the case of interactive online maps, the code generating the map is in fact delivered to the map user and could be used for cartographic analysis. The core idea of our novel method proposed for map analysis is to apply reverse engineering techniques on the code implementing the cartographic transformations in order to retrieve the properties of the applied map projection. However, automatic reasoning about computer code by way of static analysis (analyzing the source code without running it) is provably limited – for example, the code delivered to the map user may contain a whole library of different map projections, of which only a specific one may be actually used at runtime. Instead, we propose a dynamic analysis approach to observe and monitor the operations performed by the code as the program runs, and to retrieve the mathematical operations that have been used to calculate the coordinates of every graphical element on the map.The presented method produces, for every graphical element of the map, a transformation graph consisting of low-level mathematical operations. Cartographic projections can be identified as distinctive patterns in the transformation graph, and can be distinguished in a fully automatic way by matching a set of predefined patterns against a particular graph.Projections vary widely in their arithmetic structure, and therefore by the structure of the corresponding transformation graphs extracted from program code. Some projections can be computed directly using continuous equations involving trigonometric functions. Other projections involve solving nonlinear equations, which need to be solved by approximation. Composite projections use different projections depending on some threshold value. Yet other projections, such as the Robinson projection, define a table of predefined values, between which interpolation is used etc.. In each of these cases, we expect to find the operations corresponding to the mathematical structure of the projection in the transformation graph extracted by the presented method.For verifying the method, we have implemented the patterns of several well-known cartographic projections based on the literature and have used it on the transformation graphs extracted from a variety of sample programs. To ensure a diversity of implementations, we have evaluated programs using different and independent JavaScript implementations of projections, including the open source libraries D3.js, proj4js, Leaflet, OpenLayers, and informal implementations of example programs found online. For these case studies, we could successfully identify many projections based on identifying patterns in the transformation graph in a fully automated, unsupervised manner.In the future, the proposed method may be further developed for many innovative application scenarios, such as building a “cartographic search engine” or constructing novel tools for semi-automatic cartographic analysis and review.
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Usery, E. Lynn. "Semantically Enabling Map Projections Knowledge." Kartografija i geoinformacije 19, no. 33 (June 30, 2020): 66–77. http://dx.doi.org/10.32909/kg.19.33.5.
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Map projections are an area of cartography with a firm mathematical foundation for their creation and display providing a basis for a knowledge representation. Using only variations on a single equation set, an infinite number of projections can be created, but less than 100 are in active use. Because each projection preserves specific characteristics, such as area, angles, global look, or a compromise of properties, classifications of map projections have been developed to aid in knowledge representation. These classifications are used for decision-making. They help select the correct projection for the map use. They assist users with determining the correct orientation, standard parallels and meridians. The classifications also inform the user how to adjust the selection based on size, extent, and latitude. Semantics can be used to automate map projections knowledge into a knowledge base that can be accessed by humans and machines. This work details a semantic representation of map projections knowledge and provides a simple example of a use case that exploits the knowledge base.
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Pędzich, Paweł. "Image of the World on polyhedral maps and globes." Polish Cartographical Review 48, no. 4 (December 1, 2016): 197–210. http://dx.doi.org/10.1515/pcr-2016-0014.
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Abstract Application of polyhedrons as image surface in cartographic projections has a tradition of more than 200 years. The first maps relying on polyhedrons appeared in the 19th century. One of the first maps which based on an original polyhedral projection using a regular octahedron was constructed by the Californian architect Bernard Cahill in 1909. Other well known polyhedral projections and maps included Buckminster Fuller’s projection and map into icosahedron from 1954 and S. Waterman’s projection into truncated octahedron from 1996, which resulted in the “butterfly” map. Polyhedrons as image surface have the advantage of allowing a continuous image of continents of the Earth with low projection distortion. Such maps can be used for many purposes, such as presentation of tectonic plates or geographic discoveries. The article presents most well known polyhedral maps, describes cartographic projections applied in their preparation, as well as contemporary examples of polyhedral maps. The method of preparation of a polyhedral map and a virtual polyhedral globe is also presented.
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Lapaine, Miljenko, and Nedjeljko Frančula. "Map projection aspects." International Journal of Cartography 2, no. 1 (January 2, 2016): 38–58. http://dx.doi.org/10.1080/23729333.2016.1184554.
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Usery, E. Lynn. "A Semantic Representation of Map Projections Knowledge." Abstracts of the ICA 1 (July 19, 2019): 1. http://dx.doi.org/10.5194/ica-abs-1-376-2019.
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<p><strong>Abstract.</strong> A body of knowledge for cartography requires representing knowledge of the specific sub topics in the field. Map projections is a fundamental part of the knowledge base for cartography and a wealth of material exists on knowledge of map projections. Semantic organization of such knowledge is of primary importance to the access and use of map projections knowledge. This project builds a semantic representation for the fundamental parts of map projection knowledge. The semantics capture the concepts and relations between these concepts providing the user an easy method to access the knowledge and apply it to specific problems. The semantics represent classes of projections and the properties associated with those classes as well as the appropriate use. Such a representation can be accessed by humans or machines to arrive at appropriate selection and use of map projection theory.</p>
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Lapon, Lieselot, Kristien Ooms, and Philippe De Maeyer. "The Influence of Map Projections on People’s Global-Scale Cognitive Map: A Worldwide Study." ISPRS International Journal of Geo-Information 9, no. 4 (March 26, 2020): 196. http://dx.doi.org/10.3390/ijgi9040196.
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Map projections are required to represent the globe on a flat surface, which always results in distorted representations of the globe. Accordingly, the world maps we observe in daily life contexts, such as on news sites, in news bulletins, on social media, in educational textbooks or atlases, are distorted images of the world. The question raises if regular contact with those representations of the world deforms people’s global-scale cognitive map. To analyze people’s global-scale cognitive map and if it is influenced by map projections, a short playful test was developed that allowed participants to estimate the real land area of certain regions, countries, and continents. More than 130,000 people worldwide participated. This worldwide dataset was used to perform statistical analyses in order to obtain information on the extent that map projections influence the accuracy of people’s global-scale cognitive map. The results indicate that the accuracy differs with the map projection but not to the extent that one’s global-scale cognitive map is a reflection of a particular map projection.
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Jenny, Bernhard, Tom Patterson, and Lorenz Hurni. "Flex Projector–Interactive Software for Designing World Map Projections." Cartographic Perspectives, no. 59 (March 1, 2008): 12–27. http://dx.doi.org/10.14714/cp59.245.
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Flex Projector is a free, open-source, and cross-platform software application that allows cartographers to interactively design custom projections for small-scale world maps. It specializes in cylindrical, and pseudocylindrical projections, as well as polyconical projections with curved parallels. Giving meridians non-uniform spacing is an option for all classes of projections. The interface of Flex Projector enables cartographers to shape the projection graticule, and provides visual and numerical feedback to judge its distortion properties. The intended users of Flex Projector are those without specialized mathematical expertise, including practicing mapmakers and cartography students. The pages that follow discuss why the authors developed Flex Projector, give an overview of its features, and introduce two new map projections created by the authors with this new software: the A4 and the Natural Earth projection.
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Lapaine, М., E. L. Usery, and M. V. Nyrtsov. "To the 20 anniversary of ICA Commission on Map Projections of the International Cartographic Association (2003–2023)." Geodesy and Cartography 963, no. 9 (October 20, 2020): 44–52. http://dx.doi.org/10.22389/0016-7126-2020-963-9-44-52.
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The Commission on Map Projections (CoMP) of the International Cartographic Association (ICA) was chartered and began aсting in 2003. The Commission has been active in promoting and distributing map projections research, education, and knowledge through its individual members, conferences and workshops of the ICA. Among the developments of the CoMP there are published papers of the workshops, conference sessions at the International Cartographic Conferences, and other international conferences in cartography and geoinformation. The CoMP has developed and maintained a public website with tutorial information on map projections, published research, decision systems to help in projection selection, news and announcements of the events, and an archive of the Commission’s activities. Among the publications of the CoMP there are research papers, conference proceedings, book chapters, and a book on Choosing a Map Projection. The CoMP are going to continue research and education activities, workshops, conferences, and publications to advance map projections with the 2019 to 2023 term.
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Kerkovits, Krisztián. "A Low-Distortion Map of the World Ocean Without Discontinuities." Kartografija i geoinformacije 21 (January 3, 2023): 80–91. http://dx.doi.org/10.32909/kg.21.si.6.
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Ocean maps are rarely in the scope of current studies on minimum-distortion map projec-tions. This study aims to create an uninterrupted map projection to display planet Earth as the Blue Planet: the aspect of the projection is rotated into the middle of the water surface; favourable map distortions are optimized numerically across the World Ocean. The paper starts with a short overview of existing similar projections. In the next pages, the reader may find the detailed description on the development of the new mapping. The paper concludes with maps and distortion analysis in the proposed projection and thoughts about its potential usefulness.
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Intzidou, Georgia, Nikos Lambrinos, Christos Tourtouras, and Fani Seroglou. "Metadata: A pedagogical tool for the teaching of map projections in Elementary School." European Journal of Geography 12, no. 3 (November 9, 2021): 56–69. http://dx.doi.org/10.48088/ejg.g.int.12.3.56.69.
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Digital interactive maps include a set of metadata, which show the purpose the user can use the map. Metadata in digital interactive world maps inform users about important information, such as the map projection. This research examines whether the educational and teaching use of the metadata of digital interactive maps construct a tool in the approach to the issue of map projection in Elementary School. The research was carried out in 17 Elementary Schools of Thessaloniki, Greece, where 6th-grade students (Ν = 655) were engaged in a series of activities related to metadata and map projections. ArcGIS Online was used as a didactic tool. Results showed that metadata of digital interactive maps have a great pedagogical value. The identification of the different information in the metadata, i.e., the map projection, and the students’ decision of what they can and cannot study with each map, is an important finding regarding their educational relevance.
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Lapon, Lieselot, Philippe De Maeyer, Nina Vanhaeren, Sarah Battersby, and Kristien Ooms. "Evaluating Young People’s Area Estimation of Countries and Continents." ISPRS International Journal of Geo-Information 8, no. 3 (March 2, 2019): 125. http://dx.doi.org/10.3390/ijgi8030125.
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For decades, cartographers and cognitive scientists have speculated about the influence of map projections on mental representations of the world. The development of Web 2.0 and web mapping services at the beginning of the 21st century—such as Google Maps, OpenStreetMap, and Baidu Map—led to an enormous spread of cartographic data, which is available to every Internet user. Nevertheless, the cartographic properties of these map services, and, in particular, the selected map projection or the Web Mercator projection, are questionable. The goal of this study is to investigate if the global-scale mental map of young people has been influenced by the increasing availability of web maps and the Web Mercator projection. An application was developed that allowed participants of Belgium and the US to scale the land area of certain countries and continents compared to Europe or the conterminous United States. The results show that the participants’ estimation of the actual land area is quite accurate. Moreover, an indication of the existence of a Mercator effect could not be discovered. To conclude, the young people’s mental map of the world does not appear to be influenced by a specific map projection but by personal characteristics. These elements are varied and require further analysis.
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Grieger, B. "Quincuncial adaptive closed Kohonen (QuACK) map for the irregularly shaped comet 67P/Churyumov-Gerasimenko." Astronomy & Astrophysics 630 (September 20, 2019): A1. http://dx.doi.org/10.1051/0004-6361/201834841.
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Context. Standard global map projections cannot display the complete surface of a highly irregular body such as the Rosetta target comet 67P/Churyumov-Gerasimenko because different points on the surface can have the same longitude and latitude. Aims. We present a concept of generalized longitudes and latitudes that allows us to display the complete comet in generalized versions of any standard map projection. Methods. A self-organizing Kohonen map can be used to sample the surface of any 3D shape, but the unfolded map misses some area beyond its edges. Here, we combine two square grids into an inherently closed structure that really maps the complete surface of the comet. Beyond this, the closed map is topologically equivalent to the Peirce quincuncial projection of the world, which enables the definition of generalized longitudes and latitudes. Results. While the generalized version of any map projection does not exactly share the properties of the original, such as preservation of area or shape, it behaves very similar. In particular, the generalized version of the quincuncial projection behaves very well over most of the surface area and shares the tessellation properties with its original. Conclusions. The quincuncial adaptive closed Kohonen (QuACK) map and the concept of generalized longitudes and latitudes provide means for global maps of arbitrarily irregular shapes.
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Calvert, Philip. "Map projection home page." Reference Reviews 14, no. 4 (April 2000): 37. http://dx.doi.org/10.1108/rr.2000.14.4.37.210.
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Krisztián, Kerkovits. "Secant Cylinders Are Evil—A Case Study on the Standard Lines of the Universal Transverse Mercator and Universal Polar Stereographic Projections." ISPRS International Journal of Geo-Information 13, no. 2 (February 13, 2024): 56. http://dx.doi.org/10.3390/ijgi13020056.
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The literature usually calls downscaled versions of basic conformal map projections “secant”, referring to conceptual developable map surfaces that intersect the reference frame. However, recent studies pointed out on the examples of various mappings of the sphere that this model may lead to incorrect conclusions. In this study, we examine the paradigm of secant surfaces for two popular map projections of the ellipsoid, the UTM (Universal Transverse Mercator) and the UPS (Universal Polar Stereographic) projections. Results will show that ellipsoidal map projections can exhibit further anomalies. To support the shift to a paradigm avoiding developable map surfaces, this study recommends the new term reduced map projection with a proper and simple definition to be used instead of secant map projections.
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Pędzich, Paweł. "From cartography of the Universe to molecular cartography – the use of map projections." Polish Cartographical Review 47, no. 4 (December 1, 2015): 191–201. http://dx.doi.org/10.1515/pcr-2015-0014.
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Abstract Map projections are very important in the compilation of various types of maps and spatial databases. Geographical information systems provide their users with the significant opportunities in the choice of map projections, coordinate systems, their definitions and transitions between them. The role of map projection can be considered depending on an objective, for which a map has to be used, user of this map and a form of its publication. The Internet, mobile devices and GIS caused that the map projections are used for two main purposes: data visualization and performing of calculations and analyses. The role of map projections is still important, despite the changes occurring in cartography. The rules for the applications of map projections developed over the centuries are still valid. However, the new rules resulting from the new functions of map projections are also created. The aim of this article, that is the author’s overview of map projections, is to illustrate the broad spectrum of applications for the map projections.
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de Menezes, Paulo Márcio Leal, Kairo da Silva Santos, Miljenko Lapaine, José Gomes dos Santos, Manoel do Couto Fernandes, Francisco José Corrêa Martins, and Tainá Laeta. "Analiza kartografske projekcije karte Nova Lusitania." Kartografija i geoinformacije 20, no. 35 (June 30, 2021): 48–69. http://dx.doi.org/10.32909/kg.20.35.3.
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The map named Carta Geographica de Projecçaõ Espherica Orthogonal da Nova Lusitania ou America Portugueza e Estado do Brazil from 1798, together with its 1795 (?), 1797 and 1803 versions, is undoubtedly one of the cartographic monuments developed by Portuguese cartography from the late eighteenth century. Its organizer was the geographer, astronomer, and frigate captain Antonio Pires da Silva Pontes Leme, who relied on the work of 34 people, including astronomers, geographers, and engineers, who, although only mentioned in the 1798 version, contributed to the creation of all versions. All of them are similar in appearance, but differ in size, content, details, amount, and distribution of toponyms, which will be the subject of another paper. The greatest similarity, however, concerns the defined map projection. The objective of this paper is to analyse and present the possible hypotheses and conclusions about which map projection was adopted for all versions of Nova Lusitania, through the identification of characteristics that allowed to infer and prove the adopted projection. The applied methodology verified that in the bibliographic search, the information about the map structure is insufficient. An article presented by General Djalma Polli Coelho in October 1950 states that the projection suggested by its title, as orthogonal spherical, appeared to be the Sanson-Flamsteed equal-area projection. However, the expression Carta Geographica de Projecçaõ Espherica Orthogonal allows us to infer also the transverse orthographic projection. Through parameters defined for the two projections, it was possible to establish the comparative elements for a cartographic analysis, which would allow us to conclude and prove the structure adopted for the map, allowing to conclude if the adopted projection for the Nova Lusitania was an azimuthal orthographic equatorial projection, or a Sanson-Flamsteed, sinusoidal projection on the meridian 315°, defined west-east, (counterclockwise), from the El Hierro (Ferro) Island. This meridian is referenced approx. –62°39'46" off the Greenwich meridian.
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Šavrič, Bojan, Bernhard Jenny, and Helen Jenny. "Projection Wizard – An Online Map Projection Selection Tool." Cartographic Journal 53, no. 2 (April 2, 2016): 177–85. http://dx.doi.org/10.1080/00087041.2015.1131938.
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Lapaine, Miljenko. "Connection of Conic and Cylindrical Map Projections." ISPRS International Journal of Geo-Information 13, no. 4 (March 27, 2024): 113. http://dx.doi.org/10.3390/ijgi13040113.
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In previous papers that have dealt with cylindrical map projections as limiting cases of conical projections, standard or equidistant parallels were used in the derivations. This paper shows that this is not necessary and that it is sufficient to use parallels that preserve length. In addition, unlike other approaches, in this article the limiting cases of conic projections are derived in the most natural way, by deriving the equations of cylindrical projections from the equations of conic projections in a rectangular system in the projection plane using a mathematical concept of limits. It is shown that such an approach is possible, but not always, so it should be used carefully, or even better, avoided in teaching and studying map projections.
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Kerkovits, Krisztián, and Tünde Takáts. "Reference frame and map projection for irregular shaped celestial bodies." Abstracts of the ICA 2 (October 9, 2020): 1–2. http://dx.doi.org/10.5194/ica-abs-2-42-2020.
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Abstract. Recent advancements of technology resulted in greater knowledge of the Solar System and the need for mapping small celestial bodies significantly increased. However, creating a good map of such small objects is a big challenge for the cartographer: they are usually irregular shaped, the usual reference frames like the ellipsoid of revolution is inappropriate for their approximation.A method is presented to develop best-fitting irregular surfaces of revolution that can approximate any irregular celestial body. (Fig. 1.) Then a simple equal-area map projection is calculated to map this reference frame onto a plane. The shape of the resulting map in this projection resembles the shape of the original celestial body.The usefulness of the method is demonstrated on the example of the comet 67P/Churyumov-Gerasimenko. This comet has a highly irregular shape, which is hard to map. Previously used map projections for this comet include the simple cylindrical, which greatly distorts the surface and cannot depict the depressions of the object. Other maps used the combination of two triaxial ellipsoids as the reference frame, and the gained mapping had low distortion but at the expense of showing the tiny surface divided into 11 maps in different complicated map projections (Nyrtsov et. al., 2018). On the other hand, our mapping displays the comet in one single map with moderate distortion and the shape of the map frame suggests the original shape of the celestial body (Fig. 2. and 3.).
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Ábrahámová, Andrea, and Margita Vajsáblová. "A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method." Slovak Journal of Civil Engineering 30, no. 2 (June 1, 2022): 22–29. http://dx.doi.org/10.2478/sjce-2022-0011.
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Abstract The application of alternative mathematical methods in creating cartographic projections is an interesting factor, which affects the optimization of distortions and their distribution in the projected territory. This article presents the methodology for the creation and comparison of conformal cartographic projections formed by alternative mathematical methods of minimizing the integral criterion for scale distortion in Slovakia. The creation of the variational projection is based on the Airy-Kavraiskii criterion of evaluating the projection on the displayed area by solving Laplace's equation. The second projection is created by solving Poisson's equation using Ritz's method. Our analysis showed that the variational projection of Slovakia achieves more satisfactory distortion values than the cartographic projection created using Ritz's method. The advantage of Ritz's method is that it is possible to choose a boundary condition for a predefined undistorted convex closed curve. In this paper, we have also derived specific members of the map equations for cartographic projection based on solving Poisson's equation by Ritz's method.
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Borisov, Mirko, Miro Govedarica, and Vladimir Petrovic. "Cartographic conic projections and their appliance in national cartography." Glasnik Srpskog geografskog drustva 91, no. 4 (2011): 183–204. http://dx.doi.org/10.2298/gsgd1104183b.
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This paper is dedicated to the mapping of conic projections and their appliance in producing maps of our state cartography. So far they were often applied, and will be used precisely coned, polyconed and modified polyconed projections for the official mapping (1:500 000, 1:750 000, 1:1000 000 and 1:1500 000). In particular, they cartographic conical projection at a scale of 1:1000 000 were taken into consideration. Those are the Lambert conformal conical projection with two standard parallels and the Modified polyconic projections. In addition to these cartographic conical projections, is described Boneo`s pseudoconic equivalent projections. This is one of the cartographic conical map projection that is commonly used in the preparation of thematic maps as well as for atlas editions of geographic maps both in Serbia and abroad.
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Jap, B. K., H. L. Li, and S. Lee. "3-D Structure of a Water Channel At ˜6Å Resolution as Determined by Electron Crystallography." Microscopy and Microanalysis 3, S2 (August 1997): 1031–32. http://dx.doi.org/10.1017/s1431927600012046.
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Aquaporin-1 (AQP1) is a class of water channels within the aquaporin superfamily. These channel proteins have been found in a wide variety of tissues such as kidney, lung, eye secretory gland and intestinal epithelium as well as in vacuolar membranes of plants. The major function of these channel proteins is to transport water exclusively into and out of cells. Based on amino acid sequence, it has been predicted that aquaporins contain six lipid bilayer-spanning a-helices. Models for the molecular folding of AQP1 containing six and four transmembrane a-helices have been proposed previously. Our earlier projection map at 3.5Å resolution revealed eight high density peaks which we interpreted as the projections of seven transmembrane α-helices and an eighth possibly transmembrane segment. The juxtaposition of structures seen in the projection map prevented us from unambiguously determining the exact number of transmembrane helices based on the projection map alone. We report here the three-dimensional (3-D) map at ˜6 Å resolution as determined by electron crystallography.
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Szatmári, Daniel. "Optimization Of Conformal Cartographic Projections For The Slovak Republic According To Chebyshev’s Theorem." Slovak Journal of Civil Engineering 23, no. 4 (December 1, 2015): 19–24. http://dx.doi.org/10.1515/sjce-2015-0019.
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Abstract Disadvantages of the currently used Křovák’s map projection in the Slovak Republic, such as large scale distortion, became evident after the division of Czechoslovakia. The aim of this paper is to show the results of the optimization of cartographic projections using Chebyshev’s theorem for conformal projections and its application to the territory of the Slovak Republic. The calculus used, the scale distortions achieved and their comparison with the scale distortions of currently used map projections will be demonstrated.
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HISHIYAMA, Takehide. "Questions about the Map Projection of Inoh's Map." Journal of Geography (Chigaku Zasshi) 129, no. 2 (April 25, 2020): 303–14. http://dx.doi.org/10.5026/jgeography.129.303.
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Patterson, Tom, Bojan Šavrič, and Bernhard Jenny. "Introducing the Patterson Cylindrical Projection." Cartographic Perspectives, no. 78 (May 6, 2015): 77–81. http://dx.doi.org/10.14714/cp78.1270.
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The Patterson cylindrical, a new projection designed for general-purpose mapmaking, is an alternative to other cylindrical projections. It is positioned between the Plate Carrée projection, which has a 1:2 aspect ratio, and the Miller 1 projection, which excessively exaggerates the size of polar areas. The Patterson cylindrical balances polar exaggeration against maintaining the familiar shape of continents and has a compact height-to-width aspect ratio. Creating the projection started with a graphical template made in Flex Projector that served as a guide for developing the polynomial equations, which are introduced in this article. The reference source code is available in the Java Map Projection Library.
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Nishi, Hayato, and Yasushi Asami. "Bayesian Geographical Multi-Dimensional Scaling." Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-271-2019.
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<p><strong>Abstract.</strong> Multi-dimensional scaling (MDS) is a popular method of visualizing the similarity of individuals in a dataset. When dissimilarities between individuals in a dataset are measured, MDS projects these individuals into the (typically two- or three-dimensional) map. In this map, because similar individuals are projected to be close to one another, distances between individuals correspond to their dissimilarities. In other words, MDS makes a similarity map of a dataset.</p><p>Some of the dissimilarities and distances have a strong relation to the geographical location. For example, time distances are similar to geographical distances, and regional features will be similar if the regions are close together. Therefore, it will be useful to compare the MDS projection and geographical locations. However, because MDS projection is not concerned with the rotation, parallel translation, and similarity expansion, it might be difficult to compare the projection to the actual geographical locations. When geographically related similarities are visualized, projected locations should be bound to the geographical locations.</p><p>In this article, we propose Bayesian Geographical Multidimensional Scaling (BGMDS), in which geographical restrictions of projections are given from a statistical point of view. BGMDS gives not only geographically bound projections, but also incorporates the uncertainty of the projections.</p>
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DeLucia, Alan A., and John P. Snyder. "An Innovative World Map Projection." American Cartographer 13, no. 2 (January 1986): 165–67. http://dx.doi.org/10.1559/152304086783900112.
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Šavrič, Bojan, Tom Patterson, and Bernhard Jenny. "The Equal Earth map projection." International Journal of Geographical Information Science 33, no. 3 (August 7, 2018): 454–65. http://dx.doi.org/10.1080/13658816.2018.1504949.
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Alashaikh, Ahmad H., Hasan M. Bilani, and Abdullah S. Alsalman. "Modified perspective cylindrical map projection." Arabian Journal of Geosciences 7, no. 4 (February 20, 2013): 1559–65. http://dx.doi.org/10.1007/s12517-013-0888-3.
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Baker, J. G. P. "The “Dinomic” World Map Projection." Cartographic Journal 23, no. 1 (June 1986): 66–67. http://dx.doi.org/10.1179/caj.1986.23.1.66.
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Livieratos, Evangelos. "From Map Projection to Semiotics." Kartografija i geoinformacije 21 (January 3, 2023): 92–97. http://dx.doi.org/10.32909/kg.21.si.7.
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Umberto Eco’s admiration for Charles S. Peirce (1839-1914) for ... earning a living by drawing maps ... combined with the pleasure of knowledge given by the diving to the history of our cartographic discipline, reminded me of a relevant sixty-year-old text about the great scientist and authentic thinker – maybe the greatest of Logic of his time. It is based on unpublished (until then) manuscript material, in his collection of the same name in the Houghton Library at Harvard. The sixty-year-old mathematician Carolyn Eisele (1902−2000) – devoted scholar of Peirce’s work – wrote the text in the early 1960s; it was then published in the Proceedings of the American Philosophical Society. The subject of her text is the problem of cartographic projection. But what can a cartographic projection problem have to do with logic and its practical applications, which is the greatest challenge to Peirce’s thinking?
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Bayer, Tomáš, and Milada Kočandrlová. "Reconstruction of map projection, its inverse and re-projection." Applications of Mathematics 63, no. 4 (July 20, 2018): 455–81. http://dx.doi.org/10.21136/am.2018.0096-18.
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Dowdeswell, J. A., and A. P. R. Cooper. "Digital Mapping in Polar Regions from Landsat Photographic Products: A Case Study." Annals of Glaciology 8 (1986): 47–50. http://dx.doi.org/10.3189/s0260305500001129.
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Landsat photographic products on the Space Oblique Mercator (SOM) projection are used to construct a map of Nordaustlandet (Svalbard), of known accuracy. The map includes ice divides. Accurately enlarged Landsat images were digitized. Combined digitizer and operator errors were 64 m, at the enlargement scale. Fifteen ground control points rixed the two scenes. RMS errors in control point identification were <123 m. Geographical coordinates were extracted by: 1) converting digitizer coordinates to SOM cartesian coordinates and 2) transforming these coordinates to latitude and longitude. This map production method is applicable to any imagery of known projection. The digitally stored map may be plotted on a variety of map projections and scales. Two problems in image interpretation were: I) shadows obscuring detail on NNE-facing coasts and 2) summer snow cover obscuring parts of the terrestrial ice cap margins, The map is similar to an east coast map produced from Landsat computer compatible tapes. Differences between the Landsat map and a 1:50 000-scale aerial photograph were <100 m.
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Dowdeswell, J. A., and A. P. R. Cooper. "Digital Mapping in Polar Regions from Landsat Photographic Products: A Case Study." Annals of Glaciology 8 (1986): 47–50. http://dx.doi.org/10.1017/s0260305500001129.
Full textAbstract:
Landsat photographic products on the Space Oblique Mercator (SOM) projection are used to construct a map of Nordaustlandet (Svalbard), of known accuracy. The map includes ice divides. Accurately enlarged Landsat images were digitized. Combined digitizer and operator errors were 64 m, at the enlargement scale. Fifteen ground control points rixed the two scenes. RMS errors in control point identification were <123 m. Geographical coordinates were extracted by: 1) converting digitizer coordinates to SOM cartesian coordinates and 2) transforming these coordinates to latitude and longitude. This map production method is applicable to any imagery of known projection. The digitally stored map may be plotted on a variety of map projections and scales. Two problems in image interpretation were: I) shadows obscuring detail on NNE-facing coasts and 2) summer snow cover obscuring parts of the terrestrial ice cap margins, The map is similar to an east coast map produced from Landsat computer compatible tapes. Differences between the Landsat map and a 1:50 000-scale aerial photograph were <100 m.
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Schreck, Tobias, Tatiana von Landesberger, and Sebastian Bremm. "Techniques for Precision-Based Visual Analysis of Projected Data." Information Visualization 9, no. 3 (September 2010): 181–93. http://dx.doi.org/10.1057/ivs.2010.2.
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The analysis of high-dimensional data is an important, yet inherently difficult problem. Projection techniques such as Principal Component Analysis, Multi-dimensional Scaling and Self-Organizing Map can be used to map high-dimensional data to 2D display space. However, projections typically incur a loss in information. Often, uncertainty exists regarding the precision of the projection as compared with its original data characteristics. While the output quality of these projection techniques can be discussed in terms of aggregate numeric error values, visualization is often helpful for better understanding the projection results. We address the visual assessment of projection precision by an approach integrating an appropriately designed projection precision measure directly into the projection visualization. To this end, a flexible projection precision measure is defined that allows the user to balance the degree of locality at which the measure is evaluated. Several visual mappings are designed for integrating the precision measure into the projection visualization at various levels of abstraction. The techniques are implemented in an interactive system, including methods supporting the user in finding appropriate settings of relevant parameters. We demonstrate the usefulness of the approach for visual analysis of classified and unclassified high-dimensional data sets. We show how our interactive precision quality visualization system helps to examine the preservation of original data properties in projected space.
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Spur, M., V. Tourre, G. Moreau, and P. Le Callet. "VIRTUAL DATA SPHERE: INVERSE STEREOGRAPHIC PROJECTION FOR IMMERSIVE MULTI-PERSPECTIVE GEOVISUALIZATION." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-4-2022 (May 18, 2022): 235–42. http://dx.doi.org/10.5194/isprs-annals-v-4-2022-235-2022.
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Abstract. Immersive geospatial visualization finds increasing application for navigation, exploration, and analysis. Many such require the display of data at different scales, often in views with three-dimensional geometry. Multi-view solutions, such as focus+context, overview+detail, and distorted projections can show different scales at the same time, and help place an area of interest within its surroundings. By inverting the principle of stereographic projection – projecting spatial features from a map onto a virtual sphere which surrounds the viewer – we present a novel technique for immersive geospatial focus+context that aims to mitigate problems with existing solutions. This sphere can intersect the map, dividing it into two parts: the inside of the sphere, which stays unchanged, and the outside, which gets projected to the surface, resulting in an inversion of the lens metaphor by distorting the context instead of the focus. This detail-in-context visualization maximizes the amount of context that can be legibly shown by the smooth compression inherent to the stereographic projection, and by utilizing otherwise unused screen space in the sky. The projection method allows for easy control over the projection and distortion characteristics by varying only two main parameters – the sphere’s radius and its position. The omnidirectional nature of our system makes it particularly well-suited for immersive displays by accommodating typical immersive exploration and fully utilizing the additional visual space available. Applying our system to an urban environment, we were able to solicit positive reactions during feedback sessions with experts from urbanism.
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Snyder, John P. "How Practical Are Minimum-Error Map Projections?" Cartographic Perspectives, no. 17 (March 1, 1994): 3–9. http://dx.doi.org/10.14714/cp17.942.
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Ever since the Mercator projection gained wide acceptance for general geographic world maps, there have been attempts to replace it because of its serious area dis tortion. Most minimum-error projections, however, are difficult or nearly impossible to construct without a modern computer. Does this negate their use? The answer is probably yes if most users need to digitize maps or do their own programming of formulas, but no if the goal is to make the map easier for measurement of distance, area, and shape. We too often s till choose projections to suit pre-computer criteria involving ease of cons truction, rather than to meet the needs of the map user. This paper reviews the practicality of minimum-error map proj ections and illustrates a wide range of minimum-error projections.