scholarly journals Best cylindrical map projections according to the undesirability of angular and areal distortions

2021 ◽  
Vol 3 ◽  
pp. 1-5
Author(s):  
Krisztián Kerkovits
Keyword(s):  
Calculus Of Variations ◽  
Analytic Solution ◽  
Map Projection ◽  
Map Projections ◽  
Low Distortion

Abstract. Seeking low distortion maps, it is usual to assume that areal and angular distortions are equally undesirable on the map. However, this might not be the case for certain map thematics. Should angular distortions be a bit less preferred to areal distortions, maps of unbalanced distortions may be developed. In this paper, the known analytic solution for the best cylindrical map projection is extended to such more general requirements by utilizing calculus of variations. The overall distortion of the resulted mappings are calculated and compared to each other to explore the distortion characteristics of these intentionally unbalanced map projections.

scholarly journals Polyazimuthal Map Projections

2019 ◽  
Vol 18 (32) ◽  
pp. 18-32
Author(s):  
Krisztián Kerkovits
Keyword(s):  
Map Projection ◽  
Equal Area ◽  
Practical Applications ◽  
Map Projections ◽  
Low Distortion

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.

scholarly journals A Semantic Representation of Map Projections Knowledge

2019 ◽  
Vol 1 ◽  
pp. 1-1
Author(s):  
E. Lynn Usery
Keyword(s):  
Knowledge Base ◽  
Semantic Representation ◽  
Appropriate Use ◽  
Easy Method ◽  
Map Projection ◽  
Map Projections ◽  
Semantic Organization ◽  
Body Of Knowledge ◽  
Fundamental Part

<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>

scholarly journals Polar and Equatorial Aspects of Map Projections?

2019 ◽  
Vol 2 ◽  
pp. 1-6
Author(s):  
Miljenko Lapaine ◽  
Nedjeljko Frančula
Keyword(s):  
Perspective Projection ◽  
Developable Surface ◽  
Map Projection ◽  
Map Projections ◽  
Developable Surfaces

<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>

scholarly journals Reference frame and map projection for irregular shaped celestial bodies

2020 ◽  
Vol 2 ◽  
pp. 1-2
Author(s):  
Krisztián Kerkovits ◽  
Tünde Takáts
Keyword(s):  
Celestial Body ◽  
Reference Frame ◽  
Reference Frames ◽  
Surfaces Of Revolution ◽  
Map Projection ◽  
Map Projections ◽  
Ellipsoid Of Revolution ◽  
Celestial Bodies ◽  
Best Fitting ◽  
Comet 67P

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.).

scholarly journals Map Projection Article on Wikipedia

2019 ◽  
Vol 1 ◽  
pp. 1-8
Author(s):  
Miljenko Lapaine
Keyword(s):  
Mathematical Approach ◽  
Map Projection ◽  
Map Projections ◽  
Mathematical Formulas ◽  
Near Future

<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>

A Generic Method for Azimuthal Map Projection

2015 ◽  
Vol 65 (5) ◽  
pp. 390
Author(s):  
Narayan Panigrahi ◽  
Cyan Subhra Mishra
Keyword(s):  
Reference Frame ◽  
Arbitrary Point ◽  
Spherical Coordinates ◽  
Mathematical Methods ◽  
Map Projection ◽  
Map Projections ◽  
Specific Position

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.

scholarly journals The Influence of Map Projections on People’s Global-Scale Cognitive Map: A Worldwide Study

2020 ◽  
Vol 9 (4) ◽  
pp. 196
Author(s):  
Lieselot Lapon ◽  
Kristien Ooms ◽  
Philippe De Maeyer
Keyword(s):  
Social Media ◽  
Flat Surface ◽  
Daily Life ◽  
Global Scale ◽  
Cognitive Map ◽  
Land Area ◽  
Map Projection ◽  
Map Projections ◽  
The World ◽  
Regular Contact

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.

scholarly journals Optimization Of Conformal Cartographic Projections For The Slovak Republic According To Chebyshev’s Theorem

2015 ◽  
Vol 23 (4) ◽  
pp. 19-24 ◽  
Author(s):  
Daniel Szatmári
Keyword(s):  
Large Scale ◽  
Slovak Republic ◽  
Map Projection ◽  
Map Projections

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.

scholarly journals From cartography of the Universe to molecular cartography – the use of map projections

2015 ◽  
Vol 47 (4) ◽  
pp. 191-201
Author(s):  
Paweł Pędzich
Keyword(s):  
Broad Spectrum ◽  
Geographical Information Systems ◽  
Spatial Databases ◽  
Geographical Information ◽  
The Internet ◽  
Coordinate Systems ◽  
Map Projection ◽  
Map Projections ◽  
The Universe

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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