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 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 Map production and data analysis with local parameters

4open ◽  
2019 ◽  
Vol 2 ◽  
pp. 27
Author(s):  
Hermenegildo Borges de Oliveira ◽  
Fernando Granja-Martins ◽  
Helena Maria Fernandez
Keyword(s):  
Data Analysis ◽  
Map Projection ◽  
Geographical Analysis ◽  
Equal Area ◽  
Map Projections ◽  
The North ◽  
Mainland Portugal ◽  
Area And Perimeter ◽  
Local Parameters

In this work we perform a geographical analysis of the Algarve region by using local parameters in the three map projections we consider: Transverse Mercator (TMzn), Lambert Azimuthal Equal-Area (LAEA) and Lambert Conformal Conic (LCC). We compare the Algarve maps resulting by each one of these representations when the origin of coordinates is moved from the center of mainland Portugal (that is in force) to the center of the Algarve. For the LCC map projection, the analysis takes also into account the change of the upper parallel from the North of Portugal to a latitude inside the Algarve border. The area and perimeter of the Algarve is computed and the location of its geographic center is determined in every map representation. Borders lengths that separates the Algarve from Alentejo and from Spain, and the extents of its South and West coasts, are also computed. We conclude by presenting the map, the values of area and perimeter and the location of the geographic center that should be considered for the Algarve, at different scales and for the available data.

scholarly journals First Maps for the Systematic Registration of Property in the Kingdom of Romania

2016 ◽  
Vol 73 (2) ◽  
pp. 333
Author(s):  
Doina Vasilca
Keyword(s):  
Map Projection ◽  
Equal Area ◽  
Historical Importance ◽  
Cartesian System ◽  
East And West

In this article are presented the very first maps realised in a systematic way in order to determine the boundaries and register the properties of the Kingdom of Romania, at a scale of 1:20,000 in the equal-area pseudoconical Bonne projection. This projection was not applied in a uniform way for the whole territory of the country, but differently for the areas situated east and west of the Zimnicea meridian, respectively. For each of these two zones I have shown the peculiarities of applying the Bonne projection. furthermore, I explained in detail the means of establishing the nomenclatures of the maps at a scale of 1:20,000, but also at smaller scales, 1:50,000, 1:100,000 and 1:200,000. Since the analyzed map projection preserves area measurements, I verified this property on five maps at the scale of 1:20,000, chosen from both zones. Results obtained for the zone east of the Zimnicea meridian showed a 0.0005% difference, falling within the tolerated error, but for the maps situated west of the Zimnicea meridian, the area differs by about 3%. I have proved that this large difference in the area of the analyzed maps, identified at the eastern extremity of the mapped zone, is due to the fact that they are not actually bordered by the Zimnicea meridian, but by a line related to the Cartesian system used. The Bonne projection maps made for the entire Romanian Kingdom by specialists of the Romanian Army nowadays possess significant historical importance, both in terms of mapping and cadastre.

An equal-area map projection for irregular objects

Icarus ◽  
2005 ◽  
Vol 175 (2) ◽  
pp. 382-389 ◽  
Author(s):  
M.G. Berthoud
Keyword(s):  
Map Projection ◽  
Equal Area

scholarly journals Some Equal-area, Conformal and Conventional Map Projections: A Tutorial Review

2016 ◽  
Vol 10 (3) ◽  
Author(s):  
Ebrahim Ghaderpour
Keyword(s):  
Fundamental Form ◽  
Positioning Systems ◽  
Equal Area ◽  
Map Projections ◽  
Flat Sheet ◽  
The Earth ◽  
Global Positioning ◽  
Different Types ◽  
First Fundamental Form ◽  
Shape And Size

AbstractMap projections have been widely used in many areas such as geography, oceanography, meteorology, geology, geodesy, photogrammetry and global positioning systems. Understanding different types of map projections is very crucial in these areas. This paper presents a tutorial review of various types of current map projections such as equal-area, conformal and conventional. We present these map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for them in detail. The first fundamental form and the Gaussian fundamental quantities are defined and applied to obtain the plotting equations and distortions in length, shape and size for some of these map projections.

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>

Equal Area Map Projection for Irregularly Shaped Objects

2000 ◽  
Vol 27 (2) ◽  
pp. 91-100 ◽  
Author(s):  
Yang Cheng ◽  
Jean J. Lorre
Keyword(s):  
Map Projection ◽  
Equal Area
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