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Open access

Paweł Pędzich

Abstract

The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

Open access

Paweł Pędzich

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.

Open access

Paweł Pędzich

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.

Open access

Paweł Pędzich

Abstract

The aim of the author of this article is to show the users of Geographical Information Systems how to present the distortions in a simple way. The intention of the author is also to popularize the knowledge in the scope of map projections and to inform the users of the maps that, despite all the advanced modern tools, an elimination of the problem, connected with the map projections and cartographical distortions occurring in them, has failed so far.

The author presents a brief overview of the measures in the scope of distortions and methods of their presentation. It is also shown how the users can generate the maps, presenting a distortion by themselves. It is much easier to perform this type of visualization with the help of “matplotlib library”, basically everyone can compile such a map.

Open access

Paweł Pędzich and Marta Kuźma

Abstract

The paper presents methods of area calculation, which may be applied for big geodesic polygons on the ellipsoid. Proposal developed by the authors of this paper is discussed. The proposed methods are compared with other, alternative methods of area calculation of such polygons. Test calculations are performed for administrative units in Poland. The obtained results are also compared with areas of those units registered in statistical annals. Utilisation of the equal-area map projections of the ellipsoid onto a plane seems to be the best solution for the discussed task. In the case of small distances between points we may expect accurate results of calculations, since the area size is influenced by the projection reductions only, which are small in such cases. In some cases their influence on results of calculations may be neglected. Then, only re-calculation of co-ordinates from the GRS80 ellipsoid to the cartographic, equal-area projection is required.

Open access

Jacek Augustyniak, Marta Kuźma and Paweł Pędzich

Abstract

Maps, depicting the warfare, are elaborated according to the rules developed over the years. Although, they are not free of errors. The authors draw our attention to the diversity of methods related to the cartographic presentations, which are shown on the historical maps. This is quite understandable, because every such a map introduces an individual point of view on the historical facts. It is noted, that the most commonly used methods are the qualitative ones, among which, for instance, first of all, the method of signature is frequently used.

In the case of historical maps displaying an event in the specific sequence of times, a loss of cartographic information always occur. This is connected both with the complexity of historical facts and with the difficulty in reading a map, which should present the dynamics of this phenomenon in a complete way. The dynamic variables, such as the time of exposure, duration, frequency, order, degree of change and synchronisation, should be taken into account on the maps of warfare.

The use of information technology makes it possible to develop not only the simple maps presenting the course of warfare in the statistic and schematic ways, but also the maps, which are rich in various types of multimedia information.

Multimedia cartographic presentations can be enriched with the photos and panoramas showing the direct effects of warfare and the pseudo three-dimensional visualization showing the battle from a selected direction. The proprietary software let to combine the sequence of photos into a presentation, allowing to take a virtual tour of the areas directly affected by the hostilities. Network services, such as WMS, WFS, WCS, provide the integrated data from the different sources for us. So, we can connect the archival maps with the contemporary satellite images, defining, thus, the location of a specific place in the terrain.

The authors do not cover the issue of complexity connected with the elaboration of maps presenting the combat operations. The most important problems, which have not been discussed in this article, are the following ones: lack of base maps from the period to which the presented issues related, deliberate distortion of map contents, historical and cartographic imprecisions presented on the maps, appropriate selection of the methods of cartographic presentation related to the phenomena, which are presented on the maps.