ISSN 2079-3537      

 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             

Scientific Visualization, 2022, volume 14, number 1, pages 18 - 31, DOI: 10.26583/sv.14.1.02

Comparative Graphical Analysis of Distortions of Some Cartographic Projections

Authors: S.V. Ktitrov1, D.A. Ryslyaev2

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Russian Federation

1 ORCID: 0000-0002-7963-9151, svktitrov@mephi.ru

2 ORCID: 0000-0001-6781-1519, rislaev97@gmail.com

 

Abstract

The article is devoted to the problem of distortion of the size and shape of extended objects on maps when projecting the Earth's surface. Various types of projections are considered, their classification is briefly given. The Mercator, Albers, Kavraisky and azimuthal equidistant projections were selected for analysis.

Distortions differ depending on the projection. It is pointed out that traditional graphical methods of distortion demonstration, such as distortion ellipses, cannot give a complete picture for extended objects without additional calculations. The authors propose an approach based on combining projected objects to solve the problem of rapid and visual detection of distortions.

Scale coefficients of projection methods were been analyzed to identify areas with the minimal distortion. Both expressions for coefficients and graphical dependences on latitude and longitude are given.It is proposed to use the Mercator projection when the figure is shifted to the equator region as a way to obtain the minimal distorted figure. Thus, a figure on a plane can be obtained. It is closest in shape and size to an object on the earth's surface.

Comparisons are carried out for various model objects (parallelogram, rectangle, circle, rhombus) located both near the equator and at the 60th parallel. The combination method demonstrates the distortion produced by various projection methods.

Visualization is performed by means of the author's software including the SINUS-D program for system simulation, as well as specially developed programs in C++ where preliminary data preparation, projection, displacement of objects are carried out and a program in Python that uses third-party libraries to display objects against the background of the globe.

The approach to the analysis of the representation of cartographic information proposed by the authors and implemented in the programs developed by the authors can be useful primarily in studying the features of cartographic projections, but it also has practical potential in everyday use to facilitate the planning of activities and more accurate accounting and allocation of resources.

 

Keywords: cartographic projection, visualization, comparative analysis, error, distortion, distortion ellipse, scale factor.