Nedjeljko Frančula

The paper is a review on map projections. The introductory part gives the definition of map projections, their classification, and describes the basic problem, which is the impossibility of mapping a spherical or ellipsoidal surface into a plane without distortion. The following chapter presents the historical development of map projections, from their beginnings more than 2,500 years ago to the present day. The following is a description of the development and application of map projections in Croatia. In particular, official map projections in Croatia and map projections in Croatian education are investigated.

The United Nations called on the international community to move forward together. Through the Sustainable Development Goals (SDG), a plan was set until 2030. The use of maps, mapping technology and the skills of cartographers help synthesize and visualize complex data. Maps allow insights into trends and comparisons between different areas and over different time periods. Mapping helps in better understanding and implications of each sustainable development goal. For this purpose, the paper presents map projections with a special emphasis on mapping for a sustainable world. Map projection is not only the transformation of geospatial data, but of any data related to space. Presented is a modern classification of map projections that differs from the usual division into cylindrical, conical and azimuthal. For maps of the world adapted to the goals of sustainable development, the Winkel Triple projection is proposed. Different map projections bring with them significantly different distortions. The energy consumption for displaying a digital map varies greatly when using different projections. This is the area of a new branch of cartography − green cartography. In the article, we take a critical look at the research of digital maps and their carbon footprint and warn against maps made in map projections that should not be researched in the future. The article is intended for everyone who is interested in cartography as an auxiliary profession in sustainable development, but also for cartographers who do not think critically enough about map projections.

Miljenko Lapaine was born in Zagreb on 4 April 1952. After primary school and junior music school, he attended a mathematics gymnasium and music high school. He then studied mathematics and graduated in 1976 from the Faculty of Natural Sciences and Mathematics of the University of Zagreb, majoring in theoretical mathematics.

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.

Godine 2020. objavljen je Kartografski rječnik u izdanju Hrvatskoga kartografskog društva i Naklade Dominović. Od objavljivanja prvoga i jedinoga Višejezičnoga kartografskoga rječnika u Hrvatskoj prošlo je više od 40 godina. U tom razdoblju mnogo toga novoga dogodilo se u svijetu, što su autori pokušali obuhvatiti novim rječnikom. U ovom radu opisat ćemo probleme s kojima smo se susreli u radu na pripremi toga rječnika.

This paper explains that the terms “horizontal and vertical scales” are not appropriate in map projections theory. Instead, the authors suggest using the term “scales in the direction of coordinate axes.” Since it is not possible to read a local linear scale factor in the direction of a coordinate axis immediately from the definition of a local linear scale factor, this paper considers the derivation of new formulae that enable local linear scale factors in the direction of coordinate x and y axes to be calculated. The formula for computing the local linear scale factor in any direction defined by dx and dy is also derived. Furthermore, the position and magnitude of the extreme values of the local linear scale factor are considered and new formulas derived.

The Web Mercator projection is a projection of a relatively recent date. There has been a lot of controversy about its application. Some believe that this projection is not a projection of either the sphere or the surface of the ellipsoid. Therefore, in this paper, several projections of the surface of a rotational ellipsoid into a plane are investigated and it is shown that the Web Mercator projection is one of such projections. Namely, although the equations of this projection are identical to the equations for the projection of the sphere, the basic difference is in the choice of the area of definition, i.e., the domain of the projection. Furthermore, we have shown that the Web Mercator projection can also be interpreted as double mapping: mapping an ellipsoid to a sphere according to the normals and then mapping the sphere to the plane according to the formulas of the Mercator projection for the sphere. The Web Mercator projection is not a conformal projection, but it is close in properties to the Mercator projection.

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