Map Projections
Miljenko Lapaine
Abstract.
The paper is a review of the map projection theory and applications all over the world and in Croatia. First of all, cartography is shortly presented as a discipline dealing with foundation, production, promotion and studying of maps. Theory of map projections is a branch of cartography studying the ways of projecting the curved surface of the earth and other heavenly bodies into the plane. After a brief review of the history of map projections the paper gives the general outline of map projections and persons dealing with their theory on the territory of Croatia. In addition, the problem of the state map projection selection, which is one of the basic issues of the Croatian official cartography, has been explained.
Keywords: cartography, map projections, history, Croatia
6 Selection of the Croatian Official Projection
One of the basic issues of the official cartography is the selection of the state projection, i.e. the selection of the state co-ordinate system. Such a selection was increasingly important at the beginning of the century, and then at the moment of creating the Independent State of Croatia (Nezavisna država Hrvatska), and is so at the present time. The issue of selecting the projection and coordinate systems was inititated in 1921. The director of cadastre at that time appointed a well-known geodetic scientist, professor A. Fasching who came from Budapest, to solve this problem. The complexity of the job can be seen from the references (93).
Fig. 4 Correct and distorted presentation of Croatia
As soon as one starts to talk about map projections, all experts unintentionally remember the famous saying by Jordan: “No institution goes so deeply into the essence of the entire land survey and mapping of a country, as the selection of the projection and coordinate system. If a mistake is made here, it takes revenge on many generations.” According to Abakumov (2) we felt in Croatia these prophetic words to full extent on our skins. From former Austro-Hungarian Monarchy we have inherited a few co-ordinate systems. Every expert working in the field of geodesy knows well what kind of troubles and difficulties are caused still today by the co-ordinates of the control points at our territory. Abakumov wrote in 1942 about the issue of selecting the most appropriate projection for the Independent State of Croatia and considered two variants of Gauss-Krüger projection, their advantages and disadvantages.
Gauss-Krüger projection is widely applied in geodetic practice (29). In many European countries this projection has been adopted as official state projection. It is well known that it was selected in 1924 for the territory of former Yugoslavia and that the Cartesian co-ordinates of points of state triangulation have been so far calculated and presented in this projection. Regarding new circumstances, and above all the shape of the Republic of Croatia and its spreading, it is necessary to be familiar with its most appropriate projections.
The scientific and professional project Selection of State Map Projection was suggested to the State Geodetic Administration in 1994, 1995, 1997 and 1998. Here are some examples showing the necessity of making competent judgement about the selection of map projection at the territory of Croatia.
1) Today more and more people are dealing with the production of maps by using computers. The interest in maps and cartography is undoubtedly growing. There were 16 reports at the CAD Forum’93 within the frame of the section on spatial information systems, and the majority of them were accompanied by the presentation of various maps. In one of these works (118) the transformation of the entire contents into the 5th system of Gauss-Krüger projection has been applied for the purpose of unified cartographic presentation, and the contents referred to the entire Croatia. It can be shown (60) that the application of the 5th system of Gauss-Krüger projection to the entire Croatia has no justification. On one hand we have obvious lack of symmetry in presentation, and on the other hand the distortions in the eastern part of the state are unnecessarily too large.
2) In Geodetski list No. 1 from 1997 there was an article published about the selection of map projection for the maps at small scales (30). In the introduction the authors point out the main reason that initiated the article: “The indirect motive are very often more and more frequent distorted presentations of Croatia as the result of insufficient knowledge in cartography, especially the knowledge about map projections and their selection for the maps of certain areas.” The article has 10 pages, extensive reference list and two illustrations. How can we then explain the fact that the cover pages of the third number of Geodetski list from 1998 contain deliberately distorted map of Croatia.
3) It is not alarming if for example an architect or forester make a map of Croatia in inadequate map projection, or if a lawyer has some thoughts of his own about GaussKrüger projection, but something like that should not be accepted by the qualified engineer of geodesy. For example, if we say that Gauss-Krüger projection has been applied with the following parameters:
• six degrees zone with the mean meridian of 16°30’
• scale reduction coefficient at the meridian of contact is 0.9997
• additional constant is 2 500 000,
and the title contains State Geodetic Administration (37, 83), then it is obvious that the State Geodetic Administration did not pay enough attention to the map projections. There is namely no need to point out the six degrees zone because there is only one zone being approximately like that. Furthermore, it is not the matter of meridian of contact but of the central meridian of the area to be projected. Moreover, once in the time of logarithmic tables it had some sense to add some constant to the rectangular co-ordinates in GaussKrüger projection in order to avoid the computation with negative numbers, but today, in the time of computers or cybernetic era it looks rather exotic. Finally, it is not correct to credit all that to Prof. Frančula (83), because Frančula has never formulated his suggestion of map projection for the small-scale maps of Croatia in such a way. In order to illustrate the inability of recognising the problem of map projection I shall use the copy of the distorted map of Croatia to be found on the cover pages of at least two written materials made by the State Geodetic Administration, see Fig. 4. It is very instructive to see the figure at the page 162 in the Proceedings of the symposium “State Geodetic Bases and Land Information Systems” held in 1999 in Opatija (63). The figure shows the distortion that was caused by unauthorised intervention of the technical editor (spreading of the picture in only one direction), which made the text under the picture lose its meaning, and the efforts of the author to indicate the unnecessary deformed presentations have failed. Some other examples of unnecessary distorted representations of the Croatian territory can be found in (30, 31).
At the end of this paper I would like to report that the State Geodetic Administration of the Republic of Croatia recognised the problem of mathematical basis for official cartography and ordered from the Faculty of Geodesy, University of Zagreb the elaboration of the project “Proposal for Official Map Projections of the Republic of Croatia” at the end of 1999 (64).
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