In previous papers that have dealt with cylindrical map projections as limiting cases of conical projections, standard or equidistant parallels were used in the derivations. This paper shows that ...this is not necessary and that it is sufficient to use parallels that preserve length. In addition, unlike other approaches, in this article the limiting cases of conic projections are derived in the most natural way, by deriving the equations of cylindrical projections from the equations of conic projections in a rectangular system in the projection plane using a mathematical concept of limits. It is shown that such an approach is possible, but not always, so it should be used carefully, or even better, avoided in teaching and studying map projections.
The article belongs to the field of theoretical research on map projections. It is observed that there is no unique and generally accepted definition of standard parallels in the cartographic ...literature. For some authors, a standard line is a line along which there is no distortion, and for others, it is a line along which there is no distortion of length. At the same time, it is forgotten that the length distortions at any point generally change and depend on the direction. The main goal of this article is very simple: the sentence “linear deformation is zero in all directions” is expressed using a mathematical formula. Besides that, the paper introduces equidistance in a broader sense. This is a novelty in the theory of map projections. Equidistance is defined at a point, along a line and in an area, especially in the direction of the parallels and especially in the direction of the meridian. This enables an unambiguous definition of standard parallels. Theoretical considerations are illustrated with examples of cylindrical projections. The practical value of the proposed approach is manifested in the possibility of a better understanding of the distribution of distortions in any map projection used.
Map projections are usually interpreted by mapping a sphere onto an auxiliary surface, and then the surface is developed into a plane. It is taken as a fact without proof that the parallels in which ...the auxiliary surface intersects the sphere are mapped without distortions. In a previous paper, based on a theoretical consideration and illustrated with several examples, the author concluded that explaining cylindrical projections as mapping onto a cylindrical surface is not a good approach, because it leads to misunderstanding important properties of projection. In this paper I prove that there are no equal-area, equidistant, or conformal cylindrical projections for which the standard parallel will coincide with secant parallel after folding the map into a cylinder.
In books and textbooks on map projections, cylindrical, conic and azimuthal projections are usually considered separately. It is sometimes mentioned that cylindrical and azimuthal projections can be ...interpreted as limiting cases of conic, but this is rarely proven. The goal of this article is to show in a rigorous and systematic way how to generally approach solving the problem of transition from a conic to a corresponding cylindrical projection. This article points to the fact that J. H. Lambert showed as early as 1772 that a conformal cylindrical projection is created from a conformal conic projection. Following his idea, this paper shows that not only conformal, but also equal-area and equidistant cylindrical projections can be derived from corresponding conic map projections. Although it seems that the paper deals with quite well known and intuitive property of conic projections, it will also show that the transition from the conic to the corresponding cylindrical projection is not always possible.
U ovom radu istražuje se doprinos Vinka Paletina kartografiji. Taj se doprinos može raščlaniti na tri područja: pomorstvo i navigacija, izrada globusa i izrada karata. Budući da su o Vinku Paletinu ...kao pomorcu pisali drugi, ovaj se rad samo kratko osvrće na to. Ovaj rad predstavlja priručnik „Umijeće navigacije“ (L’arte del navegar) u prijevodu Vinka Palatina na temelju primjeraka te knjige koji se čuvaju u Nacionalnoj i sveučilišnoj knjižnici u Zagrebu, knjižnici Državnog arhiva u Zadru i još nekim knjižnicama izvan Hrvatske. Uz kopije naslovnica i
Paletinova predgovora donosi se sadržaj toga priručnika s posebnim osvrtom na treće poglavlje u kojem se govori o pomorskim kartama. U literaturi se spominju tri globusa autorstvo kojih se pripisuje Vinku Paletinu. Dva od njih sigurno nisu njegovo djelo, a o trećem nema gotovo nikakvih podataka. Problem je možda u talijanskoj riječi mappamundi, koja označava globus, ali i kartu svijeta. U radu se iscrpno govori o Paletinovoj karti Španjolske iz 1551. te je prikazano nekoliko karata Španjolske koje su prethodile njegovoj. Konačno, rad upućuje na vrijednost Paletinove karte koja je poslužila mnogim kartografima kao uzor i predložak za njihove karte Španjolske.
New Cartographic Dictionary Lapaine Miljenko
Kartografija i geoinformacije,
01/2020, Letnik:
19, Številka:
33
Journal Article
Odprti dostop
The Croatian Cartographic Society and Dominović d.o.o. published recently a new Cartographic Dictionary. The authors are Prof. Emer. Nedjeljko Frančula, Prof. Emer. Miljenko Lapaine and Ivo-Pavao ...Jazbec.
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.
A problem in ‘Basic Cartography’ Lapaine, Miljenko
International journal of cartography,
01/2024, Letnik:
10, Številka:
1
Journal Article
Recenzirano
In cartographic literature, map projections are usually interpreted as mapping to auxiliary development surfaces, and then these surfaces are developed into a plane. The so-called secant projections, ...i.e. projections in which the auxiliary surface intersects the Earth's sphere or ellipsoid are especially emphasized. It is stated and taken as a fact without proof that the parallels in which the auxiliary surface intersects the sphere are mapped without distortions. An example of such an approach is the publication Basic Cartography, published several years ago by the International Cartographic Association. This paper proves that standard parallels and secant parallels generally do not match. It turns out that the widely accepted facts about secant and standard parallels, which can also be found even in the most recent literature, are wrong and need to be revised. The paper concludes that explaining cylindrical projections as mapping on a cylindrical surface is not a good approach, because it leads to misunderstanding important properties of projection.
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