In 2005, Google Maps was launched on the internet as a service intended to aid orientation in space and navigation from one point to another by car, public transport, on foot, by bicycle, or by ...plane. In making the mathematical basis of the maps, Google Maps applied a procedure in which geodetic coordinates on the ellipsoid φ and λ were mapped into a plane according to the formulas of the normal Mercator projection for mapping a sphere.
In the middle of 1990s, Google made available world maps which can be zoomed in to the largest scales, with the maps collectively named Google Maps. Google Maps is primarily intended to facilitate ...navigation by car, public transport, bicycle, airplane or on foot. Such maps require a conformal or approximately conformal projection because it is important that e.g. perpendicular streets in any city in the world also appear approximately perpendicular on the map. To make orientation easier, it is important that north always points to the same direction on a map. The same requirements apply to maritime and aerial navigation, where advantages of the Mercator projection have been known for almost 500 years.
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.
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.
Miljenko Lapaine rođen je u Zagrebu 4. travnja 1952. Nakon osnovne škole i niže muzičke škole pohađao je matematičku gimnaziju i srednju muzičku školu. Zatim je studirao matematiku i diplomirao 1976. god. na Prirodoslovno-matematičkom fakultetu Sveučilišta u Zagrebu, na smjeru teorijska matematika.
Map Projection Transitions Frančula, Nedjeljko; Lapaine, Miljenko
Kartografija i geoinformacije,
06/2013, Letnik:
12, Številka:
19
Book Review, Journal Article
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Map Projection Transitions is a very successful web application about map projections. The web page ( http://www.jasondavies.com/maps/transition ) presents a world map with graticule and country ...borders in the oblique Aitoff projection, with the South Pole. The map is not static, but animated. The South Pole moves toward the bottom and Earth rotates around its poles. The animation lasts five seconds, after which the projection changes and movement continues for five seconds, after which the projection changes again. Names of projections appear in a separate window. There are a total of 56 projections. The South Pole eventually becomes invisible and the North Pole appears at the top. Various parts of Earth appear in the center of the map by rotating around the poles.
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.
Web-Mercatorova projekcija je projekcija relativno novijeg datuma o čijoj je primjeni bilo dosta kontroverzija. Neki smatraju da ta projekcija nije projekcija ni sfere ni plohe elipsoida. Stoga je u ovom radu istraženo nekoliko projekcija plohe rotacijskog elipsoida u ravninu i pokazano da je web-Mercatorova projekcija jedna od takvih projekcija. Naime, premda su jednadžbe te projekcije istovjetne jednadžbama za projekciju sfere, osnovna je razlika u odabiru područja definicije, odnosno domene projekcije. Nadalje, pokazali smo da se web-Mercatorova projekcija može interpretirati i kao dvostruko preslikavanje: preslikavanje elipsoida na sferu po normalama te preslikavanje sfere u ravninu po formulama Mercatorove projekcije za sferu. Web-Mercatorova projekcija nije konformna projekcija, ali je po svojstvima bliska Mercatorovoj projekciji.
Cartographic Content on Twitter Nedjeljko Frančula
Kartografija i geoinformacije,
07/2017, Letnik:
16, Številka:
27
Journal Article
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Twitter has recently become an important channel of information. It is used by governments, politicians, sportsmen, artists and even scientists. We were interested in how much cartographers used ...Twitter and what kind of cartographic content can be found on Twitter.