20.500.12556/RUL-175891 Zemljevidi in njihove projekcije magistrsko delo Maps and their projections V magistrskem delu se na kratko sprehodimo skozi zgodovino kart in poskusimo premisliti, katere lastnosti zemljevida so za nas pomembne. Podrobneje preučimo družino konformnih stožčastih projekcij ter Mercatorjevo in stereografsko projekcijo, za kateri se izkaže, da sta robna primera te družine. Poiščemo bijekcijo med Mercatorjevo in stereografsko karto. Bolj se posvetimo tudi popačenosti projekcij. Ugotovimo, da obstaja kartografska projekcija z minimalnim popačenjem na zaprtem disku in da je to azimutna ekvidistančna projekcija, katere predpis tudi izpeljemo. Na popačenje pogledamo še nekoliko drugače in spoznamo Tissotove indikatrise ter poiščemo predpis zanje za nekate pogostejše karte. Na koncu še pokukamo v svet poliedrnih projekcij. In the thesis we briefly go through the history of maps and try to find out which properties of maps are important to us. More accurately we study the family of the conformal conical projections, Mercator and stereographic projection. For Mercator and stereographic projections we find out, they are the limit cases of conformal conical projections. We also study more accurately the distortion of distances in map projections. We find out that the cartographic projection with the minimum distortion on a closed disc exists and this is the azimuthal equidistant projection, for which we find also the prescription. We look at the distortion from a different point of view, and we meet the Tissot’s indicatrix. We find the prescriptions for the indicatrix in some more common cartographic projections. In the end we make a brief look in the world of polyhedral projections. projekcija zemljevid sfera distorzija Tissot indikatrisa polieder Mercatorjeva projekcija stereografska projekcija azimutna ekvidistančna projekcija projection map sphere distortion Tissot indicatrix polyhedron Mercator projection stereographic projection azimuthal equidistant projection true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-11-13 08:15:03 2025-11-13 08:15:13 2025-12-16 03:46:59 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 156638 256576515 1390.pdf 1390.pdf 1 15968E22785BF5CCC6E825ADD87C9101 7d927ed6c136d8554003d440353a0dae4c5d978d7686dd160d1b18f5f50cb497 2a70d3ab-c060-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=221828 Fakulteta za matematiko in fiziko 0 0 0