{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-V80W257X/023a6f89-46bb-4a57-b48c-e9f526a78a08/PDF","dcterms:extent":"1599 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-V80W257X/a82b52c6-d038-443d-9a8d-834c7939e3be/TEXT","dcterms:extent":"17 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-V80W257X","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-FNN1A9OB"},{"@xml:lang":"sl","#text":"Obzornik za matematiko in fiziko"}],"dcterms:issued":"2012","dc:creator":["Jaklič, Gašper","Kanduč, Tadej","Praprotnik, Selena","Žagar, Emil"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:59"},{"@xml:lang":"sl","#text":"str. 1-10"}],"dc:identifier":["ISSN:0473-7466","COBISSID:16255577","URN:URN:NBN:SI:doc-V80W257X"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"Dijkstra's algorithm"},{"@xml:lang":"sl","#text":"Dijkstrov algoritem"},{"@xml:lang":"sl","#text":"energijski funkcional"},{"@xml:lang":"en","#text":"energy functional"},{"@xml:lang":"sl","#text":"interpolacijski problem"},{"@xml:lang":"en","#text":"interpolation problem"},{"@xml:lang":"en","#text":"macroelements"},{"@xml:lang":"sl","#text":"makroelementi"},{"@xml:lang":"sl","#text":"matematika"},{"@xml:lang":"en","#text":"mathematics"},{"@xml:lang":"en","#text":"numerical analysis"},{"@xml:lang":"sl","#text":"numerična analiza"},{"@xml:lang":"sl","#text":"polinomske krivulje"},{"@xml:lang":"en","#text":"polynomial curves"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Z najmanj truda na Šmarno goro!|"},"dc:description":[{"@xml:lang":"sl","#text":"Finding a curve on the surface with constraints is a difficult problem frequently encountered in civil engineering at road and railway construction. In this article, an optimal mountain ascent (in the sense of energy consumption) is considered. Discrete terrain data are given. A smooth terrain description is constructed using macroelements. An energy functional which depends on terrain inclination and on path length, is defined. By computing energy on the boundaries of polynomial patches, the problem transforms into a discrete problem of finding the cheapest path on a mesh of polynomial curves. Numerical results indicate that the resulting paths are good approximations of the natural rutes. Some examples on real data are presented"},{"@xml:lang":"sl","#text":"Iskanje krivulj na ploskvi z danimi omejitvami je v splošnem težak problem. Nanj naletimo npr. v gradbeništvu pri gradnji cest in železnic na razgibanem terenu. V članku se omejimo na problem iskanja vzpona na goro, pri katerem porabimo najmanj energije. Dane so diskretne meritve terena, na podlagi katerih s pomočjo makroelementov konstruiramo gladek opis reliefa. Energijski funkcional definiramo v odvisnosti od naklona in dolžine poti. Z izračunom energije na robovih polinomskih ploskev zastavljeni problem prevedemo na diskretni problem iskanja najcenejše poti na mreži polinomskih krivulj. Numerični rezultati kažejo, da se dobljene poti dobro ujemajo z naravnimi, kar predstavimo na primeru realnih podatkov"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-V80W257X","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-V80W257X"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-V80W257X/023a6f89-46bb-4a57-b48c-e9f526a78a08/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-V80W257X/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-V80W257X"}}}}