20.500.12556/RUL-111194 Interpolacija triangulacij v prostoru z gladkimi ploskvami magistrsko delo Interpolating triangulations in space with smooth surfaces Digitalna rekonstrukcija objektov se pogosto pojavlja v najrazličnejših inženirskih področjih, kot so interaktivno skiciranje ploskev, skeniranje 3D objektov in medicinska interpretacija slik. V nalogi predstavimo metodo, ki iz triangulacije v prostoru rekonstruira gladek prostorski model površine objekta. Uporabimo lastnosti trikotnih Bézierovih krp, prostorov zlepkov in makro elementov, kjer več pozornosti posvetimo Clough-Tocherjevemu prostoru makro elementov, saj nam predstavlja bazo, na kateri sloni algoritem. Prednosti metode so interpolacija ploskev s poljubno topologijo, preprosta implementacija, gladkost in numerična stabilnost. Naloga vsebuje algoritme in nekaj primerov. Implementacija je narejena v programskem jeziku Python. Digital object reconstruction often occurs in a wide range of engineering fields, such as interactive surface sketching, 3D object scanning and medical interpretation of images. In the paper, we present a method that reconstructs a smooth spatial surface model from a given 3D triangulation. We use the properties of triangular Bézier patches, spline and macro element spaces, where we pay more attention to the Clough-Tocher macro element space, as it represents the base of the algorithm. The advantages of the presented method are complex surface interpolation, simple implementation, smoothness and numerical stability. The paper also contains algorithms and some examples. The implementation is done in the Python programming language. triangualcija polinom zlepek interpolacija makro element triangulation polynomial spline interpolation macro element true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2019-09-26 07:45:03 2019-09-26 07:45:08 2024-05-29 13:32:29 0000-00-00 00:00:00 2019 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 102013 18730585 902.pdf 902.pdf 1 2BBE1EF18DB8C74655C716BA93C3B596 3e3099631a9043d2c220eda58fc7efcbfeb4cc5fa1d9b33f6b8a87bd19acb4cf 53fbfe40-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=123022 Fakulteta za matematiko in fiziko Fakulteta za računalništvo in informatiko 0 0 0