Interpolacija triangulacij v prostoru z gladkimi ploskvami : magistrsko delo

Kren, Domen (author), Jaklič, Gašper (mentor)

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.

• Language: Slovenian
• Keywords: triangualcija, polinom, zlepek, interpolacija, makro element
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics; FRI - Faculty of Computer and Information Science
• Year: 2019
• PID: 20.500.12556/RUL-111194
• UDC: 519.6
• COBISS.SI-ID: 18730585
• Publication date in RUL: 26.09.2019

KREN, Domen, 2019, Interpolacija triangulacij v prostoru z gladkimi ploskvami : magistrsko delo [online]. Master’s thesis. [Accessed 27 March 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=111194

Secondary language

• Language: English
• Title: Interpolating triangulations in space with smooth surfaces

Abstract

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.

• Keywords: triangulation, polynomial, spline, interpolation, macro element