Gaussovo a Laplaceovo vyhlazovaní na triangulovaných plochách

Bc. Zuzana Nováková

Master's thesis

Gauss and Laplacean smoothing on triangulated surfaces

Abstract:

In this thesis we study methods for smoothing and remeshing on triangulated surfaces. We focus on Laplacean and Gauss smoothing algorithms, simplification and subdivision algorithms, uniform resampling and Voronoi filtering. The first four chapters are devoted to the theory of these methods, and the last two chapters focus on the implementation of the methods and their application in R and Meshlab using real data.

Abstract:

V tejto diplomovej práci sa venujeme prieskumu metód vyhladzovania a zmeny triangulácie na triangulovaných plochách. Zameriame sa na Laplaceov a Gaussov vyhladzovací algoritmus, algoritmy zjednodušenia a zhustenia triangulácie, prevzorkovanie siete a Voronoi filtering. Prvé štyri kapitoly sa venujú teórii týchto metód a posledné dve kapitoly sú zamerané na implementáciu metód a ich aplikáciu na reálne dáta v jazyku R a v Meshlabe.

Keywords

Laplaceov vyhladzovací algoritmus, Gaussov vyhladzovací algoritmus, HC Laplaceov algoritmus, Loop subvidivízia, Butterfly subvidivízia, obrna tvárového nervu, Voronoi filtering, rovnomerné prevzorkovanie, zmena triangulácie, Delaunayova triangulácia, Meshlab, Laplacean algorithm, Gauss algorithm, HC Laplacean algorithm, Loop subdivision, Butterfly subdivision, facial palsy, uniform resampling, remeshing

Language used: Slovak

Date on which the thesis was submitted / produced: 9. 5. 2023

Thesis defence

• Date of defence: 19. 6. 2023
• Supervisor: doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
• Reader: doc. Mgr. Jan Koláček, Ph.D.

Masaryk University

Faculty of Science

Master programme / field:
Applied Mathematics / Finance and insurance mathematics