Problem teselacije NURBS ploha

master's thesis

• Author: Ana Mlinarić
• Mentor: Luka Grubišić (mentor)
• Committee member: Luka Grubišić (predsjednik povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prezentirani su različiti algoritmi teselacije NURBS ploha trokutima. Precizno su definirane plohe koje su potrebne za razumijevanje algoritama – Bézierova, B-splajn i NURBS ploha. Objašnjeno je da algoritmi teselacije NURBS ploha zahtijevaju prikaz NURBS plohe pomoću Bézierovih ploha. Objašnjeni su pojmovi uniformne, adaptivne i potpuno adaptivne teselacije te pripadnih testova za provjeru točnosti teselacije. Nadalje, predstavljen je OpenGL, sučelje za programiranje grafičkih aplikacija. Opisana je grafička struktura teselacije u OpenGL-u. Poseban naglasak stavljen je na faze koje su odgovorne za teselaciju. Definirana je razina teselacije te je objašnjena razlika između unutarnje i vanjske teselacije. Prikazano je kako razina teselacije djeluje na teselaciju pojedinog trokuta. Za kraj, opisana je implementacija rješenja koje za teselaciju koristi poseban oblik Bézierove plohe – Bézierov trokut. Opisani su koraci algoritma te su dani rezultati za tri objekta. Prikazane su slike objekata prije i nakon teselacije, uz različite razine teselacije. Veća razina teselacije daje bolje rezultate.

Abstract (english)

This paper presents various triangle tessellation algorithms of NURBS surfaces. The surfaces required for understanding algorithms are precisely defined – the Bézier, B-spline and NURBS surface. It is explained that NURBS surface tessellation algorithms require the NURBS surface to be displayed using Bézier surfaces. The terms uniform, adaptive and fully adaptive tessellation are explained, as well as the corresponding tessellation accuracy tests. Furthermore, OpenGL, the graphical applications programming interface is presented. The graphical tessellation structure in OpenGL is explained, and special emphasis is placed on the phases responsible for tessellation. The level of tessellation is defined, and the difference between inner and outer tessellation is explained. The paper also demonstrates how the level of tessellation affects the tessellation of an individual triangle. Finally, the implementation of a solution which uses a special form of the Bézier surface – the Bézier triangle is described. The algorithm steps are described, and the results for three objects are provided. Images of the object before and after the tessellation are provided, with various tessellation levels. The higher tessellation levels yield better results.

• Keywords: algoritmi teselacije; Bézierova ploha; B-splajn ploha; NURBS ploha; OpenGL
• Keywords (english): tessellation algorithms; Bézier surface; B-spline surface; NURBS surface; OpenGL
• Language: croatian
• URN:NBN: urn:nbn:hr:217:126884
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-08-30 10:10:31