Orodje za grafični prikaz lastnosti Bézierjevih in PH krivulj : magistrsko delo

Štampar, Kevin (author), Žagar, Emil (mentor)

V magistrskem delu obravnavamo Bézierjeve krivulje, racionalne Bézierjeve krivulje, zlepke Bézierjevih krivulj ter PH krivulje. Skozi delo predstavimo njihove lastnosti, ki so ključne za rabo v sistemih za računalniško podprto načrtovanje (ang. computer-aided design, okrajš. CAD) in sistemih za računalniško podprto geometrijsko oblikovanje (ang. computer-aided geometric design, okrajš. CAGD) ter algoritme, ki njihovo rabo v takšnih sistemih omogočajo. Predstavimo tudi orodje za grafični prikaz lastnosti prej naštetih krivulj - Bezeg. Ogledamo si njegove funkcionalnosti in pokažemo osnovne ideje, kako je orodje implementirano in kako so v orodju predstavljene prej naštete krivulje.

• Language: Slovenian
• Keywords: Bézierjeva krivulja, racionalna Bézierjeva krivulja, zlepek, krivulja s pitagorejskim hodografom, spletno orodje
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-163766
• UDC: 519.6
• COBISS.SI-ID: 210410243
• Publication date in RUL: 10.10.2024

Secondary language

• Language: English
• Title: Tool for graphical representation of properties of Bézier and PH curves

Abstract

In the thesis, we discuss Bézier curves, rational Bézier curves, Bézier curve splines, and PH curves. Throughout the work, we present their properties, which are crucial for use in computer-aided design (CAD) and computer-aided geometric design (CAGD) systems, as well as algorithms that enable their use in such systems. We also introduce a tool for the graphical visualization of the properties of the aforementioned curves - Bezeg. We examine its functionalities and demonstrate the basic ideas of how the tool is implemented and how the aforementioned curves are represented in the tool.

• Keywords: Bézier curve, rational Bézier curve, spline, pythagorean hodograph curve, web tool