Intervalske Bézierove krivulje in ploskve : diplomsko delo

BOROVŠAK, TADEJ (author), Krajnc, Marjetka (mentor)

Med oblikovanjem in izdelavo predmetov s pomočjo računalnika moramo podatke večkrat prenašati med različnimi CAD/CAM sistemi. Zaradi razlik med zmogljivostmi posameznih sistemov moramo podatke med prenosom aproksimirati. V diplomskem delu si bomo ogledali intervalske Bézierove krivulje in ploskve, ki predstavljajo eno izmed mnogih aproksimacijskih shem, razvitih v ta namen. Na kratko si bomo ogledali intervalsko aritmetiko ter opisali osnovne lastnosti intervalskih Bézierovih krivulj. Ogledali so bomo osnovne algoritme, ki jih uporabljamo pri delu z Bézierovimi krivuljami in ploskvami, in jih posplošili na intervalske Bézierove krivulje ter ploskve. Vse algoritme bomo implementirali v programskem jeziku Octave oziroma Matlab in grafično prikazali rezultate, ki jih dobimo z uporabo algoritmov na izbranih primerih.

• Language: Slovenian
• Keywords: Bézierove krivulje, Bézierove ploskve, intervalska aritmetika, računalništvo, računalništvo in informatika, univerzitetni študij, diplomske naloge, interdisciplinarni študij
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Publisher: [T. Borovšak]
• Year: 2014
• Number of pages: 51 str.
• PID: 20.500.12556/RUL-29968
• COBISS.SI-ID: 1536143555
• Publication date in RUL: 09.10.2014

Licences

• License: CC BY-SA 2.5 SI, Creative Commons Attribution-ShareAlike 2.5 Slovenia
• Link: https://creativecommons.org/licenses/by-sa/2.5/si/deed.en
• Description: You are free to reproduce and redistribute the material in any medium or format. You are free to remix, transform, and build upon the material for any purpose, even commercially. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

Secondary language

• Language: English
• Title: Interval Bézier curves and surfaces

Abstract

Process of creating real world objects usually involves usage of more than one CAD/CAM system. Communicating product data between diverse systems that use incompatible internal representation schemes necessitates data conversion and approximation. Main focus of the thesis will be on Bézier curves and surface patches that offer a way of converting data while retaining information about the approximation error made during conversion. We will briefly review basic building blocks such as intervals, interval arithmetic and Bernstein basis functions, and then resume with describing interval Bézier curves and surface patches. Crucial algorithms that allow us to work with Bézier curves, Bézier surface patches and their interval counterparts will be implemented. We will conclude this thesis with short review of a few selected examples of interval Bézier curves and surface patches.

• Keywords: Bézier curves, Bézier surface patches, interval arithmetic, computer science, computer and information science, diploma, interdisciplinary studies