Primjena kvaterniona u računalnoj grafici

undergraduate thesis

• Title (english): Quaternions in Computer Graphics
• Author: Ante Kolobarić
• Mentor: Mate Puljiz (mentor)
• Committee member: Mate Puljiz (predsjednik povjerenstva)
• Committee member: Stjepan Šebek (član povjerenstva)
• Committee member: Filip Martinović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2024-06-24, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U radu se opisuju dvije metode prezentiranja rotacija u 3D svijetu, jedna metoda je opis rotacija preko Eulerovih kutova dok je druga metoda, opisivanje rotacija koristeći kvaternione. Detaljno se opisuju obe metode, također opisana su svojstva svake od metoda. Prikazani su i načini kako iz jednog sustava prijeći u drugi (jedna metoda opisa u drugu). Razmatranje razlika tih dviju metoda te usporedba jedne u odnosu na drugu. Opis kako se jedna, a kako druga metoda može koristiti za interpolaciju. Za potpunije razumijevanje izgrađena je aplikacija gdje korisnik može rotirati objekt u 3D prostoru modifikacijom Eulerovih kutova ili kvaterniona te vidjeti kako promjena jedne komponente utječe na promjenu drugih, također moguće je vidjeti kako izgleda kad se izazove gimbal lock na objektu.

Abstract (english)

The paper describes two methods of presenting rotations in the 3D world, one method is the description of rotations via Euler angles, while the other method is the description of rotations using quaternions. Both methods are described in detail, the properties of each method are also described. Ways to convert from one system to another (one method of description to another) are also shown. Consideration of the differences between these two methods and a comparison of one in relation to the other. Description of how one and how the other method can be used for interpolation. For a more complete understanding, an application was built where the user can rotate the object in 3D space by modifying the Euler angles or quaternions and see how the change of one component affects the change of others, it is also possible to see what it looks like when gimbal lock is triggered on the object.

• Keywords: 3d rotacija; kvaternioni; eulerovi kutovi; interpolacija; gimbal; gimbal lock; ins; imu; slerp
• Keywords (english): 3d rotation; quaternions; Euler angles; interpolation; gimbal; gimbal lock; ins; imu; slerp
• Language: croatian
• URN:NBN: urn:nbn:hr:168:717563
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2024-10-12 21:05:45