Primjena matematike u izradi računalnih igara

master's thesis

• Author: Kristian Golubić
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu su opisani različiti tipovi problema s kojima se programer može susresti prilikom izrade igre. To je najprije reprezentacija objekata na računalu te prevođenje objekta iz trodimenzionalnog svijeta u dvodimenzionalni. Objašnjen je problem prepoznavanja sudara dvaju objekata. U radu je detaljno opisano rješenje tog problema pomoću smještanja objekata u sferu ili AABB objekt, a spomenuta su još neka moguća rješenja. Opisan je problem pronalaženja najkraćeg puta kao i njegovo rješenje Dijkstrinim algoritmom te različitim implementacijama grafa. Naglašena je važnost strategije u igri te je opisan minimax algoritam za strategiju igranja savršeno informiranih determinističkih igara za dva igrača, kao i njegova optimizacija. Također, u radu je spomenuta važnost fizikalnih zakonitosti i njihovih primjena prilikom izrade igre.

Abstract (english)

This paper describes various problems which programmers face during the process of creating a video game. The first problem is representation of objects in a computer and turning objects from the three-dimensional to the two-dimensional space. The problem of collision detection of two objects is also explained. The paper describes solutions of that problem using a sphere or an AABB object as surrounding objects. In the paper are mentioned some other solutions, too. It describes the shortest path problem and the solution using Dijkstra’s algorithm and various implementations of graphs. This paper emphasizes the importance of strategy in the game and describes minimax algorithm for deterministic games where two players are perfectly informed. There is also mentioned importance of physical laws and their use during the process of creating a video game.

• Keywords: izrada računalne igre; problem prepoznavanja sudara dvaju objekata; problem pronalaženja najkraćeg puta; Dijkstrin algoritam; strategija
• Keywords (english): creating a video game; problem of collision detection; shortest path problem; Dijkstra's algorithm; strategy
• Language: croatian
• URN:NBN: urn:nbn:hr:217:939160
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-25 08:49:53