Mathematics in video games

Image Provided By UnSplash

Video games, from the breathtaking open worlds of Red Dead Redemption 2 to the pixel-perfect jumps of Super Mario Bros., owe much to mathematics, a common ingredient (Lal, 2018). Every jump, explosion, and graphic are part of the sets of equations and algorithms that give birth to the mathematics of the game. Without this, modern gaming would not have come into existence.

Physical simulations are one of the most basic applications of mathematics in video games. Newtonian mechanics forms the basis of how characters walk, jump, and collide. F1 24 and other racing games, for instance, use velocity and friction equations to simulate tire grip, while shooters calculate bullet trajectories using parabolic motion (Eberly, 2010).

Computer graphics is a crucial application involved as well; linear algebra plays a leading role in it, especially in a 3D environment. The objects in a three-dimensional game that are represented as polygons are manipulated using matrices and vectors. This facilitates transformations such as rotation, scaling, and positioning, thus transforming life into complex virtual worlds (Shirley & Marschner, 2021). Moreover, ray tracing, which is intelligently applied to create realistic lighting effects, also depends on geometric algorithms for simulating reflections and shadows. 

Mathematics also governs game AI or artificial intelligence. For instance, elements within a game do not simply move randomly, but as a result of pathfinding algorithms such as A* (A-Star) to find the shortest possible route towards targeted objectives (Millington & Funge, 2018). 

Games like Minecraft and No Man's Sky create unique worlds automatically, without manual design. They utilize procedural generation, which refers to mathematical algorithms that act as noise functions and fractals to generate landscapes, caves, and planets, creating dynamically and randomly unique spaces for the player such that no two players experience the same game (Källén, 2011).

Though difficult to notice, mathematics is really the unseen architect that governs any aspect of gaming, from the physics that dictates a character's movement to the AI that seeks to provide the player with a challenge. With every technological advancement, a suitable mathematical approach to the development of games will ultimately move the boundaries of gaming possibilities. 

References

Lal, A. K. (2018b, October 25). Red Dead Redemption 2 tech analysis: Animations, physics, post-processing effects, weather systems and more. GamingBolt. https://gamingbolt.com/red-dead-redemption-2-tech-analysis-animations-physics-post-processing-effects-weather-systems-and-more 

Artificial Intelligence for games Ian Millington and John Funge. (2009). . Morgan Kaufmann/Elsevier. 

Marschner, S., & Shirley, P. (1970, January 1). Fundamentals of Computer Graphics. Fundamentals of Computer Graphics - Repository Institut Informatika dan Bisnis Darmajaya. http://repo.darmajaya.ac.id/5422/