Calculus in video games

by Cody Casasata

Submitted : Spring 2017

Calculus is vital for video game programming. When taught alongside Physics, gives you the background necessary to understand crucial elements to game design. More specifically how objects can interact and move using concepts from calculus including derivatives, integrals, as well as the inclusion of sequencing.  In this project, I explored the use of calculus the development of games and virtual simulations, and how it has enhanced the realism of gaming in recent years. During my exploration, I used my basic understanding of physics and calculus to derive equations of motion for an object launched at an angle. This is but one of the numerous possible physical interaction between objects in a game or simulation. Furthermore, I incorporated the newly derived formulae into a program that would calculate the total horizontal distance covered by an object launched at an angle. This value would change depending on the initial velocity of the object, the amount of time it spends in the air, and the angle at which it is launched. For simplicity reasons, I chose to neglect air resistance in my calculation as its effect can be minimal depending on the mass of the object in question. I could draw numerous conclusions on how game developers use calculus to produce more physically accurate virtual environments.

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