One of the basic areas of both video game and animation is designing 3D images on a computer using mathematical formulas. Made from a combination of polygons, these images can range from a rabbit to a junk heap. It's these polygons that the images the player sees, from the character to the scenery to the enemies and obstacles, are made of. Where objects are located, and where the character is in reference to those objects, is all decided by mathematical formulas. Even in basic, 2D games, math is what tells the game whether or not the character jumped onto a solid platform, or fell into a hole.
Another area of video game development that uses math is the design of the physics of the world. Whether the game world is a simple or complicated one, there are still necessary physics that must be applied. If a player pushes the jump button, then how high the character will jump has to be decided. If a soccer ball is kicked, it can't go in a straight line, so the programmer must apply necessary algorithms to decide the drag speed of gravity, how the ball will slow over distance, and so on. The same can be said for first-person shooters, which have to figure in drag and drop for bullets fired over a long distance.
How much damage a character takes from certain actions requires mathematical formulae. For instance, falling from a certain height has to be figured in, especially if falling from greater heights does more damage. In addition, simple math, like how many points a character may earn for performing certain actions, has to be figured in mathematically. Also, the way a character's life bar or hit points works is decided by math. In roleplaying games, where a character has a certain "to-hit" percentage decided by their stats, there must be a mathematical formula to decide the chance that the character does, in fact, hit his or her enemy.
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