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Calculating the Distance in 1D, 2D and 3D

Finding the distance between two points is a trivial task in any programming language yet, has a wide range of uses. Some examples include if you would like to check if you are near to a powerup, find the precise distance between you and a checkpoint or even finding out which player an enemy is nearest to for a simple targeting system. In the following examples I will be using pseudo code as well as working C code.