/vr/ - Retro Games

>>3103161
You can go far with just 1s and 0s. Perhaps the most important thing we have learned about the information age is just how useful it is to represent things in the abstract as data and manipulate that data with mathematics.

Think about it. The english alphabet can be interpreted as a base-26ish number system. Thus, if a word is interpreted as a number, you can convert any word into its binary equivalent. In fact, several words taken as a whole themselves can be encoded as a number if you count space as a part of the "english alphabet" base. In this manner, a book for instance can be assigned a unique number.

To address your question, calculus is realized in three ways on a computer: symbolically, analytically, and numerically.

1) Symbolically: the computer manipulates text strings by formal rules to derive results. This is only used for solving theoretical problems with a computer algebra systems, and practically never sees direct application.

2) Analytically: the programmer has a closed form solution that they implement directly. For instance, if you need to know the derivative of x^2, you can precompute 2*x and implement a function that let's you specify x on the fly. Fastest solution and most common solution.

3) Numerically: As soon as you move out of the class room, precious few problems can be solved for analytically. In this case, one must discretize the problem and resort to approximations. For instance, integration hardly ever results in simple formulas, however the definition of the Reimann Integral can be easily implemented to easily evaluate nasty integrals. Computer games use this if analytic solutions aren't available.

Physics and geometry is usually described with a combination of vectors and calculus (uncreatively called vector calculus). Finite dimensional vectors are very easy to realize on a computer. In regards to caluclus, some combination of analytics and numerics is used.

However video game physics can be very easy...

If only the game was this cool.

>>2639437