Mathematics

Total 15 Posts
This tag aggregrates all tutorials about the beauty of mathematics!

Intersection of Line Segments

In this tutorial we improve the collision detection "algorithm" of the previous tutorials by restating the problem as a line or segment intersection problem.

Basic Ad Hoc Collision Response

In this tutorial the equation of reflection off of any hypersurface, i.e. off a line in 2D and off a plane in 3D, is derived from the known observation that the angle of incidence equals the angle of reflection.

The Berlekamp - Massey Algorithm

This tutorial introduces linear feedback shift registers (LFSR) and explains the Berlekamp - Massey algorithm to find the shortest LFSR for a given binary output sequence. An implementation of the algorithm in C++ is provided as well.

Galileo versus Newton

The goal of this tutorial is to define and investigate the structure of space-time and the corresponding group of transformations and to analyze the constraints imposed by Galileo's principle of relativity on Newton's equation of motion.

Of Planes and Triangles

This tutorial explains how to describe planes as two-dimensional subspaces of the standard euclidean space, both in parametric and in normal form, as well as how to compute the normal vector of a triangle.

The Centroid of Convex Polygons

While the centroid of a polygon is indeed its center of mass, the mass is uniformly distributed over its entire surface, not only at the vertices. This tutorial explains how to compute the coordinates of the centroid of a convex polygon.

And then, there was sound

This tutorial briefly explains the key physical concepts of sound as well as how to set up a basic sound system for games.