### Review: Collision Geometry

In this tutorial we will give a mathematically sound review of the concepts and geometrical objects used in previous tutorials to handle collision detetion.

"Most good programmers do programming not because they expect to get paid or get adulation by the public, but because it is fun to program."

In this tutorial we will give a mathematically sound review of the concepts and geometrical objects used in previous tutorials to handle collision detetion.

Particle Systems are physics models that model small particles. Long ago those systems have been introduced to game engines and are the foundation of creating a realistic looking environment. They are great to, for example, model explosions, vapor trails and general lights in a game.

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

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.

This tutorial introduces the notion of friction. Basically speaking, friction is any force that retards or consumes energy from another system - like Facebook.

A projectile is an object that is launched into motion and then allowed to follow a path determined solely by the influence of gravity. Air resistance and the Earth's rotation are ignored for the moment.
Projectile movement is implemented in C++ using symplectic Euler integration.

This tutorial extends our study of kinematics to motion in two dimensions, allowing for a wider range of physical phenomena to be simulated with our symplectic integrator.