## Friday, 17 February 2012

### Why circles (and spheres)?

One interesting question is: "Why are circles (and by extension spheres) better for games?". I don't just mean computer games but a wide variety of games and sports use balls: marbles, billards, tennis, pétanque and football. Still more use circles: curling, shuffleboard and air-hockey.

It's not that they roll better. Curling and air hockey show two ways to overcome roll resistance, and few of these contests are concerned with balls travelling great distance. Besides in such games the maximum distance is achieved through the air not on the ground.

The reason is that collisions involving circles and spheres are much simpler than those involving any other shape. So much so that they are easily understood intuitively, in games like billiards but also by anyone kicking a ball or hitting one with a bat. Even mathematically advanced concepts like drag and topspin can be easily understood.

Compare this to the dynamics of one of the simplest other shapes, a cube. Drop a cube on a surface and its motion is so complex that it seems chaotic. Add in a bit of initial uncertainty and enough energy and the outcome of the motion, measured by which side it finally comes to rest on, is essentially random. Which is how dice work.

(It's worth noting that there's a big difference between 2D and 3D dynamics for squares and cubes – the latter is an order of magnitude more complex. It's only circles and spheres that can be treated essentially the same way)

The implication for game design is if game objects are all round it is far cheaper and easier to simulate their motion in a plausible way. This also generates much more predictable results for players, which can make the game seem less random and arbitrary. It's noticeable for example that many of the 2D physics Flash games out there are stacking games. They have a full 2D collision engine, then constrain the game so it only works if things don't rotate, almost like sticky balls.