Reblog: Making Your Balls Bounce

Neil Brown’s “The Sinepost” blog here talks about an application of mathematics I’ve long found interesting but never really studied, that of how to simulate physics for game purposes. This particular entry is about the collision of balls, as in for a billiard ball simulation.

It’s an interesting read and I do want to be sure I don’t lose it.

The Sinepost

In this post, we will finally complete our pool game. We’ve already seen how to detect collisions between balls: we just need to check if two circles are overlapping. We’ve also seen how to resolve a collision when bouncing a ball off a wall (i.e. one moving object and one stationary). The final piece of the puzzle is just to put it all together in the case of two moving balls.

Bouncy Balls

The principle behind collision resolution for pool balls is as follows. You have a situation where two balls are colliding, and you know their velocities (step 1 in the diagram below). You separate out each ball’s velocity (the solid blue and green arrows in step 1, below) into two perpendicular components: the component heading towards the other ball (the dotted blue and green arrows in step 2) and the component that is perpendicular to the other…

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