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Re: Some simple 2d gamerelated maths questionsby moritz (Cardinal) 
on Aug 27, 2008 at 21:29 UTC ( #707321=note: print w/replies, xml )  Need Help?? 
First of all the game is quite nice, but there's a simple method with which you can win every level pretty fast, which kind of kills the fun as it is now.
<Reveal this spoiler or all in this thread>
How can I tell whether the circular sprit intersects with an arbitrary line. I don't know how familiar you are with linear algebra, it really helps ;) (Update: When I talk about "points", I really mean "position vectors to points". Thanks FunkyMonk) I'll call the end points of your line A and B, the center of your sprite M, the point on the line which is the closest to M is called C (all those are vectors), the radius of the sprite is r (a scalar value). Since C is on the line between A and B, it must be expressible in the form A + x * (BA). Since it's the closest point to M, the connection line from C to M is perpendicular to the original line, or as a formula:
The only unknown part in this equation is x, which you can calculate from that equation, but to which I'm too tired at the moment. If 0 <= x <= 1 and M  C < r, then it circle touches or intersects the line. Likewise if MA <= r or MB <= r it also touches or intersects. In all other case it doesn't. To get a realistic bouncing behaviour, the angle between (dx, dy) and (MC) after the bounce has to be negative of what it was before the bounce.
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