[gameprogrammer] Bouncing Ball (Sleeping in math class)

Okay, I realize I should have paid better attention (or taken better 
notes) in College Algebra for this, but here's my issue.  I've got the 
"bouncing ball"...  That's easy.  NOW, I want the ball to bounce 
(accurately) off of some arbitrarily sized rectangle in the middle of 
the window.

I've got some bounding-box collision detection going on to determine if 
I need to do something more.  Right about as I finished that, I realized 
how much MORE I needed to do, and that simply swapping the x/y delta 
value would no longer be suitable.  I've looked online, but cannot find 
a tutorial which discusses this.

I need two things.  First, to figure out WHERE the collision hits -- 
which vertex or line segment I need to bounce the ball off of.  Second, 
I need to figure out how to get the NEW vector of the ball's movement.

I can get the plane of reflection:

if sub 'o' is the origin of the ball
and sub 'r' is the point (at radius of circle) of impact

(Yo - Yr) / (Xo - Xr) = slope from center of ball
-(Xo - Xr) / (Yo - Yr) = slope of reflection

But now my problem is this:  how do you reflect a vector across a plane 
that isn't (1, 0), (0, 1), or (x, y)?

Also, will there be any problems because I process the reflection the 
first frame AFTER it happens (meaning that the ball has already 
intersected the square)?  and how do I handle that if need be?

So sorry for asking the (doubtlessly) simple math question et al...

Thanks,
--Scott


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