Seemingly simple ball & line collision?

I have a开发者_Go百科 ball accelerating due to gravity 9.81. I also have some lines, which can be moved around and have their slopes changes by the user. How do I handle bouncing collisions between the ball and the lines to make them bounce off at the correct angle. All my collision detection works fine, I was just wondering if there was a way of using the slope of the line to find the resultant vector of the ball after collision.

I am writing in Objective-C with XCode 4 on Mac OS 10.6.8

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I think you need the "normal" vector of the "surface" with which the ball collided, and then "flip" the "velocity" vector of the ball accordingly.

To clarify: The "normal" of the line is a perpendicular vector to the line, of unit length. Think of it like: The line represents a plane, which would have a normal vector.

From the top of my head: Let N be the normalized (unit lenght) "normal" vector of the line, let v be the velocity vector of the ball.

1. Project v onto N using a dot product (p = v DOT N)

2. Add the vector 2*p*N to v (v = v + 2*p*N)

I think that should do the trick...

I would also recommend using a physics engine as already pointed out.

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Have you considered enlisting one of the handful of engines out there to do the dirty work for you? Cocos2D, Box2D and Chipmunk are three that come to mind.

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The easy way to do it (in my opinion):

• When you create the line calculate the matrix that would rotate it to be horizontal and calculate the inverse of that matrix.
• When the ball collides with the line:
  1. rotate the velocity vector by the rotation matrix
  2. change the sign of the y component
  3. rotate the velocity vector by the inverse of the rotation matrix.

The rotation matrix is given by:

( cos A ,  sin A )
( -sin A , cos A )

The inverse rotation matrix is given by:

( cos A , -sin A )
( sin A ,  cos A )

where A is the angle between the line and the horizontal.

The above uses standard mathematical conventions (positive x and y is the upper right quadrant, 0 radians is in the positive direction along the x axis and angles increase anticlockwise.