如何计算球的下一方向

Question

I don't know how to calculate the next direction of a ball when it touches to wall.

Example the ball is moving X +5 and Y +3 but after when it touches to wall, the direction should change like on real life. (Like a billiard)

http://i.stack.imgur.com/Y5AOZ.png

Answer 1

The simplest simulation mechanic is: if you hit a side wall, multiply x velocity by -1 . If you hit a top or bottom wall, multiply y velocity by -1 .

Assuming your rails are a rectangle comprised of lines that are parallel to the x-axis or y-axis of your coordinate system (ie straight lines), then this will satisfy the angle of incidence = angle of reflection constraint. If not, then you have to do some math involving the angles.

You may also want to consider the impulse of the walls and the friction between the ball and the surface of your table to calculate how much slower the ball moves after a collision and over time. Otherwise your balls won't stop moving. Both of these would (most likely) be a simple constant that affects both the x and y components of your velocity in the same way (ie multiply both by the same constant, eg 0.99 for friction, etc). This should give you a reasonably accurate simulation, with some tuning.

Answer 2

Real life physics has the angle of incidence equalling the angle of reflection. In other words, if the ball comes in at a 30 degree angle, it is bounced out at a 30 degree angle.

You need two points (on the ball's path) to calculate the angle that it hits the wall. Use that same angle as the "reflection angle". Make sure you adjust as needed to use the same frame of reference for everything.

The routine that calculates the next position of the ball is responsible for keeping it on this track.

Basic algebra and trig gives you the equations that you solve to get the values you need. For example, the slope (angle) of a line is given by y = mx + c. (y,x are the coords, m is the slope, c is a constant). This is pretty straightforward - it's just basic algebra.