Bouncing a ball off a wall with arbitrary angle?

问题:

I'm trying to let the user draw a paddle that they can then use to hit a ball. However, I cannot seem to get the ball to bounce correctly because the x and y components of the ball's velocity are not lined up with the wall. How can I get around this?

I tried the advice given by Gareth Rees here, but apparently I don't know enough about vectors to be able to follow it. For example, I don't know what exactly you store in a vector - I know it's a value with direction, but do you store the 2 points it's between, the slope, the angle?

What I really need is given the angle of the wall and the x and y velocities as the ball hits, to find the new x and y velocities afterwards.

回答1:

Gareth Rees got the formula correct, but I find the pictures and explanation here a little more clear. That is, the basic formula is:

Vnew = -2*(V dot N)*N + V
where
V = Incoming Velocity Vector
N = The Normal Vector of the wall

Since you're not familiar with vector notation, here's what you need to know for this formula: Vectors are basically just x,y pairs, so V = (v.x, v.y) and N = (n.x, n.y). Planes are best described by the normal to the plane, that is a vector of unit length that is perpendicular to the plane. Then a few formula, b*V = (b*v.x, b*v.y); V dot N = v.x*n.x+v.y*n.y, that is, it's a scalar; and A + B = (a.x+b.x, a.y+b.y). Finally, to find a unit vector based on an arbitrary vector, it's N = M/sqrt(M dot M).

If the surface is curved, use the normal at the point of contact.