In Houdini, here are a couple of ways to fire
a ball from one point, fly into the air, and have it land in at a
given point. These are both available in the hip file here.
The first method is to use a ray sop and a user
defined curve. The arc of the ball depends on the initial
velocity. Description here.
The second method is a simplified mathematical relationship
described below:
Math
behind shooting a ball with distance, frames and vertical
velocity control
The diagram above shows equal increments in x, so if we use the
frames as the total time, the change in x is:
Note that frames is the total number of frames and
frame is the current frame.
dx = distance / frames
The change in y is equal to the y component of the starting
velocity, call it vy, minus the current frame times (2 * vy) /
frames. Written as:
dy = vy - frame * (2 * vy ) / frames
This makes sense since dy(0) = vy, dy(1/2 frames) = 0 at the top
of the curve, and dy(frames) = -vy
