I originally posted a much simpler (and less helpful) question, and have edited this to be more specific.
This animation from wikipedia shows basically what I want to accomplish, however - I'm hoping to have it flipped around, where it starts progressing more towards the destination and "up" (in this image), and then arcs more directly to the end point. However, I only have access to a starting point and ending point, what I am hoping to do is be able to determine the other points by specifying a "height" (or width, whatever you want to call it), to determine how high the arc actually goes. http://en.wikipedia.org/wiki/File:Bezier_3_big.png (can't post image due to low rep)
I would like to be able to call a function with the start and end points and a height, and have it return all the points along the way of the curve.
Help or direction would be appreciated.
Without loss of generality, suppose the ending point is on the x axis and the starting point is above and to the left of the ending point.
Imagine the starting point is at the top of a cliff, and the ending point is at the bottom of a cliff. Imagine you throw a ball horizontally from the starting point, such that gravity will pull it down so that it smacks exactly into the ending point.
That curve seems to have the properties you want. It starts shallow and then increases towards the vertical as the ball accelerates.
By changing the angle at which you throw the ball initially you can make the curve more shallow at the beginning. By changing the strength of gravity you can make it more steep at the end.
Does that curve fit your needs? Finding that curve is a pretty basic physics problem.
