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.
Help or direction would be appreciated.
I had a related problem, where I knew the four points (start, end, two control points) and needed to generate the height (which it turns out is called the Sagitta). Here's my question:
Find sagitta of a cubic Bézier-described arc
My maths isn't strong enough to work it backwards, but you may be able to decode it from one of the very helpful answers there.