# How to calculate a Bézier curve with only start and end points?

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.

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Can you post a sketch of what you are trying to accomplish? Also, you could look into quadratic Bézier curves. –  Rahul Oct 28 '10 at 4:32
Well, a (cubic) Bézier requires four points, so as it stands, you still have two degrees of freedom for your problem. You might have to think about how to position those other two points to get what you want. –  Ｊ. Ｍ. Oct 28 '10 at 4:37
en.wikipedia.org/wiki/B%C3%A9zier_curve#Generalization In a parametric equation, $x=B(t)$, and $y=B(t)$ –  muntoo Oct 28 '10 at 5:16
If I'm reading this correctly, he wants a cubic bezier identical to the one in the picture but reflected across the $y$ axis, and scaled vertically (fixed at the start and end points). He wants to be able to have the two other points in the bezier a function of the height (vertical scale) of the curve. –  Justin L. Oct 28 '10 at 5:48