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Bezier curve conversion between value graph and speed graph

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Hello everyone,

 

I have a question about the formula for graph conversion between value graph and speed graph on Graph Editor. Especially, when those graphs are Bezier Curves.

 

On the value graph you can define the Bezier curve by moving the control points oht x and y axises, which position can be gotten as spacial tangent values by the AE SDK. On the other hand, on the speed graph you can define the curve by moving the control points only on x axis and these are defiend by these two values "speed" and "influence". (please refer the defenition of AEGP_KeyframeEase). I guess, the speed graph is differentail of value graph mathematically, and I would like to know how those two bezier curves are converted each other. especially, given two control points on speed graph, how do you get the two control points on value graph?

 

スクリーンショット-2013-12-19-1.21.14.jpg

 

The reason why I am trying to figure out this formula is that there is only Speed Graph for path animation on Graph editor. As you can see below, even if Value Graph is selected the editor shows us Speed graph, which is I guess because the unit of this variation is not a simple unit something like pixel or seconds.

スクリーンショット 2013-12-19 0.53.59.png

 

I know it is not a question about the functions of AE, but more like about mathematics. However, I would really appreciate if someone can shed some light on here or refer me some good website that I can research.

 

Thanks!


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