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Manual Curve Equation?

I know there are lots of ways to create a Curve but wondering how I can manually. Anyone know a Math site explaining this? Also maybe implementing it.

I have distance / height & speed but need the formula …
Curve

For more explination, it’s more for acceleration to clear an object.

There’s lots of names for it: Falloff, Curve, Interpolation, etc. It’s all about the how the value changes over time.

Squirrel over at GMU has some amazing GDC talks on this topic. This one deals with “curves” Math for Game Programmers: Fast and Funky 1D Nonlinear Transformations - YouTube

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Thanks will watch.