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In After Effects, I want to animate an object from a position A = (960, 540), being the center of my 1920x1080 composition, to a position B = (960 - offset, 540) to the left, where offset is a positive number. My composition will be used as Motion Graphics template, so this offset needs to be adjustable with a Slider Control so that users can tweak the amount of movement.

In this question, a method is shown where a slider can be used to interpolate between two positions. However, I want to have the temporal interpolation to be predefined, and it is more complicated than the simple linear or ease interpolation that expressions allow for.

Thus, I want to be able to set the keyframe values with the slider, but I want the keyframe interpolation to be done with the graph editor. How can I make this work?

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Use the values of the keyframes as the driver for a linear expression, and scale them with the slider:

const firstKF = thisProperty.key(1); //which KeyFrames to use as the driver
const lastKF = thisProperty.key(2); // NB you could use multiple keyframes with this expression
const initialValue = [960, 540]; // the start pos—could also use [thisComp.width, thisComp.height]/2
const offsetAmt = thisLayer.effect("offset slider")("Slider"); //pickwhip the slider control here
const finalValue = initialValue + [offsetAmt, 0];

linear(value, firstKF, lastKF, initialValue, finalValue)

This will scale the original motion as you've keyframed it to match the motion with the offset applied.

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