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I would like to translate a plane along its normal by using a slider.
I'd like to be able to move this slider that would indicate the distance of the current translation and do the translation in the 3D view. Moving the plane along its normal in the 3D view would also act on the slider and make it change its value so that we can see the quantity of the translation.

Is there anyway to script that?

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You can use custom properties bpy.props.

But I don't see any benefit here.

Simply parent your plane to an empty object. Use the empty to transform the plane and the z-location of the plane to translate the plane along its normal.

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