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They say:

The timing protocol provides the means of starting an animation a certain number of seconds into its duration using two properties: beginTime and timeOffset. The beginTime specifies the number of seconds into the duration the animation should start and is scaled to the timespace of the animation's layer. The timeOffset specifies an additional offset, but is stated in the local active time. Both values are combined to determine the final starting offset.

I know about timespaces. But I have trouble grasping their words here.

"is scaled to the timespace of the animation's layer."

Lets say I have this: animator speed = 1.0 layer of the animated view's speed = 2.0 superlayer's speed = 2.0 beginTime = 1.0

then it would begin in realtime after 0.25 seconds? (double superlayer speed, which doubles sublayer speed, so we have quad speed. and local speed of animator is 1. so still quad speed.).

And the timeOffset is stated "in the local active time". They mean the time distorted by speed? i.e. if the speed property of the animator object is 1.0, that's the local active time here?

Local active time could really mean a lot of different things to me. For example clock time, or time throughout the timespace hierarchy how it affects the time in the bottom. Would be great if someone could point out the details here.