FPS stair climbing...

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Shambler
 #1
Store the target Y distance off the ground that you want the camera to reach, e.g. PlayerHeight.

Then you just code something like
 If CameraY<PlayerHeight then CameraY=CameraY+(PlayerHeight-CameraY)/10)


This will smoothly move the camera into position.

If the camera does not move into position fast enough just reduce the 10 to a smaller value.