Figure 4: The push range. The path of the object is shown by the dotted arrow. (a) The (counter clockwise) push range if no friction is assumed between the object and the obstacle. (b) The push range if there is friction between O and the obstacle. (c) The (clockwise) push range if O is pushed around an endpoint of an obstacle (no friction). (d) Pushing cannot continue because P is forced outside the push range by an obstacle.
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