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Suppose I drawn a set of objects that will fill an angular wedge of approximately 58° of a circumscribed circle.

Now I want to stretch these object so that they fill a wedge of exactly 60°; more formally I want to scale the polar angle of polar coordinates of the control points. [Later I want to replicate these object 6 times to fill an entire circle.]

Is this possible?

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Draw a 60 degr. reference wedge and put your image there. Warp your image:

Object > Envelope Distort > Make by Warp > Arc, vertical, preview, bend=0

Finally rotate the warped object. Undo and repeat, if not near enough.

enter image description here

No rotation is needed, if you position the original and the reference so that the half angle is horizontal The Smokeman sits on a horizontal surface, so it's easier to rotate him back.

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