I have a set of points that are used to draw a shape. I want to rotate this shape without moving its start and end points. I tried to illustrate what I want in the image below (original shape on left, interpolated on right). Are there any algorithms to do that? I researched Hermite Spline and Bezier Curves but I did not think they are applicable in my problem.My goal is achieving this action with only 2D transformations: 
Rotating a set of points around two fixed points
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