I apologise in advance if the question is not clear. Suppose I have 4 points on the X-Y plane. Their relative positions with respect to each other are fixed. So any 2 points will have a fixed distance away from each other. In a short time interval, the X-Y plane undergoes a small rotation about a certain unknown point resulting in the displacement of the 4 points as shown in the image attached. If the displacement vectors of the 4 points are given, is it possible to calculate the angle of rotation of the X-Y plane? The axis of rotation is unknown.An illustration of what I mean can be found here Ideally I wish to find a mathematical expression with the displacement vectors with which i can compute the angular displacement.
2026-03-26 09:45:56.1774518356
Finding angular displacement from displacement vectors
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Hint:
The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.
Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.