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Space Transformations

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Hey guys, I am not sure if such a thing is possible, but here goes. Suppose I have a triangle formed by three vertices. Each vertex has a velocity. So the shape of the triangle is changing as the three vertices move. Now is it possible to transform the space/three velocities such that the shape of the triangle does not change or remains constant? Supposing the above was possible, then I would be able to tackle my problem of triangle-vertex collision as follows: a) Since the shape of the triangle is not changing, the triangle has one uniform velocity. b) Apply the same transformation to the vertex, not both of them are in the same vector space. Compute the collision detection (this has become a linear problem in time now). Thanks!!

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