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I'm trying to do approximate matching of one plane geometry with n points to a big set of other plane geometries. The aim is to get the closest shape (rotation and scale agnostic)

My idea would be to "normalize" all the shapes coordinates in the database to [0-1, 0-1] to omit the scaling correction and than compare it to the given (blue) geometry.

I've looked at a couple of papers of Helmut Alt, especially Discrete Geometric Shapes - Matching, Interpolation and Approximation (under 3.2Approximate Matching) but I can't extract the correct math to a function (I'm trying to do this in javascript)

Maybe someone has an idea on how to do this or a different approach.

Thanks!

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