The _GeometricTransform
could have the method
@abstractmethod
def jacobian(self, coords)
which returns the Jacobian matrix Jacobian matrix and determinant - Wikipedia for the given points. This can for example be used for optimisation methods as least_squares — SciPy v1.14.0 Manual.
I think it is rather straight forward to implement for the different transformations.
Do you think this is a valuable contribution or is it too specific? If wanted I can take care of the implementation.