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Conformal mapping

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For quite a while, I've been trying to understand how the Least Squares Conformal Mapping works, specially the "conformal mapping" part... I've read several papers, but I still don't understand them well... somehow, I understand maths much better if I read them as code, than as math terminology.

So far, I understand the whole thing is a projection from one space to another, in which the transform is done using complex numbers as part of the process... the other part of the process involves solving very large linear equations. I've tried to see some code that does the stuff (Blender modifer, and another one I don't remember its name) both do the complex number parts, but also both rely on a third party library to solve the linear equations, so it's not possible to see "the whole thing" in the same piece of source code, and without understanding the latter, I can't understand the former.

My guess is that the complex numbers are used to "weight" different parts of the surface, but the weights are interdependant, so all of them must be solved at the same time, and for that's the linear equation solver..

So, any help? some pseudocode would be great... thanks!

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