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Idea: Split input mesh into multiple (approximately quadratic) patches. Compute a discrete harmonic parametrization for each one. Some vertices will have neighbors which lie in another patch. The requirement for harmonic parametrization

must take this into account.

Introduce transition functions which represent the transformation between patches and .
transforms the parameter which is given in the local coordinates of patch into the local coordinate system of patch .

Obviously, and

Thus, the harmonic parametrization system becomes:


Problem: For vertices close to patch corners, the transformation used to map neighbors to the local coordinate system might be ambiguous.
Solution: Fix parameters of corner vertices to the patch corners. Let the remaining vertices relax.