Our algorithm computes two piecewise smooth harmonic scalar functions, whose isolines tile the input surface into well-shaped quadrangles, without any T-junctions. Our main contribution is an extension of the discrete Laplace operator which encompasses several types of line singularities. The resulting two discrete differential 1-forms are either regular, opposite or switched along the singularity graph edges. We show that this modification guarantees the continuity of the union of isolines across the lines, while the locations of the isolines themselves depend on the global solution to the modified Laplace equation over the whole surface.
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