Abstract
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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Alliez, P. (2007). Quadrangle Surface Tiling Through Contouring. In: Martin, R., Sabin, M., Winkler, J. (eds) Mathematics of Surfaces XII. Mathematics of Surfaces 2007. Lecture Notes in Computer Science, vol 4647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73843-5_2
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DOI: https://doi.org/10.1007/978-3-540-73843-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73842-8
Online ISBN: 978-3-540-73843-5
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