Robust Field-aligned Global Parametrization: Supplement 1, Proofs and Algorithmic Details
نویسندگان
چکیده
Torus with a single 3-5 pair. The nonexistence of a quadrangulation with a single 3-5 pair for a torus has been proved in [Barnette et al. 1971]. Remarkably, [Jucovič and Trenkler 1973] shows that for any choice of non-regular vertex valences, constrained by the formula for Euler’s characteristics, and any genus other than 1, a quadrangulation with vertices with these valences exists (if vertices of valence 4 can be added); and for tori, the 3-5 pair is the only exception. We note that this does not guarantee that for any vector field there is a quadrangulation consistent with it, as the topology of the field also includes holonomies along non-contractible loops.
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