Abstract
S. Mitchell proved that a necessary and sufficient condition for the existence of a topological hexahedral mesh constrained to a quadrilateral mesh on the sphere is that the constraining quadrilateral mesh contains an even number of elements. S. Mitchell’s proof depends on S. Smale’s theorem on the regularity of curves on compact manifolds.
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References
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Carbonera, C.D., Shepherd, J.F., Shepherd, J.F. (2006). A Constructive Approach to Constrained Hexahedral Mesh Generation. In: Pébay, P.P. (eds) Proceedings of the 15th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34958-7_25
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DOI: https://doi.org/10.1007/978-3-540-34958-7_25
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