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Analysis of Non-Meshable Automatically Generated Frame Fields

Viertel, Ryan, Matthew Staten, Franck Ledoux

Research Note, 25th International Meshing Roundtable, Sandia National Laboratories, September 26-30 2016


25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016

Ryan Viertel, Sandia National Laboratories, US,
Matthew Staten, Sandia National Laboratories, US,
Franck Ledoux, Commissariat Energie Atomique, FR,

Research Note Abstract
Recent methods for frame field generation in two and three dimensions are reviewed. Frame fields generated automatically in 2D and 3D are analyzed with respect to quad and hex mesh generation. Problems are identified with automatically generated frame fields that prevent mesh generation via current methods. Specifically, there exist geometries that contain limit cycles and cannot be parameterized or decomposed by separatrices of the frame field. In 3D, singularity lines occur that minimize the field curvature but do not align with the frame field. These types of singularities make it impossible to create a mesh that both follows the frame field, and simultaneously respects the singularity as an irregular node in the mesh. Specific examples are presented that illustrate these problems. For each example, streamlines are used to help visualize properties of the frame fields, problems are analyzed, and options to potentially mitigate such problems are discussed.

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