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Reconstructing High-Order Surfaces for Meshing

Jiao, Xiangmin and Duo Wang

Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.143-160, October 3-6 2010

INTERNATIONAL
MESHING
ROUNTABLE

19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

Department of Applied Mathematics,
Stony Brook University,
Stony Brook, NY 11794,

Summary
We consider the problem of reconstructing a high-order surface from a given surface mesh. This problem is important for many meshing operations, such as generating highorder finite elements, mesh refinement, mesh smoothing and mesh adaptation. We introduce two methods, called Weighted Averaging of Local Fittings (WALF) and Continuous Moving Frames (CMF). These methods are both based on weighted least squares polynomial fittings and guarantee C0 continuity. Unlike existing methods for reconstructing surfaces, our methods are applicable to surface meshes composed of triangles and/or quadrilaterals, can achieve third and even higher order accuracy, and have integrated treatments for sharp features. We present the theoretical framework of our methods, experimental comparisons against other methods, and its applications in a number of meshing operations.

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