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Triangle mesh generation combining edge splitting and angle-based smoothing

Johnson, Samuel, Robert Renka

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

INTERNATIONAL
MESHING
ROUNTABLE

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

Samuel Johnson, University of North Texas, US, samuelbjohnson@live.com
Robert Renka, University of North Texas, US, robert.renka@unt.edu

Poster Abstract
We describe a simple mesh generation method which alternates between refinement using long edge bisection, and optimization combining Delaunay edge swaps with a new, efficient angle-based smoothing procedure. We compare our method to the existing method described by Tournois et al. (2009), which considers the following problem: Given geometric constraints and a size constraint defined by a function which restricts maximum edge length, we seek to generate meshes with the highest triangle quality and the fewest additional vertices possible. We improve upon this existing method by replacing the slowly converging Centroidal Voronoi Tesselation optimization with a much faster method involving minimization of a weighted sum of squared simplex volumes. We also improve upon the refinement step by splitting edges one at a time, prioritizing the longest edges first, reducing the number of Steiner points. Our test cases included a wide variety of starting meshes, varying by domain boundary complexity and number of vertices, and accounted for both constant and variable sizing functions. Results across all test cases demonstrate that our method consistently reduces the number of Steiner points and runs significantly faster, while retaining similar triangle quality measures, when compared to the existing approach.

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