Interleaving Delaunay refinement and optimization for practical isotropic tetrahedron mesh generation

Abstract

We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewise smooth surfaces. Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria. This interleaving is shown to be more conservative in number of Steiner point insertions than refinement alone, and to produce higher quality meshes than optimization alone. A careful treatment of boundaries and their features is presented, offering a versatile framework for designing smoothly graded tetrahedral meshes.

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Index Terms

• Computing methodologies

  • Artificial intelligence

    • Computer vision

      • Image and video acquisition

  • Computer graphics

    • Image manipulation

    • Rendering

    • Shape modeling

• Mathematics of computing

  • Mathematical analysis

    • Numerical analysis

      • Interpolation

• Theory of computation

  • Randomness, geometry and discrete structures

    • Computational geometry