Bijective and coarse high-order tetrahedral meshes

Abstract

We introduce a robust and automatic algorithm to convert linear triangle meshes with feature annotated into coarse tetrahedral meshes with curved elements. Our construction guarantees that the high-order meshes are free of element inversion or self-intersection. A user-specified maximal geometrical error from the input mesh controls the faithfulness of the curved approximation. The boundary of the output mesh is in bijective correspondence to the input, enabling attribute transfer between them, such as boundary conditions for simulations, making our curved mesh an ideal replacement or complement for the original input geometry.

The availability of a bijective shell around the input surface is employed to ensure robust curving, prevent self-intersections, and compute a bijective map between the linear input and curved output surface. As necessary building blocks of our algorithm, we extend the bijective shell formulation to support features and propose a robust approach for boundary-preserving linear tetrahedral meshing.

We demonstrate the robustness and effectiveness of our algorithm by generating high-order meshes for a large collection of complex 3D models.

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Index Terms

• Computing methodologies

  • Computer graphics

    • Shape modeling

• Mathematics of computing

  • Mathematical analysis

    • Numerical analysis

      • Mesh generation