Field‐Aligned and Lattice‐Guided Tetrahedral Meshing

We present a particle‐based approach to generate field‐aligned tetrahedral meshes, guided by cubic lattices, including BCC and FCC lattices. Given a volumetric domain with an input frame field and a user‐specified edge length for the cubic lattice, we optimize a set of particles to form the desired lattice pattern. A Gaussian Hole Kernel associated with each particle is constructed. Minimizing the sum of kernels of all particles encourages the particles to form a desired layout, e.g., field‐aligned BCC and FCC. The resulting set of particles can be connected to yield a high quality field‐aligned tetrahedral mesh. As demonstrated by experiments and comparisons, the field‐aligned and lattice‐guided approach can produce higher quality isotropic and anisotropic tetrahedral meshes than state‐of‐the‐art meshing methods.