# Browsing by Author "Ni, Saifeng"

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Item Field-Aligned and Lattice-Guided Tetrahedral Meshing(John Wiley & Sons Ltd.) Ni, Saifeng; Zhong, Z.; Huang, J.; Wang, W.; Guo, Xiaohu; Ni, Saifeng; Guo, XiaohuShow more 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.Show more Item Variational Volumetric Meshing(2018-08-29) Ni, Saifeng; Guo, XiaohuShow more Domain discretization, also referred to as mesh generation, is one of the fundamental steps of many computation based applications. Although mesh generation techniques have evolved rapidly over the years, some volumetric meshing problems like sliver suppressing in tetrahedral meshing, field-aligned tetrahedral meshing, and hexahedral meshing are still not fully resolved. In this dissertation, we bring some insights to those problems. This dissertation discusses variational-based methods to tackle mesh generation problems, i.e., we model these problems in the energy optimization framework. An energy which inhibits small heights is proposed to suppress almost all the badly-shaped elements in tetrahedral meshing. By iteratively optimizing vertex positions and mesh connectivity, slivers are harshly suppressed even in anisotropic tetrahedral meshing. Besides that, a particle-based field alignment framework is introduced. Specifically, a Gaussian Hole Kernel is constructed associated with each particle to constrain the formation of the desired one ring structure aligned with the frame field. The minimization of the sum of Gaussian hole kernels induces an inter-particle potential energy whose minimization encourages particles to have the desired layout. A cubic one ring structure leads to high quality hexahedral-dominant meshing. The one ring structures of the Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattice leads to high quality field-aligned tetrahedral meshing. This is the first time both Riemannian distance alignment and direction alignment problems have been considered in tetrahedral meshing. Also, field-aligned tetrahedral meshing better preserves the rotation geometry and also creates better anisotropic meshes.Show more