相关论文: Triangulation of Simple 3D Shapes with Well-Center…
We propose a template-driven triangulation framework that embeds raster- or segmentation-derived boundaries into a regular triangular grid for stable PDE discretization on image-derived domains. Unlike constrained Delaunay triangulation…
Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is…
Standard PolyCube-based hexahedral (hex) meshing methods aim to deform the input domain into an axis-aligned PolyCube volume with integer corners; if this deformation is bijective, then applying the inverse map to the voxelized PolyCube…
The Sierpinski tetrahedron has a remarkable property: It is projected to squares in three orthogonal directions, and moreover, to sets with positive Lebesgue measures in numerous directions. This paper proposes a method for characterizing…
The zero level set of a piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in $\mathbb{R}^3$ is a piecewise-planar hyper-surface. We prove that if a family of consistent tetrahedral subdivions…
This paper presents a method to generate high quality triangular or quadrilateral meshes that uses direction fields and a frontal point insertion strategy. Two types of direction fields are considered: asterisk fields and cross fields. With…
A novel meshing scheme, based on regular tetra-kai-decahedron, also referred to as truncated octahedron, cells is presented for use in spatial topology optimization. A tetra-kai-decahedron mesh ensures face connectivity between elements…
Many time-dependent problems in the field of computational fluid dynamics can be solved using space-time methods. However, such methods can encounter issues with computational cost and robustness. In order to address these issues,…
Triangle-hinge models [arXiv:1503.08812] are introduced to describe worldvolume dynamics of membranes. The Feynman diagrams consist of triangles glued together along hinges and can be restricted to tetrahedral decompositions in a large N…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
The space of shapes of a polyhedron with given total angles less than 2\pi at each of its n vertices has a Kaehler metric, locally isometric to complex hyperbolic space CH^{n-3}. The metric is not complete: collisions between vertices take…
If a finite element mesh contains concave elements, it is said to tangled. Tangled meshes can occur during mesh generation, mesh optimization, and large deformation simulations, and will lead to erroneous results during finite element…
0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation or M can be shown to be one of the…
We propose an approach to find constant curvature metrics on triangulated closed 3-manifolds using a finite dimensional variational method whose energy function is the volume. The concept of an angle structure on a tetrahedron and on a…
This paper will extend a known relationship between the circumradius and dihedral angles of a tetrahedron in three-dimensional Euclidean space to three-dimensional affine space over a general field not of characteristic two, using only the…
Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i -…
Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists mathematicians for centuries. Recently, organizing principles for the types of structures associated with the…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.