Harmonic functions for quadrilateral remeshing of arbitrary manifolds

Quadrilateral Remeshing

The use of polygonal meshes, especially triangle meshes, is manifold but a lot of algorithms require the mesh to be structured in a certain way and cannot be applied to an arbitrarily shaped mesh. The process of replacing an arbitrary mesh by a structured one is called remeshing. Triangle meshes with subdivision connectivity are an important class of structured meshes and have been studied thor...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Polyhedral Finite Elements Using Harmonic Basis Functions

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our poly...

Jaal: Engineering a High Quality All-Quadrilateral Mesh Generator

In this paper, we describe the implementation of an open source code (Jaal) for producing a high quality, isotropic all-quadrilateral mesh for an arbitrary complex surface geometry. Two basic steps in this process are: (1) Triangle to quad mesh conversion using Suneeta Ramaswamy’s tree matching algorithm and (2) Global mesh cleanup operation using Guy Bunin’s one-defect remeshing to reduce irre...

Stress Analysis of Skew Nanocomposite Plates Based on 3D Elasticity Theory Using Differential Quadrature Method

In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results f...