On the Rigidity of Polygonal Meshes
نویسنده
چکیده
A polygonal mesh is a connected subset of a polyhedral surface. We address the problem whether the intrinsic metric of a mesh, i.e., its development, can determine the exterior metric. If this is the case then the mesh is rigid. Among the non-rigid cases even flexible versions are possible. We concentrate on quadrangular meshes and in particular on a mesh with a flat pose in which the quadrangles belong to a tesselation. It is proved that this mesh admits a self-motion and that all its flexions represent discrete models of cylinders of revolution. These flexions can be generated from a skew line-symmetric hexagon by applying iterated coaxial helical motions.
منابع مشابه
A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes
In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox–de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and doe...
متن کاملSolving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods
In this paper we introduce a discontinuous Galerkin method on polygonal meshes. This method arises from the Discontinuous Galerkin Composite Finite Element Method (DGFEM) for source problems on domains with micro-structures. In the context of the present paper, the flexibility of DGFEM is applied to handle polygonal meshes. We prove the a priori convergence of the method for both eigenvalues an...
متن کاملA new scheme for e cient and direct shape optimization of complex structures represented by polygonal meshes
In this paper, a new shape optimization approach is proposed to provide an e cient optimization solution of complex structures represented by polygonal meshes. Our approach consists of three main steps: (1) surface partitioning of polygonal meshes; (2) generation of shape design variables on the basis of partitioned surface patches; and (3) gradient-based shape optimization of the structures by...
متن کاملThe mimetic finite difference method on polygonal meshes for diffusion-type problems
New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived. The first order convergence rate for the fluid velocity and the second-order convergence rate for the pressure on polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments.
متن کاملAdaptive Bem-based Fem on Polygonal Meshes from Virtual Element Methods
Polygonal meshes are especially suited for the discretization of boundary value problems in adaptive mesh refinement strategies. Such meshes are very flexible and incorporate hanging nodes naturally. But only a few approaches are available that handle polygonal discretizations in this context. The BEM-based Finite Element Method (FEM) and a residual based error estimate are reviewed in the pres...
متن کامل