Anisotropic polygonal remeshing pdf
The 𝕄-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by a tensor. The methods offered in this paper can be used alone or in conjunction with other NPR techniques to improve artistic 3D renderings of arbitrary surfaces. Architectural geometry Most contributions in this ﬁeld are concerned with the optimiza-tion of geometric properties of polygonal meshes approximating a free-form surface. tensor has the property that it measures anisotropic stretch faithfully and penalizes undersampling more severely than oversampling. Our framework is extensively evaluated by optimizing ellipsoid packing and generating appealing geometric structures on a variety of freeform surfaces. Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. Keywords Structured surface mesh generation Æ Anisotropy Æ Remeshing Æ Surface parameterization 1 Introduction Surface meshes are widely used in manufacturing, medical and scientiﬁc applications. Interaction between edges As shown in Figure 2, let us consider a plate in a finite polygonal do- main.
Finite element methods make heavy use of such remeshing algorithms (Kunert, 2002). Applications of discrete curvature have been around a while, for example this PDF  from 2003, so maybe this paper provides theoretical context for existing work. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. In this paper, we introduce a framework for the generation of grid-shell structures that is based on Anisotropic Centroidal Voronoi Tessellations. We emphasize that each new extensive unknown (such as density) needs to be de ned in such a way that the overall process preserves conservation. The analysis we present here follows the technique described by Chan and Elman  and Donato and Chan . Shape-anisotropic polymeric micro- and nanoparticles are of significant interest for the development of novel composite materials, lock-and-key assemblies, and drug carriers. based anisotropic remeshing in terms of inner products and thus is able to naturally extend to using a given Riemannian metric.
Anisotropic and feature sensitive triangular remeshing using normal lifting.
Anisotropic Quad Remeshing Several works have also focused on using quadrangles for remeshing, due to their appealing tensor-product nature. The authors use curvature directions to drive the remeshing process and determine appropriate edges for the remeshed version in anisotropic regions. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. Figure 3: Degeneracy removal for a typical mesh generated by a CAD tesselation unit.
First of all, the remeshing algorithm must be able to deal with wide varieties of input polygonal surfaces. Temperature, flux, convection, radiation, and other time-dependent boundary conditions can be prescribed, as well as unique capabilities for handling gaps, cooling passages, and coupled electrostatics heat transfer (Joule effect) structural analysis. Figure 4: Isotropic remeshing preserves the surface geometry while optimizing the tessellation perferring close-to-equilateral triangles. The improved graph filtering and layout is combined with a novel computer graphics anisotropic shading of the dense crisscrossing array of edges to yield a full social network and scale-free graph visualization system. The latter is an appropriately scaled W 1 2 pWqnorm naturally associated with our problem. Anisotropic graded meshes and quasi-optimal rates of convergence for the FEM on polyhedral domains in 3D.
The mesh coarsening process after clustering can be done in an isotropic or anisotropic fashion. in Generalized barycentric coordinates Chapters on linear solvers, Tutte's embedding thm. Polygonal and radial faults in the same tier have a similar range of maximum throws and spacing but differ in length and aspect ratios. propose a polygonal remeshing method using the intrinsic anisotropy of natural or man-made geometry. Abstract Polygonal meshes are used to model smooth surfaces in many applications. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). The computation of integral invariants used for feature extraction can greatly beneﬁt from the new remeshing approach. Figure 3: Recent results on remeshing, shell animation, medical data compression, and smoothing (2003).
mapping a mesh to a planar domain, has been investigated extensively.
Mesh adaptation can be carried out through two alternative mechanisms, by global remeshing of the entire domain based on meshing techniques, or by local mesh modiﬁcations. Anisotropic Mesh Generation and Adaptation This paper describes a versatile computational program for automatic two-dimensional mesh generation and remeshing adaptation of triangular, quadrilateral and mixed meshes. The majority of work in this area has focused on remeshing with triangle elements, yet quadrilateral meshes are best suited for many occasions, such as physical simulation and defining Catmull-Clark subdivision surfaces. Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The ABLMG-based adaptive mesh generation method proposed in this paper is an anisotropic re-meshing method. Both quantitative analysis and visual results demonstrate the effectiveness of this approach. PROJECTS Polygon Soup Remeshing Implemented the marching cube algorithm to compute triangular mesh from signed distance eld. We present a novel approach to remesh a surface into an isotropic triangular or quad-dominant mesh using a unified local smoothing operator that optimizes both the edge orientations and vertex positions in the output mesh.
Increasing the value to 3 or 4 will create a triangle shaped fiber that is capped off at the end. Our algorithm for adaptive anisotropic remeshing is simple to implement, takes up only a small fraction of the total simulation time, and provides substantial computational speedup without compromising the fidelity of the simulation.
User can point to parts of the original mesh to add a face to the simplified result. eral anisotropic meshes (such as on Fig.1, left, and Fig.2) in the energy norm ~~e;W.
polygon-assisted compression scheme for synthetic images 25, where an image is decomposed into polygonal data and the details, similar to a progressive image. Using this mapping, the remeshing algorithm preserves the user-defined feature vertex correspondence and the shape correlation between the models.
Often these meshes need to be remeshed for improving the quality, density or grad-edness. Due to these wide varieties of applications, the remeshing algorithm must meet many requirements, and none of the existing remeshing algorithms can meet all of the requirements. The scheme can be applied only to synthetic images for which we have polygonal data, while the mesh structure is obtained by analyzing the given image in the progressive image representation. Polygonal Meshes can represent arbitrary topology and re-solve ﬁne detail as found in laser scanned models, for example. A tailored anisotropic remeshing method is also employed to better initialize the optimization and ensure the quality of the result.
Journal of Computational and Applied Mathematics.
However, currently there exist few well-elaborated standard vi-sualization approaches tailored to grid-free methods. A cascade set of geodesic disk ﬁlters rotate on the 2-sphere and col-lect spherical patterns and so to extract geometric features for various 3D shape analysis tasks. Column (b) shows a visualization of the proxies found by a standard remeshing algorithm, while (c)shows theproxies obtained taking symmetryinto account. By ex-ploiting properties of the mapping between a surface ' and its image manifold 'f, one can recognize and extract feature regions. A 44 complete survey of all the remeshing techniques is 45 beyond the scope of this paper. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch.
An “immersed” finite element method based on a locally anisotropic remeshing for the incompressible Stokes problem. estimation of the curvature tensor ﬁeld on a polygonal surface often leads to excessive degenerate points, where anisotropy disappears.
Here we denote by in the in ow boundary and by out the out ow/no-ow boundary, i.e. As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In particular, we consider remeshing algorithms that increase the number of vertices, i.e.