Results 1  10
of
86
Anisotropic Polygonal Remeshing
"... In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when cre ..."
Abstract

Cited by 203 (16 self)
 Add to MetaCart
In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. 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. After extracting and smoothing the curvature tensor field of an input genus0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply pointsampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.
A Simple Mesh Generator in MATLAB
 SIAM Review
, 2004
"... Abstract. Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple MATLAB code, described in more detai ..."
Abstract

Cited by 89 (4 self)
 Add to MetaCart
(Show Context)
Abstract. Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple MATLAB code, described in more detail than usual, so the reader can experiment (and add to the code) knowing the underlying principles. We find the node locations by solving for equilibrium in a truss structure (using piecewise linear forcedisplacement relations) and we reset the topology by the Delaunay algorithm. The geometry is described implicitly by its distance function. In addition to being much shorter and simpler than other meshing techniques, our algorithm typically produces meshes of very high quality. We discuss ways to improve the robustness and the performance, but our aim here is simplicity. Readers can download (and edit) the codes from
An Approach to Combined Laplacian and OptimizationBased Smoothing for Triangular, Quadrilateral, and QuadDominant Meshes
 INTERNATIONAL MESHING ROUNDTABLE
, 1998
"... Automatic finite element mesh generation techniques have become commonly used tools for the analysis of complex, realworld models. All of these methods can, however, create distorted and even unusable elements. Fortunately, several techniques exist which can take an existing mesh and improve its qu ..."
Abstract

Cited by 72 (4 self)
 Add to MetaCart
(Show Context)
Automatic finite element mesh generation techniques have become commonly used tools for the analysis of complex, realworld models. All of these methods can, however, create distorted and even unusable elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. Smoothing (also referred to as mesh relaxation) is one such method, which repositions nodal locations, so as to minimize element distortion. In this paper, an overall mesh smoothing scheme is presented for meshes consisting of triangular, quadrilateral, or mixed triangular and quadrilateral elements. This paper describes an efficient and robust combination of constrained Laplacian smoothing together with an optimizationbased smoothing algorithm. The smoothing algorithms have been implemented in ANSYS and performance times are presented along with several example models.
Optimal Triangulation and QuadricBased Surface Simplification
 Journal of Computational Geometry: Theory and Applications
, 1999
"... Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fa ..."
Abstract

Cited by 65 (1 self)
 Add to MetaCart
Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fast and produces high quality approximations in practice. Here we provide some theory to explain why the algorithm works as well as it does. Using methods from differential geometry and approximation theory, we show that in the limit as triangle area goes to zero on a differentiable surface, the quadric error is directly related to surface curvature. Also, in this limit, a triangulation that minimizes the quadric error metric achieves the optimal triangle aspect ratio in that it minimizes the L 2 geometric error. This work represents a new theoretical approach for the analysis of simplification algorithms. Keywords: triangle aspect ratio, curvature, approximation theory, anisotropic mesh gen...
A crystalline, red green strategy for meshing highly deformable objects with tetrahedra
 In 12th Int. Meshing Roundtable
, 2003
"... Motivated by Lagrangian simulation of elastic deformation, we propose a new tetrahedral mesh generation algorithm that produces both high quality elements and a mesh that is well conditioned for subsequent large deformations. We use a signed distance function defined on a Cartesian grid in order to ..."
Abstract

Cited by 65 (13 self)
 Add to MetaCart
(Show Context)
Motivated by Lagrangian simulation of elastic deformation, we propose a new tetrahedral mesh generation algorithm that produces both high quality elements and a mesh that is well conditioned for subsequent large deformations. We use a signed distance function defined on a Cartesian grid in order to represent the object geometry. After tiling space with a uniform lattice based on crystallography, we use the signed distance function or other user defined criteria to guide a red green mesh subdivision algorithm that results in a candidate mesh with the appropriate level of detail. Then, we carefully select the final topology so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, we compress the mesh to tightly fit the object boundary using either masses and springs, the finite element method or an optimization approach to relax the positions of the nodes. The resulting mesh is well suited for simulation since it is highly structured, has robust topological connectivity in the face of large deformations, and is readily refined if deemed necessary during subsequent simulation.
Anisotropic Voronoi Diagrams and GuaranteedQuality Anisotropic Mesh Generation
 in SCG ’03: Proceedings of the nineteenth annual symposium on Computational geometry
, 2003
"... We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteedquality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of aniso ..."
Abstract

Cited by 60 (2 self)
 Add to MetaCart
(Show Context)
We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteedquality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of anisotropic Voronoi diagrams of arbitrary dimensionalitymost notably circumstances in which a site can see its entire Voronoi cell. In two dimensions, the anisotropic Voronoi diagram dualizes to a triangulation under these same circumstances. We use these properties to develop an algorithm for anisotropic triangular mesh generation in which no triangle has an angle smaller than 20 # , as measured from the skewed perspective of any point in the triangle.
ImageConsistent Surface Triangulation
, 2000
"... Given a set of 3D points that we know lie on the surface of an object, we can define many possible surfaces that pass through all of these points. Even when we consider only surface triangulations, there are still an exponential number of valid triangulations that all fit the data. Each triangulatio ..."
Abstract

Cited by 59 (1 self)
 Add to MetaCart
Given a set of 3D points that we know lie on the surface of an object, we can define many possible surfaces that pass through all of these points. Even when we consider only surface triangulations, there are still an exponential number of valid triangulations that all fit the data. Each triangulation will produce a different faceted surface connecting the points. Our goal is to overcome this ambiguity and find the particular surface that is closest to the true object surface. We do not know the true surface but instead we assume that we have a set of images of the object. We propose selecting a triangulation based on its consistency with this set of images of the object. We present an algorithm that starts with an initial rough triangulation and refines the triangulation until it obtains a surface that best accounts for the images of the object. Our method is thus able to overcome the surface ambiguity problem and at the same time capture sharp corners and handle concave regions and o...
Direct Anisotropic QuadDominant Remeshing
, 2004
"... We present an extension of the anisotropic polygonal remeshing technique developed by Alliez et al. Our algorithm does not rely on a global parameterization of the mesh and therefore is applicable to arbitrary genus surfaces. We show how to exploit the structure of the original mesh in order to perf ..."
Abstract

Cited by 53 (5 self)
 Add to MetaCart
We present an extension of the anisotropic polygonal remeshing technique developed by Alliez et al. Our algorithm does not rely on a global parameterization of the mesh and therefore is applicable to arbitrary genus surfaces. We show how to exploit the structure of the original mesh in order to perform efficiently the proximity queries required in the line integration phase, thus improving dramatically the scalability and the performance of the original algorithm. Finally, we propose a novel technique for producing conforming quaddominant meshes in isotropic regions as well by propagating directional information from the anisotropic regions.
Anisotropic centroidal Voronoi tessellations and their applications
 SIAM J. SCI. COMPUT
, 2005
"... In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Llo ..."
Abstract

Cited by 47 (7 self)
 Add to MetaCart
(Show Context)
In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay triangulation under the given Riemannian metric. The ACVT is applied to optimization of two dimensional anisotropic Delaunay triangulation, to the generation of surface CVT and high quality triangular mesh on general surfaces. Various numerical examples demonstrate the effectiveness of the proposed method.