Improvement of Triangular and Quadrilateral Surface Meshes 1

2005

This paper presents a new procedure to improve the quality of triangular meshes defined on surfaces. The improvement is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes certain objective function. This objective function is derived from an algebraic quality measures of the local mesh (the set of triangles connected to the adjustable or free node). The optimization is done in the parametric mesh, where the presence of barriers in the objective function maintains the free node inside the feasible region. In this way, the original problem on the surface is transformed into a two-dimensional one on the parametric space. In our case, the parametric space is a plane, chosen in terms of the local mesh, in such a way that this mesh can be optimally projected performing a valid mesh, that is, without inverted elements. In order to show the efficiency of this smoothing procedure, its application is presented.

Computer Methods in Applied Mechanics and Engineering, 2004

A procedure is presented to improve the quality of surface meshes while maintaining the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices in a series of element-based local parametric spaces such that the vertices remain on the original discrete surface. The movement of the mesh vertices is driven by a non-linear numerical optimization process. Two optimization approaches are described, one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh.

2000

A procedure is presented to improve the quality of surface meshes while maintain- ing the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices in a series of element-based local para- metric spaces such that the vertices remain on the original discrete surface. The movement of the mesh vertices is driven by a non-linear

Engineering with Computers, 2004

A procedure has been developed to improve polygonal surface mesh quality while maintaining the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices so that they remain on the original discrete surface. The repositioning is performed in a series of triangular-facet-based local parametric spaces. The movement of the mesh vertices is driven by a nonlinear numerical optimization process. Two optimization approaches are described, one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh.

Improvement of the quality of surface meshes is important for mesh generation and numerical simulation. The challenge with surface mesh improvement is to improve element quality while preserving the surface characteristics as much as possible. A procedure is presented here to optimize the quality of elements in surface meshes by node repositioning while keeping the nodes on the original mesh faces and close to their original locations. The nodes are repositioned in a series of local parametric spaces derived from individual mesh elements rather than a global parametric space constructed from the complete mesh. The local parametric spaces are derived from barycentric mapping of triangles and isoparametric mapping of quadrilaterals. The procedure has been tested successfully on a number of complex triangular and quadrilateral meshes. Quantitative measures are presented to prove that the mesh quality is improved and the deviation of the optimized mesh from the original mesh is small.

Computing and Visualization in Science, 1998

This paper presents a surface mesh optimization method suitable to obtain a geometric finite element mesh, given an initial arbitrary surface triangulation. The first step consists of constructing a geometric support, G 1 continuous, associated with the initial surface triangulation, which represents an adequate approximation of the underlying surface geometry. The initial triangulation is then optimized with respect to this geometry as well as to the element shape quality. A specific application of this technique to the geometric mesh simplification is then outlined, which aims at reducing the number of mesh entities while preserving the geometric approximation of the surface. Several examples of surface meshes intended for different application areas emphasize the efficiency of the proposed approach.

Proceedings of the 20th International Meshing …, 2012

A wide range of surfaces can be defined by means of composite parametric surfaces as is the case for most CAD modelers. There are, essentially, two approaches to meshing parametric surfaces: direct and indirect. Popular direct methods include the octree-based method, the advancing-front-based method and the paving-based method working directly in the tridimensional space. The indirect approach consists in meshing the parametric domain and mapping the resulting mesh onto the surface. Using the latter approach, we propose a general "geometry accurate" mesh generation scheme using geometric isotropic or anisotropic metrics. In addition, we introduce a new methodology to control the mesh gradation for these geometric meshes in order to obtain finite element geometric meshes. Application examples are given to show the pertinence of our approach.

Engineering with Computers, 2011

In this article the authors present PolyFront, a new triangulation algorithm for two dimensional domains with holes. PolyFront is based on a normal offsetting technique, where a domain is triangulated starting from a discretization of its boundary and constructing the mesh layer by layer going toward the interior of the domain. The authors propose some numerical experiments to compare this algorithm with other four mesh generators. This comparison shows that the algorithm gives good quality meshes with reduced computational time.

It is very important to improve the quality of surface meshes for numerical simulations, solid mesh generation, and computer graphics applications. Optimizing the form of the mesh elements it is necessary to preserve new nodes of the mesh as close as possible to a surface approximated by the initial mesh. This paper proposes a novel technique in which both of the requirements to mesh improvement are implemented. In the method presented here the new location of each node is found using values of principal curvatures in this node. Such procedure allows preserving new mesh very close to the initial surface while improving element quality. The method has been successfully tested on triangular meshes both for analytical surfaces (sphere, ellipsoid, paraboloid) and for arbitrary surfaces with great number of points. Comparison of the deviation of the mesh optimized by our method and by Laplacian smoothing from the original analytical surfaces shows advantage of the proposed method.

This paper presents a new procedure to improve the quality of triangular meshes defined on surfaces. The improvement is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes certain objective function. This objective function is derived from an algebraic quality measures of the local mesh (the set of triangles connected to the adjustable or free node). The optimization is done in the parametric mesh, where the presence of barriers in the objective function maintains the free node inside the feasible region. In this way, the original problem on the surface is transformed into a two-dimensional one on the parametric space. In our case, the parametric space is a plane, chosen in terms of the local mesh, in such a way that this mesh can be optimally projected performing a valid mesh, that is, without inverted elements. In order to show the efficiency of this smoothing procedure, its application is presented.

Computer Graphics Forum, 2013

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semiregular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing.

Computer Methods in Applied Mechanics and Engineering, 2005

A method for generating geometric surface meshes from a discrete surface, called a reference mesh, is presented. First, the geometrical singularities are extracted from the reference mesh. Then, an almost smooth surface interpolating the reference mesh vertices is associated to the reference mesh. Finally, the reference mesh is adaptively refined via the smooth geometry in order to obtain an adequate approximation of the underlying geometry. Some numerical examples are given to show the efficiency of our approach. The method can transform a mesh composed of linear elements to a mesh constituted by quadratic elements.

Sistemas y Telemática, 2008

Polygonal meshes and particularly triangular meshes are the most used structure for 3D modelling. The 'direct edges' data structure is the most efficient way to represent them and subdivision surfaces is an appropri-SISTEMAS & TELEMÁTICA Vol. 6 No. 12 • Julio-Diciembre de 2008 ate method to generate them. From a review of subdivision surfaces we chose the '√3 subdivision' method for mesh generation. Our main challenge was to take advantage of the direct edges data structure and to find the right formulas for an efficient implementation. We decided to use files in the 3DS file format and convert them to the direct edges data structures for use in our application. We tested our algorithm with arbitrary mesh topologies and calculated efficiency. Our implementation will be used in the creation of a virtual dog head.

Computer-aided Design, 1998

In this work, a new method for mesh simpli cation and surface reconstruction speci cally designed for the needs of CAD/CAM engineering design and analysis is introduced. The method simpli es the original free-form face model by rst constructing restricted curvature deviation regions, generating a boundary conforming nite element quadrilateral mesh of the regions, and then tting a smooth surface over the quadrilateral mesh using the plate energy method. It is more general in scope than existing methods because it handles models with free-form faces and non-manifold geometry, not just triangular or polygonal faces. It produces a high-quality quadrilateral mesh which is suited for both Finite Element Analysis and CAD/CAM. The smooth surface obtained by energy functional stabilization over limited curvature regions preserves the number of quadrilateral elements, and is best suited for surface modeling.

International Journal for Numerical Methods in Engineering, 1999

This paper proposes a method to evaluate the size quality as well as the shape quality of constrained surface meshes, the constraint being either a given metric or the geometric metric associated with the surface geometry. In the context of numerical simulations, the metric speciÿcations are those related to the ÿnite element method. The proposed measures allow to validate the surface meshes within a general mesh adaption scheme, the metric map being usually provided via an a posteriori error estimate. Several examples of surface meshes are proposed to illustrate the relevance of the approach.