Curvature Based Mesh Improvement (original) (raw)
Related papers
Two Techniques to Improve Mesh Quality and Preserve Surface Characteristics
International Meshing Roundtable, 2004
In this paper we present two novel techniques to improve the quality of triangle surface meshes while preserving surface characteristics as much as possible. In contrast to previous approaches we do not tend to preserve mesh nodes on the original discrete surface. Instead, we propose two techniques, which allow to keep resulting mesh close to the smooth surface approximated by the original mesh. The first technique called trapezium drawing (TD) is iterative and can be easy implemented for all types of meshes. It does not use any information about surface geometry. On the contrary, in the second technique to find new location each node of the mesh we use value of maximum curvature defined at this node. We show that the second approach called curvature-based mesh improvement (CBMI) gives the best results in the sense of keeping new mesh very close to the original surface and preserving surface characteristics such as normals and curvatures. But unlike TD it can be applied only for meshes representing smooth surfaces without sharp edges and corners. Several quantitative measures are presented to demonstrate the effectiveness of both proposed techniques.
An Approach to Improving Triangular Surface Mesh
JSME International Journal Series C, 2005
Our method is based on an implementation of quasi-statistical modeling for improving meshes by producing mesh elements with modeled values of different mesh quality parameters. In this paper we implement this approach to triangular surface mesh. Considering the initial distribution of the mesh quality parameter values, we assume that after improvement the distribution of elements of the mesh varies from a rather random distribution to a smoother one, such as a normal distribution. The preliminary choice of the desirable distribution affects the new parameter values modeled by the formula presented here. Uncertainty of the smoothed vertex positions of the mesh element affords to use a statistical approach in sense of random variable modeling to connect quasi-statistical modeling and mesh improvement techniques. The so-called "kernel" method allows creating different applicable to a mesh processing algorithms, which can be interpreted as a kind of smoothing technique to determine vertex direction movement with the distribution control of the shape of mesh elements. An aspect ratio is mainly used in present research as a mesh quality parameter. The geometry of the initial mesh surface is preserved by local mesh improving such that the new positions of the interior nodes of the mesh remain on the original discrete surface. Our method can be interpreted as a kind of smoothing technique with using the distribution control of the mesh quality parameter values. This method is comparable with optimization-based approach for avoiding the invalid elements of the mesh by producing a mesh with a rather homogeneous distribution of the mesh elements. Experimental results are included to demonstrate the functionality of our method. This method can be used at a pre-process stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing the better-input parameters for these processes.
Optimization of Surface Mesh Quality Using Local Parametrization
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.
JSME International Journal Series C, 2005
In this paper, we introduce a new approach to surface mesh improvement problem. In contrast to previous methods we do not tend to preserve new mesh vertices on the original discrete surface. Instead our technique keeps mesh nodes very close to a smooth or piecewisesmooth surface approximated by an initial mesh. As a result, the algorithm is able to improve mesh quality while preserving essential surface characteristics and features. Proposed approach can be applied iteratively not only to polygonal meshes but also to 2D and 3D curves that allows to treat sharp edges and surface boundaries. We demonstrate effectiveness of our method using various triangular and quadrilateral meshes. Also we compare our algorithm with some commonly used techniques and analyze their advantages and disadvantages.
Geometric surface mesh optimization
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.
Triangular and quadrilateral surface mesh quality optimization using local parametrization
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.
An Adaptive Parametric Surface Mesh Generation Method Guided by Curvatures
Proceedings of the 22nd International Meshing Roundtable, 2014
This work presents an adaptive mesh generation strategy for parametric surfaces. The proposed strategy is controlled by curvatures and the error measured between the analytical and discrete curvatures guides the adaptive process. The analytical curvature is a mathematical representation that models the domain, whereas the discrete curvature is an approximation of that curvature and depends directly on the used mesh. The proposed strategy presents the following aspects: it is able to refine and coarsen regions of the mesh; it considers the local error measures to ensure good global quality; it ensures good transition of the mesh and it deals with any type of parametric surfaces since it works in the parametric space.
Improvement of Triangular and Quadrilateral Surface Meshes 1
In this paper, we present a new technique called Trapezium Drawing to improve surface mesh quality while maintaining the essential surface characteristics. In contrast to previous methods we do not tend to preserve new mesh vertices on the original discrete surface. Instead our approach allows keeping new mesh close to the surface approximated by the initial mesh. All operations are performed directly on the surface. As a result our technique is robust and runs at interactive speeds. It can be applied to triangular and quadrilateral meshes iteratively. Various quantitative measures are presented to demonstrate the effectiveness of proposed technique.