Surface mesh enhancement with geometric singularities identification (original) (raw)
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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.
An Adaptive Parametric Surface Mesh Generation Method Guided by Curvatures
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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.
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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.
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.
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.
Dynamic meshes for accurate polygonization of implicit surfaces with sharp features
Proceedings International Conference on Shape Modeling and Applications
The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. In this paper, we adapt methods developed in [3, 17, 19] for crease enhancement and combine them with a mesh regularity improving technique [18, 30] in order to fit implicit surfaces with sharp edges by triangle meshes. Consider an