Due to their simplicity triangle meshes are often used to represent geometric surfaces. Their main drawback is the large number of triangles that are required to represent a smooth surface. This problem has been addressed by a large number of mesh simplification algorithms which reduce the number of triangles and approximate the initial mesh. Hierarchical triangle mesh representations provide a...

In this paper, a hierarchical shape decomposition algorithm is proposed, which integrates the advantages of skeleton-based and minima-rulebased meaningful segmentation algorithms. The method makes use of new geometrical and topological functions of skeleton to define initial cutting critical points, and then employs salient contours with negative minimal principal curvature values to determine ...

Multiresolution modelling techniques are important to cope with the increasingly complex polygonal models available today such as high-resolution isosurfaces, large terrains, and complex digitized shapes 21. Large triangle meshes are difficult to render at interactive frame rates due to the large number of vertices to be processed by the graphics hardware. Level-of-detail (LOD) based visualizat...

A bounded aspect-ratio coarsening sequence of an unstructured mesh M 0 is a sequence of meshes M 1 ; : : : ; M k such that: M i is a bounded aspect-ratio mesh, and M i is an approximation of M i?1 that has fewer elements, where a mesh is called a bounded aspect-ratio mesh if all its elements are of bounded aspect-ratio. The sequence is node-nested if the set of the nodes of M i is a subset of t...

While traditional computer aided design (CAD) is mainly based on piecewise polynomial surface representations, the recent advances in the efficient handling of polygonal meshes have made available a set of powerful techniques which enable sophisticated modeling operations on freeform shapes. In this tutorial we are going to give a detailed introduction into the various techniques that have been...

CAD model repair is often a necessary precursor to mesh generation, due primarily to the inconsistencies between the tolerances used by the designer and the tolerances required by the analyst. This paper presents a method for meshing directly on imperfect CAD models without needing to repair the model. This is done via a hierarchical grid topology structure that defines a surface grid by a mesh...

〈Summary〉 3D structure of proteins deeply relates to their functionality. It is wellknown that functions of proteins strongly appear in the bumpy parts of the molecular surfaces, and therefore geometric analysis of protein molecular surfaces is important. We propose a technique to extract geometric features of protein molecular surfaces, and a visual interface to effectively visualize the extra...

In this paper a novel procedure for the representation of 3D surfaces using 3D hierarchical adaptive wireframes is presented. The 3D surfaces are generated by dense depth maps. The procedure is based on pyramidal analysis using the Quin-cunx Sampling Minimum Variance Interpolation (QMVINT) lters. The use of this method minimizes the variance (which is a measure of the entropy) of the interpolat...

We present a method for analytically calculating an anti-aliased rasterization of arbitrary polygons or fonts bounded by Bézier curves in 2D as well as oriented triangle meshes in 3D. Our algorithm rasterizes multiple resolutions simultaneously using a hierarchical wavelet representation and is robust to degenerate inputs. We show that using the simplest wavelet, the Haar basis, is equivalent t...

This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution – a smooth coarse-scale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in ...