Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, example, fundamental methods shape analysis mesh processing. Subspace Iteration Method is a robust solver these problems. In practice, however, Lanczos schemes often faster. this paper, we introduce Hierarchical (HSIM), novel sparse that operates o...

Adaptive refinement of finite element approximations on tetrahedral meshes is generally considered to be a non-trivial task. (We wish to stress that this paper deals with mesh refinement as opposed to remeshing.) The splitting individual finite elements needs to be done with much care to prevent significant deterioration of the shape quality of the elements of the refined meshes. Considerable c...

We introduce a new preconditioner for elliptic PDE’s on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second-generation wavelets which can be adapted to the unstructured mesh, the true boundary conditions, and ev...

A variety of multiresolution models for arbitrary triangle meshes have been presented in the last years. In order to achieve an interactive visualization, multiresolution models must store and retrieve data efficiently. In this paper, we present a first step to evaluate and compare multiresolution models. We propose a set of tests to measure the speed performance of the models for interactive v...

This paper presents a novel progressive mesh model based on collapse tree, which can accomplish the disordered expansions and collapses of the simplified mesh and is able to restore the mesh just in a specific area. With arbitrary collapse and expansion, we design an edge collapse algorithm for mesh optimization. Its summary process can be described as follows: generating a series of new simpli...

We focus on the class of regular models defined by Várady et al. for reverse engineering purposes. Given a 3D surfaceM represented through a dense set of points, we present a novel algorithm that convertsM to a hierarchical representationHM. InHM, the surface is encoded through patches of various shape and size, which form a hierarchical atlas. IfM belongs to the class of regular models, thenHM...

A multi-resolution approach is presented for data on a large class of hierarchical and nested grids. It is based on a procedural interface and a set of hierarchical and adaptive visualization methods. Such a method consists of a recursive traversal of mesh elements from the grid hierarchy combined with an adaptive stopping according to some error indicator which is closely related to the visual...

This paper presents a novel algorithm for hierarchical random accessible mesh decompression. Our approach progressively decompresses the requested parts of a mesh without decoding less interesting parts. Previous approaches divided a mesh into independently compressed charts and a base coarse mesh. We propose a novel hierarchical representation of the mesh. We build this representation by using...

An anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is considered. The adaptation method generates anisotropic adaptive meshes as quasiuniform ones in some metric space. The associated metric tensor is computed by means of a posteriori hierarchical error estimates. A global hierarchical error estimate is employed in this study to obtain reliabl...

S. Katz ( ) ·G. Leifman ·A. Tal Department of Electrical Engineering Technion – Israel Institute of Technology {sagikatz@tx, gleifman@tx, ayellet@ee}.technion.ac.il ∗ This work was partially supported by European FP6 NoE grant 506766 (AIM@SHAPE), by the Israeli Ministry of Science, grant 01-01-01509 and by the Ollendorff foundation. Abstract Mesh segmentation has become a necessary ingredient i...