Gross , Staadt and Gatti : Efficient Triangular Surface Approximations 3
نویسندگان
چکیده
| We present a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to analyze the resulting coeecients. In surface regions, where the partial energy of the resulting coeecients is low, the polygonal approximation of the surface can be performed with larger triangles without loosing too much ne grain details. However, since the localization of the WT is bound by the Heisenberg principle the meshing method has to be controlled by the detail signals rather than directly by the coeecients. The dyadic scaling of the WT stimulated us to build an hierarchical meshing algorithm which transforms the initially regular data grid into a quadtree representation by rejection of unimportant mesh vertices. The optimum triangulation of the resulting quadtree cells is carried out by selection from a look-up table. The tree grows re-cursively as controlled by detail signals which are computed from a modiied inverse WT. In order to control the local level-of-detail, we introduce a new class of wavelet space lters acting as \magnifying glasses" on the data. We show that our algorithm performs a low algorithmic complexity, so that surface meshing can be achieved at interactive rates, such as required by ight simulators. However , other applications are possible as well, such as mesh reduction in complex data, FEM or radiosity meshing. The method is applied on diierent types of data comprising both digital terrain models and laser range scans. In addition , quantitative investigations on error analysis are carried out.
منابع مشابه
Efficient Triangular Surface Approximations Using Wavelets and Quadtree Data Structures
We present a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to analy...
متن کاملFast Multiresolution Surface Meshing
We present a new method for adaptive surface meshing and triangulation which controls the local level–of–detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi–orthogonal tensor product wavelet transform (WT) and to analy...
متن کاملSimplification of Tetrahedral Meshes Using a Quadratic Error Metric
In order to effectively visualize the results of huge numerical simulations it is critical that the size of datasets be efficiently reduced to a manageable size. Various methods have been developed to address this problem by constructing sequences of tetrahedral meshes approximating scalar-valued functions. Several methods rely on iterative vertex insertion. For example, methods described by Ha...
متن کاملAvoiding Errors In Progressive Tetrahedralizations
This paper describes some fundamental issues for robust implementations of progressively refined tetrahedralizations generated through sequences of edge collapses. We address the definition of appropriate cost functions and explain on various tests which are necessary to preserve the consistency of the mesh when collapsing edges. Although being considered a special case of progressive simplicia...
متن کامل