Hierarchical Decomposition of Datasets on Irregular Surface Meshes
نویسندگان
چکیده
In this paper we introduce multiresolution analysis (MRA) algorithms intended to be used in scientific visualization, and based on a non-nested set of approximatingspaces. The need for non nested spaces arises from the fact that the required scaling functions do not fulfill any refinement equation. Therefore we introduce in the first part the concept of approximated refinement equation, that allows to generalize the filter bank and exact reconstruction algorithms. The second part shows how this concept enables to define a MRA scheme for piecewise constant data defined on an arbitrary planar or spherical triangularmesh. The ability to deal with arbitrary triangular meshes, without subdivision connectivity, can be achieved only through the use of non nested approximating spaces, as introduced in the first part.
منابع مشابه
Multiresolution Analysis on Irregular Surface Meshes
Wavelet-based methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all waveletbased methods is a hierarchy of meshes that satisfies subdivisionconnectivity: this hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree unifor...
متن کاملFiedler trees for multiscale surface analysis
In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For t...
متن کاملOptimal biorthogonal wavelet decomposition of wire-frame meshes using box splines, and its application to the hierarchical coding of 3-D surfaces
Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces generated by box splines. A family of box splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box spline, the optimal positioning of the wire-frame nodes is determined for each level...
متن کاملAdaptive meshes and shells: irregular triangulation, discontinuities, and hierarchical subdivision
Adaptive meshes are dynamic networks of nodal masses interconnected by adjustable springs. They are useful for nonuniformly sampling and reconstructing visual data. This paper extends the adaptive mesh model in the following ways: it (i) develops open adaptive meshes and closed adaptive shells based on triangular and rectangular elements, (ii) proposes a discontinuity detection and preservation...
متن کاملGeneralizing lifted tensor-product wavelets to irregular polygonal domains
Approximation, B-Splines, Geometry Compression, Lifting, Subdivision Surfaces, Tessellations, Wavelets We present a new construction approach for symmetric lifted B-spline wavelets on irregular polygonal control meshes defining two-manifold topologies. Polygonal control meshes are recursively refined by stationary subdivision rules and converge to piecewise polynomial limit surfaces. At every s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998