This paper discusses the dimension of spline spaces S(m,n,m−1, n−1,T ) over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space S(m,n,m− 1, n− 1,T ) and a univariate spline space whose definition depends on the l-edges of the extended T-mesh. We decompose the univariate spline space into direct sums in the sense of isomorphism using the theory...

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional informat...

Highly detailed models are commonly used in computer games and other interactive rendering applications. Intuitive editing methods are thus also required in addition to rendering algorithms. Progressive meshes are often employed to improve the rendering performance by reducing the number of rasterized triangles. The classical work flow is to generate a model and then use simplification algorith...

Micromobility protocols like Cellular IP, Hawaii and Hierarchical Mobile IP (in this paper applied to a single IP domain), are developed to solve problems of handoff latency and control overhead of Mobile IP. Hereby, a tree access network topology is assumed. For reasons of robustness against link failures and load balancing, extra uplinks and mesh links in the topology are desired. This paper ...

This paper presents a novel selective refinement scheme of progressive meshes. In previous schemes, topology information in the neighborhood of a collapsed edge is stored in the analysis phase. A vertex split or edge collapse transformation is possible in the synthesis phase only if the configuration of neighborhood vertices in the current mesh corresponds to the stored topology information. In...

A view-dependent progressive mesh (VDPM) coding algorithm is proposed in this research to facilitate interactive 3D graphics streaming and browsing. The proposed algorithm splits a 3D graphics model into several partitions, progressively compresses each partition, and reorganizes topological and geometrical data to enable the transmission of visible parts with a higher priority. With the real-t...

We present the construction of additive multilevel preconditioners, also known as BPX for solution linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. show that locality spline functions, naturally defined on a structure, can be suitably exploited to design and analyze efficient decompositions. By obtaining smaller subspaces respect standard tensor-pr...

Collision Detection must choose a trade-off between approximative complexity, tightness of approximative fit, and cost of overlap test and distance computation. The collision detection system must be robust, efficient, and capable to deal with any kind of object. Therefore, hierarchical data structures are used to deal with complex objects. An algorithm for computing compact sphere tree hierarc...

We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite-element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core an...

We construct optimal order multilevel preconditioners for interiorpenalty discontinuous Galerkin (DG) finite element discretizations of 3D elliptic boundary-value problems. A specific assembling process is proposed which allows us to characterize the hierarchical splitting locally. This is also the key for a local analysis of the angle between the resulting subspaces. Applying the corresponding...