where it goes to the Internet (Fig. 13.1). Mesh networks decrease the cost of running the access points, as all access points in the same area share a single broadband connection. Current mesh networks use 802.11a technology to interconnect the mesh backbone [3,4]. However, 802.11a technology is a decade old and was not designed for mesh networks. In particular, 802.11 Medium Access Control (MA...

In this paper, the surface approximation using a mesh optimization approach is investigated. The mesh optimization problem is how to locate a limited number n of grid points such that the established mesh of n grid points approximates the digital surface of N points as closely as possible. The resultant combinatorial problem has an NP-hard search space of C(N, n) instances, i.e., the number of ...

Two-dimensional mesh-based motion tracking preserves neighboring relations (through connectivity of the mesh) and also allows warping transformations between pairs of frames; thus, it effectively eliminates blocking artifacts that are common in motion compensation by block matching. However, available uniform 2-D mesh model enforces connectivity everywhere within a frame, which is clearly not s...

This paper presents a method for automatically generating a hierarchical B-spline surface from an initial set of control points. Given an existing mesh of control points , a mesh with half the resolution , is constructed by simultaneously approximating the finer mesh while minimizing a smoothness constraint using weighted least squares. Curvature measures of are used to identify features that n...

In this paper we describe the generation of a displaced subdivision surface directly from a set of unorganized points. The displaced subdivision surface is an efficient mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface, and has many benefits including compression, rendering, and animation, which overcome limitations of an irregular mesh produc...

3D digitization devices produce very large sets of 3D points sampled from the surfaces of the objects being scanned. A mesh construction procedure needs to be applied to derive polygon mesh from the 3D point sets. As the 3D points derived from digitization devices based on digital imaging technologies are inherently non-uniformly distributed over regions that may contain surface discontinuities...

Robustness and speed are primary considerations when developing deformation methodologies for animatable mesh objects. The goal of this paper is to present such a robust and fast geometric mesh deformation algorithm. The algorithm is feature points based i.e. it can be applied to enable the animation of various mesh objects defined by the placement of their feature points. As a specific applica...

Under suitable assumptions on the order of nonlinearity we prove existence and uniqueness theorems for difference Dirichlet problems of divergence type. We also show that the discrete solutions converge to a solution of the continuous problem. We do not assume that our equation comes from a variational problem. Some of our results are constructive or allow for the application of constructive me...

We investigate bounds for point energies, separation radius, and mesh norm of certain arrangements of N points on sets A from a class A of d-dimensional compact sets embedded in R ′ , 1 ≤ d ≤ d′. We assume that these points interact through a Riesz potential V = | · |−s, where s > 0 and | · | is the Euclidean distance in R ′ . With δ∗ s (A,N) and ρ ∗ s(A,N) denoting, respectively, the separatio...