5883116
Subdividing Alpha Complex
Given two simplicial complexes C 1 and C 2 embedded in Euclidean space d , C 1 subdivides C 2 if (i) C1 and C 2 have the same underlying space, and (ii) every simplex in C 1 is contained in a simplex in C 2 . In this paper we present a method to compute a set of weighted points whose alpha complex subdivides a given simplicial complex. Following this, we also show a simple method to approximate a given polygonal object with a set of balls via computing the subdividing alpha complex of the boundary of the object. The approximation is robust and is able to achieve a union of balls whose Hausdorff distance to the object is less than a given positive real number e.
14650283
Quality mesh generation for molecular skin surfaces using restricted union of balls
Quality surface meshes for molecular models are desirable in the studies of protein shapes and functionalities. However, there is still no robust software that is capable to generate such meshes with good quality. In this paper, we present a Delaunay-based surface triangulation algorithm generating quality surface meshes for the molecular skin model. We expand the restricted union of balls along the surface and generate an /spl epsiv/-sampling of the skin surface incrementally. At the same time, a quality surface mesh is extracted from the Delaunay triangulation of the sample points. The algorithm supports robust and efficient implementation and guarantees the mesh quality and topology as well. Our results facilitate molecular visualization and have made a contribution towards generating quality volumetric tetrahedral meshes for the macromolecules.
7864473
Dynamic Skin Triangulation
This paper describes an algorithm for maintaining an approximating triangulation of a deforming surface in R3 . The surface is the envelope of an infinite family of spheres defined and controlled by a finite collection of weighted points. The triangulation adapts dynamically to changing shape, curvature, and topology of the surface.
10506027
Superimposing Voronoi Complexes for Shape Deformation
Edelsbrunner et al defined a framework of shape deformations with shapes bounded by skin manifold We prove that the infinitely many synthesized shapes in the deformation sequence share finitely many common Voronoi complexes Therefore, we propose a new algorithm to compute the common Voronoi complexes efficiently for the deformations, and use these common complexes to compute the synthesized shapes in real time This makes generating, visualizing, and customizing shape deformations feasible.
33621218
Superimposing Voronoi Complexes for Shape Deformation
Edelsbrunner et al. defined a framework of shape deformations with shapes bounded by skin manifold. We prove that the infinitely many synthesized shapes in the deformation sequence share finitely many common Voronoi complexes. Therefore, we propose a new algorithm to compute the common Voronoi complexes efficiently for the deformations, and use these common complexes to compute the synthesized shapes in real time. This makes generating, visualizing, and customizing shape deformations feasible.
6203082
Area and Perimeter Derivatives of a Union of Disks
We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.
13488246
Distributed medium access control for wireless mesh networks
Summary Wireless mesh networking is an emerging technology for future broadband wireless access. The ad hoc manner of wireless mesh networks (WMNs) determines that distributed medium access control (MAC) protocols are desired. Multimedia traffic with heterogeneous quality of service (QoS) requirements is expected to be supported in small-, medium-, and large-scale WMNs. Wireless mesh routers in WMNs are located in fixed sites with low (or no) mobility and no power constraints, thus comprising a robust and reliable wireless mesh backbone. Different networking characteristics between the mesh backbone and various mesh client networks give rise to the demand of heterogeneous MAC design. Due to new design purposes and new networking structures, existing MAC protocols designed for mobile ad hoc networks may not be effective or efficient for multi-purpose WMNs. This paper provides an overview of distributed MAC protocols based on their underlying design objectives and methodology, discusses their features and suitability for WMNs, and identifies potential challenges and open research issues. Copyright © 2006 John Wiley & Sons, Ltd.
46280169
Edge-gracefulness of the composition of paths with null graphs
Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,..., q} be a bijection. The induced mapping f+ : V → Zp of f is defined by f+(u) ≡ Σuυ∈Ef(uυ) (modp) for u ∈ V. If f+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm > Nn, where there are mn vertices and (m - 1)n2 edges. We show that P3 > Nn is edge-graceful if n is odd.
14350917
A non-linear dimensionality-reduction technique for fast similarity search in large databases
To enable efficient similarity search in large databases, many indexing techniques use a linear transformation scheme to reduce dimensions and allow fast approximation. In this reduction approach the approximation is unbounded, so that the approximation volume extends across the dataspace. This causes over-estimation of retrieval sets and impairs performance.This paper presents a non-linear transformation scheme that extracts two important parameters specifying the data. We prove that these parameters correspond to a bounded volume around the search sphere, irrespective of dimensionality. We use a special workspace-mapping mechanism to derive tight bounds for the parameters and to prove further results, as well as highlighting insights into the problems and our proposed solutions. We formulate a measure that lower-bounds the Euclidean distance, and discuss the implementation of the technique upon a popular index structure. Extensive experiments confirm the superiority of this technique over recent state-of-the-art schemes.