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.
2179068
Guaranteed quality triangulation of molecular skin surfaces
We present an efficient algorithm to mesh the macromolecules surface model represented by the skin surface defined by Edelsbrunner. Our algorithm overcomes several challenges residing in current surface meshing methods. First, we guarantee the mesh quality with a provable lower bound of 21/spl deg/ on its minimum angle. Second, we ensure the triangulation is homeomorphic to the original surface. Third, we improve the efficiency of constructing the restricted Delaunay triangulation (RDT) of smooth surfaces. We achieve this by constructing the RDT using the advancing front method without computing the Delaunay tetrahedrization of the sample points on the surfaces. The difficulty of handling the front collision problem is tackled by employing the Morse theory. In particular, we construct the Morse-Smale complex to simplify the topological changes of the front. Our implementation results suggest that the algorithm decrease the time of generating high quality homeomorphic skin mesh from hours to a few minutes.
16843658
Shape space from deformation
The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined, reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. The technical part of the paper focuses on the second task: the specification of a deformation mixing two or more shapes in continuously changing proportions.
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.
37186338
Shape space from deformation
The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. The technical part of this paper focuses on the second task: the specification of a deformation mixing two or more shapes in continuously changing proportions.
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.