345261
Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces
Accurately representing higher-order singularities of vector fields defined on piecewise linear surfaces is a non-trivial problem. In this work, we introduce a concise yet complete interpolation scheme of vector fields on arbitrary triangulated surfaces. The scheme enables arbitrary singularities to be represented at vertices. The representation can be considered as a facet-based "encoding" of vector fields on piecewise linear surfaces. The vector field is described in polar coordinates over each facet, with a facet edge being chosen as the reference to define the angle. An integer called the period jump is associated to each edge of the triangulation to remove the ambiguity when interpolating the direction of the vector field between two facets that share an edge. To interpolate the vector field, we first linearly interpolate the angle of rotation of the vectors along the edges of the facet graph. Then, we use a variant of Nielson's side-vertex scheme to interpolate the vector field over the entire surface. With our representation, we remove the bound imposed on the complexity of singularities that a vertex can represent by its connectivity. This bound is a limitation generally exists in vertex-based linear schemes. Furthermore, using our data structure, the index of a vertex of a vector field can be combinatorily determined
16810303
Periodic global parameterization
We present a new globally smooth parameterization method for the triangulated surfaces of arbitrary topology. Given two orthogonal piecewise linear vector fields defined over the input mesh (typically the estimated principal curvature directions), our method computes two piecewise linear periodic functions, aligned with the input vector fields, by minimizing an objective function. The bivariate function they define is a smooth parameterization almost everywhere on the surface, except in the vicinity of singular vertices, edges, and triangles, where the derivatives of the parameterization vanish. We extract a quadrilateral chart layout from the parameterization function and propose an automatic procedure to detect the singularities, and fix them by splitting and reparameterizing the containing charts. Our method can construct both quasiconformal (angle preserving) and quasi-isometric (angle and area preserving) parameterizations. The more restrictive class of quasi-isometric parameterizations is constructed at the expense of introducing more singularities. The constructed parameterizations can be used for a variety of geometry processing applications. Since we can align the parameterization with the principal curvature directions, our result is particularly suitable for surface fitting and remeshing.
16138674
Mesh editing with an embedded network of curves
We propose a new topological data structure for representing a set of polygonal curves embedded in a meshed surface. In this embedding, the vertices of the curve do not necessarily correspond to the vertices of the surface. The partition of the surface yielded by the intersecting curves is efficiently represented as a "cut-graph". The cut-graph stores combinatorial information of the network of curves. In our approach, the combinatorial form of information is systematically preferred to geometrical information since it improves both robustness and efficiency. Thanks to the topological data structure and algorithms, the cut-graph can be sketched through iterations of designing and erasing curves on the mesh surface in a "nondestructive" way, i.e. without modifying the mesh until the cutting operation is committed. We also demonstrate several prototype curve design tools inspired by 2D vector and bitmap graphics paradigms. We show how to sketch the cut-graph and how these tools can be mixedly used.
6073358
Non-photorealistic virtual environments
We describe a system for non-photorealistic rendering (NPR) of virtual environments. In real time, it synthesizes imagery of architectural interiors using stroke-based textures. We address the four main challenges of such a system — interactivity, visual detail, controlled stroke size, and frame-to-frame coherence — through image based rendering (IBR) methods. In a preprocessing stage, we capture photos of a real or synthetic environment, map the photos to a coarse model of the environment, and run a series of NPR filters to generate textures. At runtime, the system re-renders the NPR textures over the geometry of the coarse model, and it adds dark lines that emphasize creases and silhouettes. We provide a method for constructing non-photorealistic textures from photographs that largely avoids seams in the resulting imagery. We also offer a new construction, art-maps, to control stroke size across the images. Finally, we show a working system that provides an immersive experience rendered in a variety of NPR styles.
15937058
Implementing lattice Boltzmann computation on graphics hardware
The Lattice Boltzmann Model (LBM) is a physically-based approach that simulates the microscopic movement of fluid particles by simple, identical, and local rules. We accelerate the computation of the LBM on general-purpose graphics hardware, by grouping particle packets into 2D textures and mapping the Boltzmann equations completely to the rasterization and frame buffer operations. We apply stitching and packing to further improve the performance. In addition, we propose techniques, namely range scaling and range separation, that systematically transform variables into the range required by the graphics hardware and thus prevent overflow. Our approach can be extended to acceleration of the computation of any cellular automata model.
28902667
Performance analysis of a PCS network with state dependent calls arrival processes and impatient calls
This paper studies the behavior of performance evaluation for a personal communication services (PCS) network, in which the calls' arrival process may depend on the number of calls in the target cells. Each cell of the PCS network consists of a finite channel and a buffer (with finite or infinite size) for handoff calls. The handoff calls having to wait in the buffer for further communication may become impatient and leave the system if their waiting time exceeds their own patience. The mobilities of the portables are characterized by the random cell residence times of the portables. For insight into the effect of dependent calls arrival processes and the impatient calls on PCS network performance, we propose an analytical model and obtain the expressions for the following interesting conventional and new performance measures: the new call blocking probability, handoff call failure probability and the forced termination probability of a handoff call; the quasi and actual waiting time of a handoff call in the buffer; the actual call holding time of a new call; and the blocking period of time of the new calls and the handoff calls etc. We also provide an algorithm to compare these blocking probabilities and the arrival rates for handoff calls. Some special cases of our model used in previous traffic models of wireless and/or wireline communications are discussed. The results presented in this paper can provide guidelines for field data processing on updated PCS network design and performance evaluation.
8035776
Semantic Integration in Heterogeneous Databases Using Neural Networks
One important step in integrating heterogeneous databases is matching equivalent attributes: Determining which fields in two databases refer to the same data. The meaning of information may be embodied within a. database model, a conceptual schema, application programs, or data contents. Integration involves extracting semantics, expressing them as metadata, and matching semantically equivalent data elements. We present a procedure using a classifier to categorize attributes according to their field specifications and data values, then train a neural network to recognize similar attributes. In our technique, the knowledge of how to match equivalent data elements is “discovered” from metadata , not “pre-programmed”.
33595781
New Optimal Tame Towers of Function Fields over Small Finite Fields
Ihara [11] introduced the quantity A(q) = limsupg→∞ N q (g)/g where N q (g) is the maximum number of rational places of a function field with genus g and with the finite field F q as the full field of constants. Drinfeld and Vladut [2] showed that A(q) ≤ √q - 1. It was also shown by Ihara [11], and Tsfasman, Vladut and Zink [17] in special cases, that A(q)= √ q - 1 when q is a square. When q is not a square, the exact value of A(q) is currently unknown. While the problem of finding A(q) in this case is an interesting problem in its own right, much motivation comes from implications in asymptotic results in coding theory. Essentially there are three approaches to finding lower bounds for A(q): class field towers [15], modular curves [11], [17], [3], [4]and explicit towers (that is, given explicitly in terms of generators and relations) of function fields. For applications to coding theory though, explicit towers are needed. In [6], a tower of function fields over Fq is defined to be a sequence F = (F 1, F 2, F 3,.. ) of function fields F i , having the following properties: 
 
(i) 
 
F1 ⊆F2 ⊆ F3 ⊆.... 
 
 
 
 
(ii) 
 
For each n ≥ 1, the extension F n+1/ F n is separable of degree [F n+1: F n ] > 1. 
 
 
 
 
(iii) 
 
the genus g(F j ) > 1 for some j ≥ 1. 
 
 
 
 
(iv) 
 
F q is the full field of constants of each F n .