18376953
Planar point set fairing and fitting by arc splines
Abstract We fair and fit planar point sets by minimal-energy arc splines. The fairing process consists of two steps: computing the optimal tangents for curve interpolation and adjusting the point positions by smoothing the discrete curvatures. To fit the point set with minimal-energy arc curve, a simple linear algorithm is given for computing the optimal tangents. The discrete curvatures derived from the optimal tangents can be made smooth by low-pass filtering. These two linear and local algorithms are combined to generate a fair point set together with a fair G 1 arc curve within a given tolerance of the original data. The method can be used for fair shape design and measured data processing. Numerical examples are given to show the efficiency of this method.
14501670
Curve fitting and fairing using conic splines
We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bezier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bezier spline curve. For parts of the G 1 conic spline without an inflection, we can obtain a curvature continuous conic spline by adjusting the tangent direction at the joint point and scaling the weights for every two adjacent rational Bezier curves. The unwanted curvature extrema within conic segments or at some joint points can be removed efficiently by scaling the weights of the conic segments or moving the joint points along the normal direction of the curve at the point. In the end, a fair conic spline curve is obtained that is G 2 continuous at convex or concave parts and G 1 continuous at inflection points. The main advantages of the method lies in two aspects, one advantage is that we can construct a curvature continuous conic spline by a local algorithm, the other one is that the curvature plot of the conic spline can be controlled efficiently. The method can be used in the field where fair shape is desired by interpolating or approximating a given point set. Numerical examples from simulated and real data are presented to show the efficiency of the new method. q 2003 Elsevier Ltd. All rights reserved.
3643118
Skeleton-driven 2D distance field metamorphosis using intrinsic shape parameters
In this article a novel algorithm is presented for 2D shape interpolation using the intrinsic shape parameters of a piecewise linear curve. The skeletons of two given shapes are computed and the smooth transformation of distance fields is driven by metamorphosis from the skeleton of the source object to that of the target one. We introduce feature graphs, linear forms of skeletons, to guide the construction of intermediate skeleton. If the topologies of the source object and the target one are different, their feature graphs will be automatically extended with equivalent topologies. Then we apply the technique of intrinsic shape parameters to the smooth transition of the extended feature graphs, which will guide the metamorphosis of the skeletons. Not only can the new approach be capable of morphing between objects with different topological genus, but also the topologies and the shapes of the intermediate objects can be controlled efficiently.
584490
Surface interpolation of meshes by geometric subdivision
Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G^1 smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.
14514560
Cone spline approximation via fat conic spline fitting
Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fitting. An efficient fitting algorithm is also proposed for fat conic spline fitting with controllable tolerances. Several examples about approximation of general developable surfaces or other types of ruled surfaces by cone spline surfaces are presented.
16121262
On physical carrier sensing in wireless ad hoc networks
The aggregate throughput of a wireless ad hoc network depends on the channel capacity, channel utilization (i.e., the fraction of channel capacity used for generating good put), and the concurrent transmissions allowed in the network. While channel utilization is determined by MAC overhead, physical carrier sense has been used as an effective way to avoid interference and exploit spatial reuse. Prior research has attempted to identify the optimal carrier sense range that can maximize the aggregate throughput. However, the impact of MAC overhead has been ignored. In this paper, we use both an analytical model and simulation results to show that MAC overhead has significant impact on the choice of optimal carrier sense range. If MAC overhead is not taken into account properly in determining the optimal carrier sense range, the aggregate throughput can suffer a significant loss.
14739146
On designing MAC protocols for wireless networks using directional antennas
We investigate the possibility of using directional antennas for medium access control in wireless ad hoc networks. Previous research in ad hoc networks typically assumes the use of omnidirectional antennas at all nodes. With omnidirectional antennas, while two nodes are communicating using a given channel, MAC protocols such as IEEE 802.11 require all other nodes in the vicinity to remain silent. With directional antennas, two pairs of nodes located in each other's vicinity may potentially communicate simultaneously, increasing spatial reuse of the wireless channel. Range extension due to higher gain of directional antennas can also be useful in discovering fewer hop routes. However, new problems arise when using directional beams that simple modifications to 802.11 may not be able to mitigate. This paper identifies these problems and evaluates the tradeoffs associated with them. We also design a directional MAC protocol (MMAC) that uses multihop RTSs to establish links between distant nodes and then transmits CTS, DATA, and ACK over a single hop. While MMAC does not address all the problems identified with directional communication, it is an attempt to exploit the primary benefits of beamforming in the presence of some of these problems. Results show that MMAC can perform better than IEEE 802.11, although we find that the performance is dependent on the topology and flow patterns in the system.
8264127
Convex composite multi-objective nonsmooth programming
This paper examines nonsmooth constrained multi-objective optimization problems where the objective function and the constraints are compositions of convex functions, and locally Lipschitz and Gâteaux differentiable functions. Lagrangian necessary conditions, and new sufficient optimality conditions for efficient and properly efficient solutions are presented. Multi-objective duality results are given for convex composite problems which are not necessarily convex programming problems. Applications of the results to new and some special classes of nonlinear programming problems are discussed. A scalarization result and a characterization of the set of all properly efficient solutions for convex composite problems are also discussed under appropriate conditions.
206479687
A vehicle-to-vehicle communication protocol for cooperative collision warning
This paper proposes a vehicle-to-vehicle communication protocol for cooperative collision warning. Emerging wireless technologies for vehicle-to-vehicle (V2V) and vehicle-to-roadside (V2R) communications such as DSRC are promising to dramatically reduce the number of fatal roadway accidents by providing early warnings. One major technical challenge addressed in this paper is to achieve low-latency in delivering emergency warnings in various road situations. Based on a careful analysis of application requirements, we design an effective protocol, comprising congestion control policies, service differentiation mechanisms and methods for emergency warning dissemination. Simulation results demonstrate that the proposed protocol achieves low latency in delivering emergency warnings and efficient bandwidth usage in stressful road scenarios.
51886808
Kernel-Based Pronoun Resolution with Structured Syntactic Knowledge
Syntactic knowledge is important for pronoun resolution. Traditionally, the syntactic information for pronoun resolution is represented in terms of features that have to be selected and defined heuristically. In the paper, we propose a kernel-based method that can automatically mine the syntactic information from the parse trees for pronoun resolution. Specifically, we utilize the parse trees directly as a structured feature and apply kernel functions to this feature, as well as other normal features, to learn the resolution classifier. In this way, our approach avoids the efforts of decoding the parse trees into the set of flat syntactic features. The experimental results show that our approach can bring significant performance improvement and is reliably effective for the pronoun resolution task.