18068756
Uniform hyperbolic polynomial B-spline curves
This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinht, cosht, tk-3, tk-4 ...,t, 1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of curves and then prove that they have the variation dimishing properties and the control polygons of the subdivisions converge. Hyperbolic polynomial B-splines can take care of freeform curves as well as some remarkable curves such as the hyperbola and the catenary. The generation of tensor product surfaces by these new splines is straightforward. Examples of such tensor product surfaces: the saddle surface, the catenary cylinder, and a certain kind of ruled surface are given in this paper.
15110446
Normal based subdivision scheme for curve design
In this paper we propose a new kind of nonlinear and geometry driven subdivision scheme for curve interpolation. Instead of using linear combination of old vertexes, displacement vector for every new vertex is given by normal vectors at old vertexes. The normal vectors are computed adaptively for each time of subdivision, and the limit curve is G^1 smooth with wide ranges of free parameters. With this new scheme, normal vectors at selected vertexes can be interpolated efficiently. A shape preserving subdivision scheme with explicit choices of all free parameters is also presented.
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.
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.
2621753
High accuracy approximation of helices by quintic curves
In this paper we present methods for approximating a helix segment by quintic Bezier curves or quintic rational Bezier curves based on the geometric Hermite interpolation technique in space. The fitting curve interpolates the curvatures as well as the Frenet frames of the original helix at both ends. We achieve a high accuracy of the approximation by giving a proper parametrization of the curve, and the approximation order of the height function along the helix axis is 9 provided that the screw angle of the helix is fixed. Numerical examples are also presented to illustrate the efficiency of the new method.
1840328
Split-channel pipelined packet scheduling for wireless networks
To reduce medium access control (MAC) overhead and improve channel utilization, there has been extensive research on dynamically adjusting the channel access behavior of a contending station based on channel feedback information. This paper explores an alternative approach, named pipelined packet scheduling, to reduce the MAC overhead. MAC overheads can be divided into bandwidth-dependent and bandwidth-independent components and these overheads can both be reduced by using split-channel pipelining mechanisms, as demonstrated in this paper. In the past, pipelining mechanisms have not been well studied. This paper introduces two total pipelining schemes that attempt to fully pipeline contention resolution with data transmission. Further, the paper identifies shortcomings of total pipelining in the wireless environment and proposes a partial pipelining approach to overcome these shortcomings. Simulation results show that substantial performance improvement in channel utilization, average packet access delay, and access energy cost can be achieved with a properly designed scheme.
18115243
A wireless MAC protocol using implicit pipelining
In distributed multiple access control protocols, two categories of overhead are usually associated with contention resolution. One is channel idle overhead, where all contending stations are waiting to transmit. Another is collision overhead, which occurs when multiple contending stations attempt to transmit simultaneously. Either idle overhead or collision overhead being large, contention resolution algorithm would be inefficient. Prior research work tries to minimize both the idle and the collision overheads using various methods. In this paper, we propose to apply "pipelining" techniques to the design of multiple access control protocol so that channel idle overhead could be (partially) hidden and the collision overhead could be reduced. While the concept of pipelined scheduling can be applied to various MAC protocol designs in general, in this paper, we focus on its application to IEEE 802.11 DCF. In particular, an implicitly pipelined dual-stage contention resolution MAC protocol (named DSCR) is proposed. With IEEE 802.11, the efficiency of contention resolution degrades dramatically with the increasing load due to high probability of collision. Using the implicit pipelining technique, DSCR hides the majority of channel idle time and reduces the collision probability, hence, improves channel utilization, average access delay, and access energy cost over 802.11 significantly both in wireless LANs and in multihop networks. The simulation results, as well as some analysis, are presented to demonstrate the effectiveness of DSCR.
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.
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.
12349846
Second order symmetric duality in non-differentiable multiobjective programming with F
Abstract This paper is concerned with a pair of Mond–Weir type second order symmetric dual non-differentiable multiobjective programming problems. We establish the weak and strong duality theorems for the new pair of dual models under second order F -convexity assumptions. Several results including many recent works are obtained as special cases.