13366253
Efficient circular arc interpolation based on active tolerance control
In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G1 arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.
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.
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.
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.
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.
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.
1833949
DSCR: a wireless MAC protocol using implicit pipelining
In wireless networks, the collision cost is much higher than wired networks since a station cannot detect collision until a transmission is over and the expected acknowledgment does not come back. Therefore, more efficient contention resolution algorithms are desired for wireless networks to reduce the collision probability among contending stations. IEEE 802.11 defines a distributed random access MAC protocol named DCF (Distributed Coordination Function), which uses binary exponential backoff (BEB) algorithm to resolve channel contention. In DCF, a station wanting to access the channel generates a random backoff counter uniformly distributed over the interval [0, CW] (CW represents contention window). This backoff counter corresponds to the number of idle slots this station has to wait before its transmission. The contention window, CW, is exponentially increased by a factor of 2 each time when a collision happens, and reset to the minimum value upon successful transmission. An appropriate choice of CW can optimize the performance of 802.11. However, the optimum value of CW changes with the network size and 802.11 operates far from this optimum point. In particular, in a heavily contended network, the collision probability increases significantly, degrading the performance of 802.11. To improve the performance of IEEE 802.11, [1] proposes that each station continuously observes channel activities and estimates the number of contending stations, hence, dynamically tune the value of CW to the optimum point. [2] also proposes a fast collision resolution algorithm, in which the winning station occupies the channel for a certain period of time to reduce the collision probability. However, both of these two schemes are designed for wireless LANs, where all stations are within each other’s transmission range. This paper proposes a MAC protocol, named DSCR (Dual Stage Contention Resolution), uses “pipelined” two stage contention resolution algorithm to reduce collision probability and achieve better channel utilization than 802.11 in both wireless LANs and ad hoc networks. In our prior work, we developed two explicit pipelining schemes, which use a separate control channel (either to transmit RTS/CTS or to send busy tone) to pipeline contention resolution with data transmission [4]. In contrast, DSCR performs implicit pipelining in that no separate control channel is required.
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.
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.
16341163
Use of satellite-derived landscape imperviousness index to characterize urban spatial growth
Abstract Urban change analysis has traditionally been supported through land use/cover classification and map-to-map comparison. In this research, we investigate the usefulness of satellite-derived imperviousness index as an alternative for urban spatial growth characterization. The study area, Pensacola, FL, has witnessed considerable growth in population and regional economies during the past decade. The research consists of a number of procedures. First, we identify a method for landscape imperviousness estimation by synergistic use of medium-resolution satellite imagery and high-resolution color orthophoto through multivariate statistical analysis. We apply this method to map landscape imperviousness index for the years of 1989 and 2002, respectively. We assess the maps’ accuracy with the imperviousness estimation from high-resolution DOQQ imagery as the reference. The overall error is estimated to be less than 10%. Then, we analyze the spatio-temporal changing trend of landscape imperviousness index with the emphasis upon some ‘hot’ spots of development areas. We find that this trend is compatible with the urban land use/cover changing trend detected through image interpretation. We conclude that satellite-derived landscape imperviousness index is able to serve as an invaluable alternative for quick and objective assessment of urban spatial growth, particularly over large areas.
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.