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.
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.
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.
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.
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.
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.
31254944
Priority Scheduling in Wireless Ad Hoc Networks
Ad hoc networks formed without the aid of any established infrastructure are typically multi-hop networks. Location dependent contention and hidden terminal problem make priority scheduling in multi-hop networks significantly different from that in wireless LANs. Most of the prior work related to priority scheduling addresses issues in wireless LANs. In this paper, priority scheduling in multi-hop networks is discussed. We propose a scheme using two narrow-band busy tone signals to ensure medium access for high priority source stations. The simulation results demonstrate the effectiveness of the proposed scheme.
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.
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.
8765654
Virtual Reality Tools for Internet-Based Robotic Teleoperation
This paper describes the general system and software architecture for the Internet-based robotic teleoperation system using virtual reality tools. The existing technology and application are discussed in this paper. An example is also presented based on the general architecture. Finally, the conclusion and future research direction are given.
40840411
A property on convex fuzzy sets
In this note, a new result characterizing fuzzy set convexity is given under lower semicontinuous condition.