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.
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.
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.
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.
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.
1110384
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.
1335433
A wakeup scheme for sensor networks: achieving balance between energy saving and end-to-end delay
Energy saving is a critical task for sensor networks with limited energy supply. Wakeup schemes that turn off sensors' radio when communication is not necessary have great potential in energy saving. However, existing wakeup schemes encounter critical tradeoffs between energy saving and wakeup latency, and little attention has been paid to reducing the packet end-to-end delay while preserving the energy saving capability. We argue that a long delay can be detrimental for large sensor networks. We propose a wakeup scheme that helps to achieve the balance between energy saving and end-to-end delay. The conditions under which the proposed scheme can show improvement are identified.
3074931
Using directional antennas for medium access control in ad hoc networks
Previous research in wireless 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 stay silent. With directional antennas, two pairs of nodes located in each other's vicinity may potentially communicate simultaneously, depending on the directions of transmission. This can increase spatial reuse of the wireless channel. In addition, the higher gain of directional antennas allows a node to communicate with other nodes located far away, implying that messages could be delivered to the destination in fewer hops. In this paper, we propose a MAC protocol that exploits the characteristics of directional antennas. Our design focuses on using multi-hop RTSs to establish links between distant nodes, and then transmit CTS, DATA and ACK over a single hop. Results show that our directional MAC protocol can perform better than IEEE 802.11, although we find that the performance is dependent on the topology configuration and the flow patterns in the system.
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.
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.