38568907
Construction and shape analysis of PH quintic Hermite interpolants
In general, the problem of interpolating given first-order Hermite data (end points and derivatives) by quintic Pythagorean-hodograph (PH) curves has four distinct formal solutions. Ordinarily, only one of these interpolants is of acceptable shape. Previous interpolation algorithms have relied on explicitly constructing all four solutions, and invoking a suitable measure of shape—e.g., the absolute rotation index or elastic bending energy—to select the “good” interpolant. We introduce here a new means to differentiate among the solutions, namely, the winding number of the closed loop formed by a union of the hodographs of the PH quintic and of the unique “ordinary” cubic interpolant. We also show that, for “reasonable” Hermite data, the good PH quintic can be directly constructed with certainty, obviating the need to compute and compare all four solutions. Finally, we present an algorithm based on the subdivision, degree elevation, and convex hull properties of the Bernstein form, that gives rapidly convergent curvature bounds for PH curves, using only rational arithmetic operations on their coefficients.
12754524
Almost rotation-minimizing rational parametrization of canal surfaces
Almost rotation minimizing parametrization of the canal surface is given. The basic building block of our approach is the curve approximation scheme that enables us to construct a curve, called the parameter curve, on the canal surface that produces, when projected and rescaled, an almost parallel normal vector field on the spine curve. Its construction relies on our earlier methods and results on relating the geometry of the canal surface to the Lorentzian geometry of the Minkowski geometry via the Clifford algebra formalism. We then iteratively construct patches out of the parameter curves via suitable interpolation procedure. Furthermore, its rotational deviation, i.e., the angle deviation from the parallel (no rotation) frame along the spine curve, can be controlled with the use of the rotation deviation estimate of the parameter curves. Our numerical experiment shows that the rotation deviation is minuscule. When compared with other earlier results including our earlier one, our result fares extremely favorably. To facilitate the implement, a practitioners' summary is given in the appendix.
16215403
Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves
Abstract We present a new approach to medial axis transform and offset curve computation. Our algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the decomposition of the corresponding medial axis transform which is regarded as a geometric graph in the three dimensional Minkowski space R 2,1 . Each simple piece of the domain, called the fundamental domain, corresponds to a space-like curve in R 2,1 . Then using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, we approximate within the desired degree of accuracy the curve part of the medial axis transform with a G 1 cubic spline of Minkowski Pythagorean hodograph. This curve has the property of enabling us to write all offset curves as rational curves. Further, this Minkowski Pythagorean hodograph curve representation together with the domain decomposition lemma makes the trimming process essentially trivial. We give a simple procedure to obtain the trimmed offset curves in terms of the radius function of the MPH curve representing the medial axis transform.
11704041
Rational parametrization of canal surface by 4 dimensional Minkowski Pythagorean hodograph curves
Lorentzian geometry with a Minkowski Pythagorean hodograph (MPH) formalism in R/sup 3,1/ gives us a new and insightful method of rational parametrization of canal surfaces. Our previous works about MPH curves in R/sup 3,1/ shows that a curve /spl gamma/(t)=(x(t),y(t),z(t),r(t)) in R/sup 3,1/ can be represented by the PH representation map in Cl(3,1) which avoids the complex root finding algorithm. Our parametrization method gives us the flexibility to represent the canal surfaces within their fiber ambiguities. This paper constitutes the first step of our ongoing work which deals with the issues for canal surfaces in a truly new and intriguing manner such as finding rotation minimizing frames. We believe this is just the tip of the iceberg and the further work will yield many valuable applications in the area of canal surfaces.
12191931
Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
We present a new approach toward the rational parametrization of canal surfaces. According to our previous work, every canal surface with rational (respectively polynomial) spine curve and rational (respectively polynomial) radius function is a rational (respectively polynomial) Pythagorean hodograph curve in R3,1. Drawing upon this formalism and utilizing the underlying Lorentzian geometry, the problem is reduced to simple algebraic manipulations.We also illustrate how our work related to the previous work of pottmann and Peternell. Finally, we give an outline of an approach toward the rotation minimizing parametrization of canal surfaces.
17562316
Euler-Rodrigues frames on spatial Pythagorean-hodograph curves
Abstract We investigate the properties of a special kind of frame, which we call the Euler–Rodrigues frame (ERF), defined on the spatial Pythagorean-hodograph (PH) curves. It is a frame that can be naturally constructed from the PH condition. It turns out that this ERF enjoys some nice properties. In particular, a close examination of its angular velocity against a rotation-minimizing frame yields a characterization of PH curves whose ERF achieves rotation-minimizing property. This computation leads into a new fact that this ERF is equivalent to the Frenet frame on cubic PH curves. Furthermore, we prove that the minimum degree of non-planar PH curves whose ERF is an rotation-minimizing frame is seven, and provide a parameterization of the coefficients of those curves.
1950897
Secure reporting of traffic forwarding activity in mobile ad hoc networks
Nodes forward data on behalf of each other in mobile ad hoc networks. In a civilian application, nodes are assumed to be selfish and rational, i.e., they pursue their own self-interest. Hence, the ability to accurately measure traffic forwarding is critical to ensure proper network operation. These measurements are often used to credit nodes based on their level of participation, or to detect loss. Past solutions employ neighbor monitoring and reporting on node forwarding traffic. These methods are not applicable in civilian networks where neighbor nodes lack the desire or ability to perform the monitoring function. Such environments occur frequently in which neighbor hosts are resource constrained, or in networks where directional antennas are used and reliable monitoring is difficult or impossible. In this paper, we propose a protocol that uses nodes on the data path to securely produce packet forwarding reports. Reporting nodes are chosen randomly and secretly so that malicious nodes cannot modify their behavior based upon the monitoring point. The integrity and authenticity of reports are preserved through the use of secure link layer acknowledgments and monitoring reports. The robustness of the reporting mechanism is strengthened by forwarding the report to multiple destinations (source and destination). We explore the security, cost, and accuracy of our protocol.
7484493
Dual power management for network connectivity in wireless sensor networks
Summary form only given. As the energy consumption in wireless sensor nodes is dominated by the radio transmission circuitry, the network configuration must be designed to minimize the power consumption by transmission radios. Sensor nodes are generally equipped with short-range radios that require low power consumption. But the current technology allows each node to adjust its transmission power. We consider the dual power radios in which the radio of each node can be assigned high-or low-power during the network initializing stage. Our primary goal in such an assignment is to minimize the overall power consumption by radios to maximize the network lifetime while maintaining the full network connectivity, the most fundamental network functionality. Using a graph-theoretic approach, we formulate the problem as a "minimum subgraph" problem, show its NP-completeness, establish upper and lower bounds on the optimum solution, and present a near-optimal heuristic algorithm and simulation results.
9969836
Efficient route establishment and maintenance in wireless sensor networks with mobile base stations
The integration of ground wireless adhoc networks and airborne UAVs is a promising solution for realtime data collection in wireless sensor networks. Such networks play a vital role in many mission critical tasks such as forest fire-fighting and battlefield support. An important problem is to establish/maintain efficient routing structures in the ground sensor network for packet relaying. Our problem is unique in that the base stations are non-static, which necessitates frequent update of the routing structure. The performance of flooding based methods are evaluated. Particularly, in order to deal with non-uniform node density, we propose to introduce an artificial delay factor to control the flooding pattern. We mathematically prove that the delay should be proportional to local node density. Our simulation results show that the proposed method achieves good load balance among multiple base stations.
6409390
Java Memory Allocation with Lazy Worst Fit for Small Objects
Memory allocation is an important part of modern programming languages, including garbage-collected languages such as Java. We propose a fast memory allocation scheme for Java using lazy worst fit (LWF), where pointer increment is used as the primary allocation method and worst fit is used as a backup. We evaluated LWF on a working Java virtual machine with non-moving garbage collection, and the results show that LWF is practically useful since the overhead of fit allocation and the amount of fragmentation are low.
24043784
Efficient scheduling of transmissions in optical broadcast networks
All-optical networks (AONs) with a broadcast-star based physical topology offer the possibility of transmission scheduling to resolve channel and receiver conflicts. This paper considers the problem of scheduling packet transmissions in a wavelength-division multiplexed (WDM) optical network with tunable transmitters and fixed-tuned receivers. The scheduling problem is complicated by tuning latency, a limited number of channels, and arbitrary traffic demands. We first analyze scheduling all-to-all packet transmissions and obtain a new lower bound for the schedule length. The lower bound is achieved by an algorithm proposed by Pieris and Sasaki (1994). We then extend the analysis to the case of arbitrary traffic demands and obtain lower bounds for the schedule length. Two constructions for scheduling algorithms are provided through list scheduling and multigraphs. The upper bounds so obtained not only provide performance guarantees with arbitrary demands, but also nearly meet the lower bound in simulations.