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.
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.
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.
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.
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.
195605809
Designing On-Chip Network Based on Optimal Latency Criteria
A new chip design paradigm, so called Network on Chip, has been introduced based on the demand of integration of many heterogeneous semiconductor intellectual property (IP) blocks. The Network on Chip design not only requires the good performance but also the minimization of several physical constraints such as the network latency, the used area as well as the power consumption of design. This paper analyzes the average latency of heterogeneous Network on Chip architectures in which the shortest path routing algorithm is applied. This average latency includes the queuing latency and the wire latency, and is calculated for general cases of allocating IPs onto the fixed generic switching architectures such as 2-D Mesh and Fat-Tree. With different allocation schemes of IPs, the network has different average latencies. Hence, this article presents an optimal search that adopts the Branch and Bound algorithm to find out the optimal mapping scheme to achieve the minimal network latency. This algorithm automatically map the desired IPs onto the target Network on Chip architecture with the criteria of lowest network latency. Some experiments of On Chip Multiprocessor Network application are simulated. The results show that the network latency is significantly saved with the optimized allocation scheme for the several cases of generic architectures of On Chip Multiprocessor Network application.
651586
Design and control of a novel 4-DOFs parallel robot H4
This paper deals with the design and dynamic control simulation of a new type and dynamic control simulation of a new type of 4-DOFs parallel mechanism providing 3 translations and 1 rotation for high-speed handling and machining. This parallel mechanism is named as H4. A model-based dynamic control scheme is developed to improve the accuracy of the trajectory tracking. A simplified dynamic model is used for the H4 robot to decrease the cost of computation. A dynamic simulation is performed using ADAMS/sup TM/. In addition, the adept motion is used as a benchmark test to evaluate the effect of the dynamic control. The simulation results show that the dynamic control dramatically improves the trajectory tracking accuracy.
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.
10020005
Robust kernel Isomap
Isomap is one of widely used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust kernel Isomap method, armed with such two properties. We present a method which relates the Isomap to Mercer kernel machines, so that the generalization property naturally emerges, through kernel principal component analysis. For topological stability, we investigate the network flow in a graph, providing a method for eliminating critical outliers. The useful behavior of the robust kernel Isomap is confirmed through numerical experiments with several data sets.
11045243
Mobile multi-layered IPsec
To achieve high throughput in wireless networks, smart forwarding and processing of packets in access routers is critical for overcoming the effects of the wireless links. However, these services cannot be provided if data sessions are protected using end-to-end encryption as with IPsec, because the information needed by these algorithms resides inside the portion of the packet that is encrypted, and can therefore not be used by the access routers. A previously proposed protocol, called Multi-layered IPsec (ML-IPsec) modifies IPsec in a way so that certain portions of the datagram may be exposed to intermediate network elements, enabling these elements to provide performance enhancements. In this paper we extend ML-IPsec to deal with mobility and make it suitable for wireless networks. We define and implement an efficient key distribution protocol to enable fast ML-IPsec session initialization, and two mobility protocols that are compatible with Mobile IP and maintain ML-IPsec sessions. Our measurements show that, depending on the mobility protocol chosen, integrated Mobile IP/ML-IPsec handoffs result in a pause of 53–100 milliseconds, of which only 28–75 milliseconds may be attributed to ML-IPsec. Further, we provide detailed discussion and performance measurements of our MML-IPsec implementation. We find the resulting protocol, when coupled with SNOOP, greatly increases throughput over scenarios using standard TCP over IPsec (165% on average). By profiling the MML-IPsec implementation, we determine the bottleneck to be sending packets over the wireless link. In addition, we propose and implement an extension to MML-IPsec, called dynamic MML-IPsec, in which a flow may switch between plaintext, IPsec and MML-IPsec. Using dynamic MML-IPsec, we can balance the tradeoff between performance and security.