Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves
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.

title: Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
abstract: 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.

title: 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.

title: Almost rotation-minimizing rational parametrization of canal surfaces
abstract: 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.

title: Restoration in IP over WDM optical networks
abstract: An important requirement in any high speed network is to ensure the network's survivability, i.e., the ability to provide reroutes of ongoing connections after the failure of network components. We consider the problem of embedding an IP layer topology in the WDM transport network layer with the objective of achieving the network's survivability in the IP layer. Specifically, we consider the problem of embedding an arbitrary IP layer topology in a WDM wavelength-routing ring network such that the IP topology remains connected under the presence of the failure of any link in the WDM layer.

title: Realization of video object plane decoder on mesh on-chip network architecture

title: Designing On-Chip Network Based on Optimal Latency Criteria
abstract: 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.

title: Analyzing the Performance of Mesh and Fat-Tree Topologies for Network on Chip Design
abstract: The demand of integration of many heterogeneous semiconductor intellectual property (IP) blocks has been introducing a new chip design paradigm so called on chip network. This paradigm promisingly offers a packet switched network among IPs to reduce the main problems in the very deep sub micron technologies that arise from non-scalable global wire delay, failure to achieve global synchronization, errors due to the signal integrity, non-scalable bus based functional interconnection, etc. This paper introduces interconnected or switched network topologies and also analyze their performances in terms of communication protocol related to the issues such as routing strategy, buffer size, routing algorithm , etc. The above mentioned evaluations are done by utilizing the tool that has been widely used in the research domain of computer network design, so called NS-2.

title: Design and control of a novel 4-DOFs parallel robot H4
abstract: 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.