A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

Skeleton computation of orthogonal polyhedra

Skeletons are powerful geometric abstractions that provide useful representations for a number of geometric operations. The straight skeleton has a lower combinatorial complexity compared with the medial axis. Moreover, while the medial axis of a polyhedron is composed of quadric surfaces the straight skeleton just consist of planar faces. Although there exist several methods to compute the straight skeleton of a polygon, the straight skeleton of polyhedra has been paid much less attention. We require to compute the skeleton of very large datasets storing orthogonal polyhedra. Furthermore, we need to treat geometric degeneracies that usually arise when dealing with orthogonal polyhedra. We present a new approach so as to robustly compute the straight skeleton of orthogonal polyhedra. We follow a geometric technique that works directly with the boundary of an orthogonal polyhedron. Our approach is output sensitive with respect to the number of vertices of the skeleton and solves geometric degeneracies. Unlike the existing straight skeleton algorithms that shrink the object boundary to obtain the skeleton, our algorithm relies on the plane sweep paradigm. The resulting skeleton is only composed of axis‐aligned and 45° rotated planar faces and edges.     

Comparison of image reconstruction by using near‐field and far‐field data for an imperfect conductor

Image reconstruction by using near‐field and far‐field data for an imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered near and far fields are measured. By using measured fields, the imaging problem is reformulated into an optimization problem and solved by the genetic algorithm. Numerical results show that the convergence speed and final reconstructed results by using near‐field data are better than those obtained by using far‐field data. This work provides both comparative and quantitative information. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 69–73, 2001.     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A base62 transformation format of ISO 10646 for multilingual identifiers

ISO 10646 Universal Character Set (UCS) is a 31‐bit coding architecture that covers symbols in most of the world's written languages. Identifiers in programming languages are usually defined by using alphanumeric characters of ASCII, which represent mainly English words. An approach for working around this deficiency is to encode multilingual identifiers into the alphanumeric range of ASCII. For case‐sensitive languages, an encoding that utilizes [0–9][A–Z][a–z] can be more space‐efficient for multilingual identifiers. This paper proposes a base62 transformation format of ISO 10646 called UTF‐62. The resulting string of UTF‐62 is within a [0–9][A–Z][a–z] range, a total of 62 base characters. UTF‐62 also preserves the lexicographic sorting order of UCS‐4. Copyright © 2001 John Wiley & Sons, Ltd.     

Response to ‘Comments on: A cohesion measure for object‐oriented classes’

Indicating that CBMC does not satisfy the monotonic property in terms of the number of interactions, Xu and Zhou proposed an augmented definition of CBMC by adopting cut set instead of glue methods. The augmented CBMC clearly satisfies the monotonic property. However, CBMC is designed to overcome the problem with respect to the number of interactions and, therefore, focuses on the interaction pattern, especially, member connectivity. Consequently, it does not make sense to mention the monotonic property of CBMC with respect to interaction number. Moreover, the notion of glue methods allows several interpretations on the design quality of a class. However, that meaningful interpretation is not possible for the augmented definition due to the removal of the notion of glue methods. Copyright © 2001 John Wiley & Sons, Ltd.     

Extending UML to model Web 2.0‐based context‐aware applications

Web 2.0 Mashups offer entirely new opportunities for context‐aware application (CAA) developers by integrating Web 2.0 technologies to facilitate interoperability among heterogeneous context‐aware systems. From a software engineering perspective, a visualized approach for Web 2.0‐based CAA modeling is crucial. Current CAA development, however, cannot provide a conceptual model for Web 2.0‐based CAA. Therefore, the development efficiency and potential for reuse are decreased. The UML is a general purpose modeling language with potential for use in many application domains. However, UML often lacks elements needed to model concepts in specific domains, such as Web 2.0‐based CAA modeling. To address the above issues, this study presents the Web 2.0‐based CAA UML profile, a UML profile for modeling Web 2.0‐based CAA. Copyright © 2011 John Wiley & Sons, Ltd.