Book Reviews

Steinmetz, Ralf and Nahrstedt, Klara. Multimedia: Computing, Communications and Applications
Stollnitz, Eric J, Derose, Tony D and Salesin, David H. Wavelets for Computer Graphics
Prusinkiewicz, P and Lindenmayer, A. The Algorithmic Beauty of Plants
Geary, David M and McClellan, Alan L. Graphic Java: Mastering the AWT
Santos, Adelino. Multimedia and Groupware for Editing
Magnenat Thalmann, Nadia and Thalmann, Daniel. Interactive Computer Animation     

Proximity problems for points on a rectilinear plane with rectangular obstacles

We consider the following four problems for a setS ofk points on a plane, equipped with the rectilinear metric and containing a setR ofn disjoint rectangular obstacles (so that distance is measured by a shortest rectilinear path avoiding obstacles inR): (a) find aclosest pair of points inS, (b) find anearest neighbor for each point inS, (c) compute the rectilinearVoronoi diagram ofS, and (d) compute a rectilinearminimal spanning tree ofS. We describeO ((n+k) log(n+k))-time sequential algorithms for (a) and (b) based onplane-sweep, and the consideration of geometrically special types of shortest paths, so-calledz-first paths. For (c) we present anO ((n+k) log(n+k) logn)-time sequential algorithm that implements a sophisticateddivide-and-conquer scheme with an addedextension phase. In the extension phase of this scheme we introduce novel geometric structures, in particular so-calledz-diagrams, and techniques associated with the Voronoi diagram. Problem (d) can be reduced to (c) and solved inO ((n+k) log(n+k) logn) time as well. All our algorithms arenear-optimal, as well as easy to implement. An extended abstract appeared inProc. 13th Conf. on the Foundations of Software Technology and Theoretical Computer Science, Bombay, 1993, Springer-Verlag, pp. 218–227. Sumanta Guha was supported in part by a UW-Milwaukee Graduate School Research Committee Award. Ichiro Suzuki was supported in part by the National Science Foundation under Grants CCR-9004346 and IRI-9307506, the Office of Naval Research under Grant N00014-94-1-0284, and an endowed chair supported by Hitachi Ltd. at the Faculty of Engineering Science, Osaka University.     

Polycapillary Optics for Materials Science Studies: Instrumental Effects and Their Correction

The instrumental effects related to the use of a polycapillary x-ray lens as primary beam collimator are here studied and the features observed in the measurements modelled via Monte-Carlo ray-tracing. Comparison with existing procedures is presented and experimental evidence of the accuracy improvements due to the use of a correction algorithm is shown.     

Sound–Sights An Interdisciplinary Project

An interdisciplinary project between geometry, architecture and music resulted in a concert and exhibition with sound installations. Professors and students of architecture and mathematics of the Technical University of Kaiserslautern worked with a professor and students of music composition of the Music Academy of Cologne in Germany. The theoretical and historical analyses of the relationships between geometry and music formed the basis for original creative works in interdisciplinary groups. Music was composed according geometrical-architectural concepts and geometrical images, forms and processes were developed after musical ideas. Geometrical forms are combined with the music into a kinetic, visual and acoustic work of art. Through such interdisciplinary art projects it is possible to experience scientific coherence in a sensual way. The combination of geometry, architecture and music enables a visual and aural approach to formal thinking of sciences.     

A geometrical model of the cut in five-axis milling accounting for the influence of tool orientation

This paper presents a model of the cut geometry in five-axis milling. This allows the establishment of a better model of cutting force to account for the influence of the tool orientation. The formulation of the width and the thickness of the cut were derived and implemented in a computer simulation. The results of simulations were verified experimentally and a good agreement was obtained. The result shows the importance of including the influence of the tool orientation in the cut cross-section calculation.     

Size and geometry effects on ductile rupture of notched bars in a C-Mn steel: experiments and modelling

The aim of this work was to investigate the effect of specimen size and geometry on ductile fracture of a C-Mn steel with high sulphur content. Uniaxial tensile tests were conducted at 300°C on axisymmetric notched specimens having different sizes and geometries. Geometry effects were studied using specimens with various notch radii, thus inducing different stress triaxiality levels. Size effects were evidenced using homothetic samples having the same geometry. Results show that ductility is reduced on specimens with sharp notches (which is a common observation). As specimen size increases, mean ductility as well as scatter are reduced (showing a clear size effect). In order to predict rupture, locally coupled (post-processing type) and fully coupled (continuum damage mechanics) Finite Element models were used. They are based on the plastic criteria introduced by Gurson and Rousselier. In order to model size effect (decrease of ductility and scatter), initial distribution of inclusion volume fractions, measured by quantitative metallography, was accounted for in the simulations. Comparison of experiments with simulations showed that both model types could predict mean values of ductility and scatter. This revised version was published online in August 2006 with corrections to the Cover Date.     

Automated development of Tarski's geometry

Tarski's geometry, a complete first-order axiomatization of Euclidean plane geometry, is developed within the automated reasoning system OTTER. Proofs are obtained and performance statistics supplied for most of the challenge problems appearing in the literature. Few of these problems have been previously solved by any clause-based reasoning system. Further challenges are offered.     

Generation of configuration space obstacles: The case of moving algebraic curves

We present algebraic algorithms to generate the boundary of planar configuration space obstacles arising from the translatory motion of objects among obstacles. Both the boundaries of the objects and obstacles are given by segments of algebraic plane curves.Research supported in part by NSF Grant MIP-85-21356 and a David Ross Fellowship. An earlier version of this paper appeared in theProceedings of the 1987 IEEE International Conference on Robotics and Automation, pp. 979–984.     

Link between Bézier and Lagrange curve and surface schemes

A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial Bézier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for Bézier curves. A geometric derivation of this scheme is given, and the connection to Pólya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.     

Up- and Downlink Admission/Congestion Control and Maximal Load in Large Homogeneous CDMA Networks

This paper proposes scalable admission and congestion control schemes that allow each base station to decide independently of the others what set of voice users to serve and/or what bit rates to offer to elastic traffic users competing for bandwidth. These algorithms are primarily meant for large CDMA networks with a random but homogeneous user distribution. They take into account in an exact way the influence of geometry on the combination of inter-cell and intra-cell interferences as well as the existence of maximal power constraints of the base stations and users. We also study the load allowed by these schemes when the size of the network tends to infinity and the mean bit rate offered to elastic traffic users. By load, we mean here the number of voice users that each base station can serve.