Robotics is a highly interdisciplinary research topic, that requires integ- tion of methods for mechanics, control engineering, signal processing, planning, graphics, human-computer interaction, real-time systems, applied mathematics, and software engineering to enable construction of fully operational systems. The diversity of topics needed to design, implement, and deploy such systems implies that it is almost impossible for individual teams to provide the critical mass required for such endeavours.To facilitate interaction and progresson s- sor based intelligent robotics the organisation of inter-disciplinary workshops is necessarythrough which in-depth discussion can be used for cross dissemination between di?erent disciplines. The Dagstuhlfoundation has organiseda number of workshopsonModelling and Integration of Sensor Based Intelligent Robot Systems. The Dagstuhl s- inars are all organised over a full week in a beautiful setting in the Saarland in Germany. The setting provides an ideal environment for in-depth presen- tions and rich interactions between the participants. This volume contains the papers presented during the third workshopheld over the period September 28 - October 2, 1998. All papers have been reviewed by one-three reviewers over a relativly short period. We wish to thank all the reviewers for their invaluable help in making this a high quality selection of papers. We gratefully acknowledge the support of the Schloss Dagstuhl Foundation and the sta? at Springer-Verlag. Without their support the production of this volume would not have been possible.

Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.

This volume presents the proceedings of the Seventh International Workshop on Computational Geometry, CG'91, held at the University of Berne, Switzerland, March 21/22, 1991. Computational geometry is not a precisely defined field. Often, it is understood as a nearly mathematical discipline, dealing mainly with complexity questions concerning geometrical problems and algorithms. But often too, and perhaps increasingly, questions of more practical relevance are central, such as applicability, numerical behavior and performance for all kinds of input size. Topics considered in CG'91 include: - Generalizations and applications of the Voronoi diagram - Problems with rectangular objects - Path determination - Moving objects - Visibility questions - Layout problems - Representation of spatial objects and spatial queries - Problems in higher dimensions - Implementation questions - Relations to artificial intelligence.

One ofthe most important aspects in research fields where mathematics is "applied is the construction of a formal model of a real system. As for structural relations, graphs have turned out to provide the most appropriate tool for setting up the mathematical model. This is certainly one of the reasons for the rapid expansion in graph theory during the last decades. Furthermore, in recent years it also became clear that the two disciplines of graph theory and computer science have very much in common, and that each one has been capable of assisting significantly in the development of the other. On one hand, graph theorists have found that many of their problems can be solved by the use of com puting techniques, and on the other hand, computer scientists have realized that many of their concepts, with which they have to deal, may be conveniently expressed in the lan guage of graph theory, and that standard results in graph theory are often very relevant to the solution of problems concerning them. As a consequence, a tremendous number of publications has appeared, dealing with graphtheoretical problems from a computational point of view or treating computational problems using graph theoretical concepts."

The International Workshop CG '88 on "Computational Geometry" was held at the University of WA1/4rzburg, FRG, March 24-25, 1988. As the interest in the fascinating field of Computational Geometry and its Applications has grown very quickly in recent years the organizers felt the need to have a workshop, where a suitable number of invited participants could concentrate their efforts in this field to cover a broad spectrum of topics and to communicate in a stimulating atmosphere. This workshop was attended by some fifty invited scientists. The scientific program consisted of 22 contributions, of which 18 papers with one additional paper (M. Reichling) are contained in the present volume. The contributions covered important areas not only of fundamental aspects of Computational Geometry but a lot of interesting and most promising applications: Algorithmic Aspects of Geometry, Arrangements, Nearest-Neighbor-Problems and Abstract Voronoi-Diagrams, Data Structures for Geometric Objects, Geo-Relational Algebra, Geometric Modeling, Clustering and Visualizing Geometric Objects, Finite Element Methods, Triangulating in Parallel, Animation and Ray Tracing, Robotics: Motion Planning, Collision Avoidance, Visibility, Smooth Surfaces, Basic Models of Geometric Computations, Automatizing Geometric Proofs and Constructions.

Das Buch enthalt eine Einfuhrung in graphentheoretische Grundbegriffe und Basissatze. Graphen werden als Modellierungswerkzeuge fur verschiedene Anwendungen aus dem Bereich der Standortplanung, Logistik, Verkehrsplanung, des Scheduling und der Planung von Kommunikationsnetzen vorgestellt. Fur die entstehenden graphentheoretischen Probleme werden effiziente Verfahren vorgestellt und rigoros analysiert. Fur komplexitatstheoretisch "schwierige" Probleme enthalt das Buch effiziente Naherungsverfahren, die schnell Losungen mit beweisbarer Gute liefern."

Die Sensitivitatsanalyse bei diskreten Optimierungsproblemen ist ein ebenso schwieriges wie reizvolles Objekt der Unternehrnensforschung. In dieser Arbeit versucht der Verfasser, wenigstens fur die einfachsten Problernklassen - diskrete lineare Programme mit pararnetrischen Ziel- funktions- bzw. Restriktionenvektoren - eine einheitliche Darstellung zu geben und grundlegende Ergebnisse zu forrnulieren, die sich nicht zwangsweise an den verfugbaren Algorithmen orientieren, sondern starker den mathematischen Sachverhalt herausstellen. Einige Ideen lassen sich ohne Schwierigkeiten auf den Fall pararnetri- scher Koeffizientenmatrizen und auch auf nichtlineare, parametrische Problemstellungen Ubertragen. Mein besonderer DanK gilt Herrn Prof.Dr.Rudolf Henn, der mein Inter- esse an den mathematischen Methoden in den Wirtschaftswissenschaften weckte und mir mit Anregungen wertvolle Hilfe leistete. Mein Dank gilt ferner Herrn Prof.Dr.D.Bierlein und Herrn Privatdozent Dr.W.Fieger fur die mir erwiesene unterstutzung. Besonderen Dank schulde ich auch Frau Wurz, die mit groBer Sorgfalt das Manuskript tippte. AbschlieBend mochte ich der Deutschen Forschungsgemeinschaft fur die mir wahrend mehrerer Jahre gewahrte finanzielle Unterstutzung meinen Dank aussprechen.