Wolfgang Boehm – författare

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

This book is written for engineers and other practitioners using numerical methods in their work and serves as a textbook for courses in applied mathematics and numerical analysis.

This book is written for engineers and other practitioners using numerical methods in their work and serves as a textbook for courses in applied mathematics and numerical analysis.

This book is written for engineers and other practitioners using numerical methods in their work and serves as a textbook for courses in applied mathematics and numerical analysis.

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

This book is written for engineers and other practitioners using numerical methods in their work and serves as a textbook for courses in applied mathematics and numerical analysis.

This Open Access book presents the results of the "Collaborative Embedded Systems" (CrESt) project, aimed at adapting and complementing the methodology underlying modeling techniques developed to cope with the challenges of the dynamic structures of collaborative embedded systems (CESs) based on the SPES development methodology.In order to manage the high complexity of the individual systems and the dynamically formed interaction structures at runtime, advanced and powerful development methods are required that extend the current state of the art in the development of embedded systems and cyber-physical systems. The methodological contributions of the project support the effective and efficient development of CESs in dynamic and uncertain contexts, with special emphasis on the reliability and variability of individual systems and the creation of networks of such systems at runtime.The project was funded by the German Federal Ministry of Education and Research (BMBF), and the case studies are therefore selected from areas that are highly relevant for Germany’s economy (automotive, industrial production, power generation, and robotics). It also supports the digitalization of complex and transformable industrial plants in the context of the German government's "Industry 4.0" initiative, and the project results provide a solid foundation for implementing the German government's high-tech strategy "Innovations for Germany" in the coming years.

Dieses Buch wendet sich an Studenten der Mathematik bis zum Vordiplom, an Informatiker und an Interessenten aus anderen naturwissenschaftlichen Fächern. Vorausgesetzt werden nur Grundkenntnisse der Analysis und der linearen Algebra. Das Buch entstand aus einer einsemestrigen, dreistündigen Vorlesung, die der erst­ genannte Verfasser wiederholt an der TU Braunschweig hielt. Es bringt eine elemen­ tare Einführung in die Methoden der numerischen Mathematik. Hauptanliegen ist es, die Grundideen der algorithmischen Lösung verschiedenster mathematischer Aufgaben möglichst klar werden zu lassen, um den Studenten in die Lage zu ver­ setzen, verwandte Fragestellungen selbständig zu bearbeiten sowie die erlernten Prinzipien auf neue Probleme anzuwenden. Um bei den Studenten die Freude an der Praxis zu wecken, sollte der Stoff mög­ lichst lebendig dargestellt werden, ohne die Grundgedanken der Verfahren mit bezeichnungs-und beweistechnischen Schwierigkeiten zu überdecken. Um praxisnah zu sein, sind die Algorithmen stets in einer Algol 60 ähnlichen Schreibweise angegeben, die unmittelbar programmierbar ist. An einfachen Bei­ spielen wird der Ablauf der Verfahren demonstriert. Besonderen Dank verdient Frl. Dr. Ingrid Brückner, die die erste Vorlesungsmit­ schrift anfertigte und am Entstehen des Buches wesentlich beteiligt war. Für ihre Mithilfe beim Lesen der Korrekturen danken wir Frl. Dr. Brückner, Herrn Prof. Dr. Homuth und Herrn cand. math. Jürgen Rüger. Wolfenbüttel und Stuttgart Wolfgang Böhm und Günther Gose im Frühjahr 1977 IV Inhaltsverzeichnis Vorwort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . III . . . . . . . . . . . I. Grundbegriffe 1. Algorithmen und Fehlerfortpflanzung . . . . . . . . . . . . . . . . . . . ... . 1 . . . . 1.1. Algorithmen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 1 . . . . . . . . 1.2. Realisierung von Algorithmen .................................. 2 1.3. Die Beurteilung von Algorithmen ................................ 2 1.4. Aufgaben und Ergänzungen. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 3 . . . . . .

Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B­ spline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are ex­ cluded. In particular, rational Bezier and B-spline techniques are not ad­ dressed since a rigorous treatment within the appropriate context of projec­ tive geometry would have been beyond the scope of this book.

Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B­ spline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are ex­ cluded. In particular, rational Bezier and B-spline techniques are not ad­ dressed since a rigorous treatment within the appropriate context of projec­ tive geometry would have been beyond the scope of this book.