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This book is about graphics programming based on OPENGL. The program­ ming language is C++. The programs will run under various operating systems, among them WINDOWS 9x, ALPHA-STATIONS (Digital workstations) and SILI­ CON GRAPHICS workstations. Hardware is used if accessible. The book provides a graphics library. This library is based on OPENGL and expands the elemen­ tary routines. Thus, the reader is enabled to realize direct geometrical thinking without having to care much about implementation. The enclosed modules provide the reader with solutions for: • The most common intersection problems and measuring tasks of both pla­ nar and spatial geometry. • The creation ofarbitrary geometric objects, e.g., by means ofdifferent kinds of "sweeping." • The creation of the most general solids by means of Boolean operations (intersection, union, and complements of solid polyhedra). The book presents: • A well documented, versatile, and robust geometry library. The reader can use it very easily and expand it in any way he/she likes. vi Preface • A programming course that provides a deeper insight into object-oriented thinking and programming.It contains an introduction to C++ (for begin­ ners and intermediate programmers) that is influenced by the experience gained from thousands of programming hours (which may even be useful to experienced programmers).

Computer graphics --- Geometry --- Data processing. --- OpenGL. --- Computer graphics. --- Infographie --- Géométrie --- Data processing --- Informatique --- OpenGL --- Software engineering. --- Software Engineering/Programming and Operating Systems. --- Computer Graphics. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Computer software engineering --- Engineering --- Digital techniques --- Geometry - Data processing.

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The Universe of Quadrics This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective, affine, and metrical properties, covering both Euclidean and non-Euclidean geometries. While the history of conics is more than two thousand years old, the theory of quadrics began to develop approximately three hundred years ago. Quadrics play a fundamental role in numerous fields of mathematics and physics, their applications ranging from mechanical engineering, architecture, astronomy, and design to computer graphics. This text will be invaluable to undergraduate and graduate mathematics students, those in adjacent fields of study, and anyone with a deeper interest in geometry. Complemented with about three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises. The Authors Boris Odehnal, born in 1973, got his PhD and habilitation in geometry at the Vienna University of Technology. 2011–2012 professor at the Dresden University of Technology. Since 2012, he has held the position of senior lecturer in geometry at the University of Applied Arts Vienna. He is the author of several dozens of publications on geometry. Hellmuth Stachel, born in 1942, got his PhD and habilitation in geometry in Graz. In 1978, he became full professor at the Mining University Leoben, and from 1980–2011, he was full professor of geometry at the Vienna University of Technology. He has coauthored several books on mathematics and computational geometry and more than 160 articles on geometry. Georg Glaeser, born in 1955, got his PhD and habilitation in geometry at the Vienna University of Technology. Since 1998, he is full professor of geometry at the University of Applied Arts Vienna. He is the author and coauthor of more than twenty books on geometry, mathematics, computational geometry, computer graphics, and photography.

Geometry. --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Euclid's Elements --- Quadrics. --- Surfaces, Conic --- Surfaces, Quadric --- Paraboloid --- Surfaces

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The Universe of Quadrics This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective, affine, and metrical properties, covering both Euclidean and non-Euclidean geometries. While the history of conics is more than two thousand years old, the theory of quadrics began to develop approximately three hundred years ago. Quadrics play a fundamental role in numerous fields of mathematics and physics, their applications ranging from mechanical engineering, architecture, astronomy, and design to computer graphics. This text will be invaluable to undergraduate and graduate mathematics students, those in adjacent fields of study, and anyone with a deeper interest in geometry. Complemented with about three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises. The Authors Boris Odehnal, born in 1973, got his PhD and habilitation in geometry at the Vienna University of Technology. 2011–2012 professor at the Dresden University of Technology. Since 2012, he has held the position of senior lecturer in geometry at the University of Applied Arts Vienna. He is the author of several dozens of publications on geometry. Hellmuth Stachel, born in 1942, got his PhD and habilitation in geometry in Graz. In 1978, he became full professor at the Mining University Leoben, and from 1980–2011, he was full professor of geometry at the Vienna University of Technology. He has coauthored several books on mathematics and computational geometry and more than 160 articles on geometry. Georg Glaeser, born in 1955, got his PhD and habilitation in geometry at the Vienna University of Technology. Since 1998, he is full professor of geometry at the University of Applied Arts Vienna. He is the author and coauthor of more than twenty books on geometry, mathematics, computational geometry, computer graphics, and photography.

Geometry --- Mathematics --- Applied physical engineering --- toegepaste wiskunde --- economie --- wiskunde --- geometrie

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Dieses vierfarbige Lehrbuch wendet sich an Studierende der Mathematik in Bachelor- und Lehramts-Studiengängen. Es bietet in einem Band ein lebendiges Bild der mathematischen Inhalte, die üblicherweise im ersten Studienjahr behandelt werden (und etliches mehr). Mathematik-Studierende finden wichtige Begriffe, Sätze und Beweise ausführlich und mit vielen Beispielen erklärt und werden an grundlegende Konzepte und Methoden herangeführt. Im Mittelpunkt stehen das Verständnis der mathematischen Zusammenhänge und des Aufbaus der Theorie sowie die Strukturen und Ideen wichtiger Sätze und Beweise. Es wird nicht nur ein in sich geschlossenes Theoriengebäude dargestellt, sondern auch verdeutlicht, wie es entsteht und wozu die Inhalte später benötigt werden. Herausragende Merkmale sind: - durchgängig vierfarbiges Layout mit mehr als 600 Abbildungen - prägnant formulierte Kerngedanken bilden die Abschnittsüberschriften - Selbsttests in kurzen Abständen ermöglichen Lernkontrollen während des Lesens - farbige Merkkästen heben das Wichtigste hervor - „Unter-der-Lupe“-Boxen zoomen in Beweise hinein, motivieren und erklären Details - „Hintergrund-und-Ausblick“-Boxen stellen Zusammenhänge zu anderen Gebieten und weiterführenden Themen her - Zusammenfassungen zu jedem Kapitel sowie Übersichtsboxen - mehr als 400 Verständnisfragen, Rechenaufgaben und Aufgaben zu Beweisen - deutsch-englisches Symbol- und Begriffsglossar Der inhaltliche Schwerpunkt liegt auf den Themen der Vorlesungen Analysis 1 und 2 sowie Linearer Algebra 1 und 2. Behandelt werden darüber hinaus Inhalte und Methodenkompetenzen, die vielerorts im ersten Studienjahr der Mathematikausbildung vermittelt werden. Auf der Website zum Buch www.matheweb.de finden Sie - Hinweise, Lösungswege und Ergebnisse zu allen Aufgaben - Zusatzmaterialien wie Maple-Worksheets zu verschiedenen Themen des Buchs - die Möglichkeit, zu den Kapiteln Fragen zu stellen Das Buch wird allen Studierenden der Mathematik vom Beginn des Studiums bis in höhere Semester hinein ein verlässlicher Begleiter sein.

Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Matrix theory. --- Algebra. --- Mathematics, general. --- Analysis. --- Linear and Multilinear Algebras, Matrix Theory.

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Dieses Buch enthält Zusatzmaterial zu allen sechs Teilen des Lehrbuchs Arens et al., Mathematik (dritte Auflage). Es wendet sich an Studierende, die an Ergänzungen und Vertiefungen zur Linearen Algebra, der Analysis sowie der Wahrscheinlichkeitsrechnung sowie an prägnanten Kurzeinführungen zur elementaren Zahlentheorie sowie zu Begriffen der Algebra (Gruppe, Ringe, Körper) interessiert sind. Die vorliegende zweite vollständig durchgesehene Auflage ist inhaltlich um eine Reihe von Themen ergänzt: • logische Paradoxa, unendliche Produkte  • eine kurze Einführung in die Begriffe Gruppe, Ring, Körper  • Implementierungsaspekte (z.B. Aufwandsschätzungen) numerischer Methoden der linearen Algebra anhand wichtiger konkreter Verfahren  • ergänzende Hinweise zu Variablentransformationen, insb. mit Anwendungen des Wechsels zwischen abhängigen und unabhängigen Variablen in der Thermodynamik   • Bézierkurven und darauf aufbauende weitere Freiformkurven und –flächen • Hamilton’sches Prinzip inkl. Legendre-Transformation • Ergänzungen zur Statistik, insbesondere Kerndichteschätzer und Kovarianzellipsen Die Autoren PD Dr. Tilo Arens, Fakultät für Mathematik des Karlsruher Instituts für Technologie (KIT) PD Dr. Frank Hettlich, Fakultät für Mathematik des Karlsruher Instituts für Technologie (KIT) PD Dr. Christian Karpfinger, Technische Universität München Dr. Ulrich Kockelkorn war bis zu seiner Pensionierung 2006 Professor für Statistik und Wirtschaftsmathematik an der TU Berlin Dr. Klaus Lichtenegger studierte in Graz Physik und Umweltsystemwissenschaften Dr. Dr. h.c. Hellmuth Stachel, emeritierter Professor für Geometrie, TU Wien.

Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Mathematics, general. --- Mathematical and Computational Engineering.