B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science).
A supplemental Web site will provide a collection of problems with solutions available for instructors, slides for use in lectures, and programs with demos.
Audience: Approximation and Modeling with B-Splines is appropriate as an advanced undergraduate or first-year graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering, and computer science. Practitioners in these fields who are using B-splines in numerical simulations, computer-aided design, and visualization will also find the book useful in their work.
Contents Preface; Introduction; Notation and Symbols; Chapter 1: Polynomials; Chapter 2: Bézier Curves; Chapter 3: Rational Bézier Curves; Chapter 4: B-Splines; Chapter 5: Approximation; Chapter 6: Spline Curves; Chapter 7: Multivariate Splines; Chapter 8: Surfaces and Solids; Chapter 9: Finite Elements; Notes and Comments; Appendix; Bibliography; Index.
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B-splines are a fundamental tool in the fields of numerical simulations, computer-aided design, and visualization. This book emphasises the aspects of B-spline theory that are key to practical applications: approximation methods, modeling techniques, and geometric algorithms. An ideal resource for advanced undergraduate courses in approximation and geometric modeling.About the Author:
Klaus Höllig is Chair for Numerical Analysis and Geometric Modeling at the University of Stuttgart. His research focuses on B-spline techniques for partial differential equations, approximation of curves and surfaces, and geometric algorithms. He is author of Finite Element Methods with B-Splines (SIAM, 2003) and coauthor of Box Splines (Springer-Verlag, 1993).
Jörg Hörner is a Research Associate in the Department of Mathematics at the University of Stuttgart. He develops finite element techniques for NURBS domains and is coauthor of the MATLAB® package FEMB. His interests also include educational projects; in particular he is technical director of Mathematik-Online.
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