Hartmut Prautzsch Libros

Este libro ofrece una base sólida para la teoría de curvas de Bézier y B-spline, destacando su elegante estructura matemática. Se centra en las nociones centrales del Diseño Geométrico Asistido por Computadora, buscando proporcionar un tratamiento analítico claro y geométricamente intuitivo de los principios básicos del área. Además, incluye material avanzado como splines multivariados, técnicas de subdivisión y la construcción de superficies libres con cualquier grado de suavidad. El texto está excelentemente ilustrado con diagramas y figuras que complementan el contenido, enfatizando el enfoque constructivo. Se presenta una derivación uniforme de las propiedades de las representaciones de Bézier y B-spline, mostrando la belleza de esta rica estructura matemática subyacente. También se abordan construcciones de superficies de libre forma, algoritmos de subdivisión, boxsplines, simplexsplines y splines multivariados. Las numerosas ilustraciones destacan el enfoque geométrico y constructivo del libro, facilitando la comprensión de los conceptos fundamentales del Diseño Geométrico.

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.

Geometric methods and their principles are thoroughly explored, providing a strong foundation in geometric design and modeling. The book serves as a valuable resource for students, teachers, and researchers in mathematics, computer science, and engineering, equipping them to tackle various geometric problems effectively.