Approximation and Modeling with B-Splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation and Modeling with B-Splines write by Klaus Hollig. This book was released on 2015-07-01. Approximation and Modeling with B-Splines available in PDF, EPUB and Kindle. 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, some with solutions, slides for use in lectures, and programs with demos.
Modeling with Ambient B-Splines
Modeling with Ambient B-Splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modeling with Ambient B-Splines write by Nicole Lehmann. This book was released on 2013. Modeling with Ambient B-Splines available in PDF, EPUB and Kindle. The present thesis introduces a new approach for the generation of CK-approximants of functions defined on closed submanifolds for arbitrary k ∈ N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R3, we even obtain Ck-approximants of closed surfaces of arbitrary topology. The key idea of our method is a constant extension of the target function into the submanifold's ambient space. In case the reference submanifolds are embedded and Ck, the usage of standard tensor product B-splines for the approximation of the extended function is straightforward. We obtain a Ck-approximation of the target function by restricting the approximant to the reference submanifold. We illustrate our method by an easy example in R2 and verify its practicality by application-oriented examples in R3. The first treats the approximation of the geoid, an important reference magnitude within geodesy and geophysics. The second and third example treat the approximation of geometric models. The usage of B-splines not only guarantees full approximation power but also allows a canonical access to adaptive refinement strategies. We elaborate on two hierarchical techniques and successfully apply them to the introduced examples. Concerning the modeling of surfaces by the new approach, we derive numerically robust formulas for the determination of normal vectors and curvature information of a target surface which only need the spline approximant as well as the normal vectors and curvature information of the reference surface.
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Element Methods with B-Splines write by Klaus Hollig. This book was released on 2012-12-13. Finite Element Methods with B-Splines available in PDF, EPUB and Kindle. An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.
Approximation and Geometric Modeling with Simplex B-splines Associated with Irregular Triangles
Approximation and Geometric Modeling with Simplex B-splines Associated with Irregular Triangles - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation and Geometric Modeling with Simplex B-splines Associated with Irregular Triangles write by S. Auerbach. This book was released on 1990. Approximation and Geometric Modeling with Simplex B-splines Associated with Irregular Triangles available in PDF, EPUB and Kindle.
Geometric Modeling
Geometric Modeling - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Modeling write by Hans Hagen. This book was released on 2012-12-06. Geometric Modeling available in PDF, EPUB and Kindle. This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.
