Approximation and modeling with B-splines (Q2872957)

The book is focused on the approximation, modeling and design techniques and algorithms with B-splines which have good computational properties that give them some advantages comparing with piecewise polynomial form of a spline function.NEWLINENEWLINEThose nine chapters of the book cover topics as Bézier form, computing with B-spline, approximation and interpolation, spline representation of curves, surfaces and solids, hierarchical bases and finite element simulation. Thus, some basic concepts for polynomials are presented in the first chapter, followed by the Bézier form, namely, Bézier curves and rational Bézier curves in the next two chapters. In the fourth chapter, the univariate B-splines are discussed from the algorithmic point of view. Some approximation methods such as interpolation, quasi-interpolation and smoothing constitute the subject for the fifth chapter. In the sixth chapter, the authors present modeling techniques for spline curves, including fundamental geometric algorithms for knot insertion and uniform subdivision. The next two chapters are dedicated to the multivariate case, based on the tensor product concept, taking into account also hierarchical refinement. An introduction to finite element simulation, with weighted and isogeometric B-spline elements, is given in the last chapter.NEWLINENEWLINEBesides those nine chapters, the work is enriched with some appendices containing an explanation of some notations and symbols, a useful index of the main concepts, some notes on the references list and some key definitions for the reader's convenience, from linear algebra, numerical and functional analysis and elementary differential geometry, basics concepts that are used in the book. Also, a supplementary web resource is announced in connection with this book, giving a collection of problems with solutions, lectures slides, programs and demos, associated with key results and methods that are most used in practice.NEWLINENEWLINEThis work constitutes an important and useful resource for interdisciplinary research, being devoted to mathematicians, computer scientists and engineers that are interested in tools for approximation of functions and data, numerical simulation, computer-aided geometric design and manufacturing, computer graphics and medical imaging.