Box Splines

This text on box splines provides a complete treatment for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly-joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an up-to-date bibliography. It is not the book's intention to be encyclopaedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasi-interpolants and approximation power. It continues with cardinal interpolation and difference equations, and approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms.