This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.

Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first comprehensive treatment of the analogous bivariate theory. A detailed mathematical treatment of polynomial splines on triangulations is outlined, providing a basis for developing practical methods for using splines in numerous application areas. The detailed treatment of the Bernstein-Bézier representation of polynomials will provide a valuable source for researchers and students in CAGD. Chapters on smooth macro-element spaces will allow engineers and scientists using the FEM method to solve partial differential equations numerically with new tools. Workers in the geosciences will find new tools for approximation and data fitting on the sphere. Ideal as a graduate text in approximation theory, and as a source book for courses in computer-aided geometric design or in finite-element methods.

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