Spline Functions and Surfaces

The goal was to study the use of smooth piecewise polynomial spaces for the approximation of functions in one and, preferably, in several variables and find a better understanding of how well one can approximate from specific spaces, for specific schemes for approximation, including good bases for such spaces, and to make inroads on the problem of extending techniques for curve fitting by smoothly patched curves to surface interpolation. Progress was made on these questions, and on two related but unanticipated projects i a monograph on box splines to make available in easily accessible form the many results on box splines obtained by us and others since their introduction by us ten years ago and ii what now looks like the right approach to polynomial interpolation in several variables.