Mathematical Aspects of Computer Aided Geometric Design

Abstract

Computer Aided Geometric Design (CAGD) is concerned with the design, computation, and representation of curved objects on a computer. Therefore, not surprisingly, CAGD has traditionally had strong ties to some classical mathematical disciplines such as approximation theory (approximation by polynomial and piecewise polynomial functions), differential geometry (parametric surfaces), algebraic geometry (algebraic surfaces), functional analysis and differential equations (surface design by minimizing functionals), and numerical analysis. In addition, work in CAGD also requires a solid background in computer science.