ABSTRACT
We introduce the classical ideas of interpolation and approximation of preexisting data. While some of these ideas have been used extensively in many areas of applied mathematics, others of them were useful mainly to prove other theorems. However, the emergence of computer aided geometric design has modified accepted ideas of the usefulness of classical methods. Some of the already popular ones were used in fresh new ways to provide the underpinnings for some curve and surface modeling efforts (Coons' surfaces), while others which had been deemed not practical have become workhorses in CAGD through the reassessment of the methods (Bernstein/Bézier curves and surfaces).
