ABSTRACT
Affine maps preserve the structure of the mapped affine spaces. Of particu lar interest are the properties which remain invariant when figures undergo affine mappings. These properties depend on the affine rules used to con struct a figure not on the position of the figure in space. Often a special position allows for a simple proof of a general theorem. A pair of points and their midpoint form an example of a simple affine figure. The Bezier and B-spline representation of curves have affine properties which are rather intriguing and most crucial for geometric design.