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.