ABSTRACT

Geometries are more than just a set of objects, like lines and points. A geometry is also characterized by properties of these objects under the maps of the geometry. Thus Euclidean geometry is characterized by Eu­ clidean maps, which leave lengths and angles unchanged. Affine geometry is characterized by affine maps, which leave the ratio of three collinear points unchanged. Finally, projective geometry is characterized by projec­ tive maps which leave the cross ratio of four collinear points unchanged. In this chapter, we shall discuss those aspects of projective maps that will later be relevant for NURBS.