Coordinates - A survey on higher geometry

Under the name ''Higher Geometry'' usually those different geometries are summarized which in the sense of F. Klein's Erlangen program (1872) are isomorphic to subgeometries of projective geometry. In the following we give a brief survey on such geometries like multi-dimensional projective, affine and Euclidean geometry, the geometry of lines and the geometry of oriented spheres in the three-dimensional case. It is a goal of this paper to demonstrate both the elegance of the classical analytical treatment and its applicability for various tasks, e.g. in the field of CAGD. The latter however has been reduced to the presentation of references only. (C) 1997 Elsevier Science B.V.