A visibility algorithm for the projection PSd --> PS2

János KATONA, Szent István University, Faculty of Architecture,
Department of Drawing and Computer Science

Emil MOLNÁR, Budapest University of Technology
 and Economics, Department of Geometry

In the previous conference (ICAI 2004, Eger) we suggested a general method for describing geometry of k-spaces in a d-dimensional real projective metric space and for the projection of PSd onto PS2. This method allows an approach to Euclidean, hyperbolic, spherical and other geometries uniformly and it determines the visibility of the d-dimensional solids.
Applying the general method we concretize the visibility algorithm by a simple vector calculus. We emphasize that we look for objects from the viewpoint as centre along a half-line, and in this sense a line has two ideal points at infinity.
We illustrate this method by the projection of four-dimensional cube. First we apply the usual axonometric projection onto the xy plane from the ideal points of third and fourth axes, then the central projection from the „d”-distance points of the third and fourth axes, and finally we render the figure by our visibility method. Thus we look at the 2-surface of the 4-cube in front of us.
Later on, we plan to move with the centre and with the image 2-plane, while the 4-cube is standing, and apply this method to the other regular 4-solids (see the homepage of István PROK http://www.math.bme.hu/~prok), etc.