Charles Gunn

Researcher and Teacher
Matheon, Technisches Universität Berlin
Berlin, Germany

I enjoy exploring two- and three-dimensional tessellations -- euclidean, spherical and hyperbolic, especially the "insider's" view of such spaces. I have been experimenting recently with alternative perspective rendering based on a spherical canvas surrounding the viewer. This "viewable sphere" is then flattened out via stereographic projection to make the image. In contrast to standard perspective images, the resulting images are conformal (small spheres in the scene are projected to small circles in the picture) and show a large fraction of the world. I have found this technique is well-suited to visualizing space-filling tessellations. I hope my work stimulates reflection in the observer on what "true perspective" means.

View of the platycosm -a2, decorated with AMS
18" x 18"
Print of computer image

This is an insider's view of the platycosm -a2. ("Platycosm" is John Conway's term for a compact euclidean 3-manifold.) This platycosm is generated by a translation, a glide reflection and a screw motion with order-2 rotational part, in three mutually perpendicular directions. The fundamental domain is a cube, whose edges are rendered via the textured beams. The "geometry" consists of the initials AMS, in honor of one of the hosting orgranizations of the art show. The image is rendered conformally from the viewable sphere of an insider positioned in the scene. I sometimes call this "six-point perspective" rendering since one may see vanishing points not just in the x,y, and z directions but also in the -x, -y, and -z directions.