Seminar in Real & Complex Geometry

Thursday, 9.01.2014, 16:30-18:00, Schreiber building, room 210

Alfred Inselberg, Tel Aviv University

Representing hypersurfaces in parallel coordinates


A smooth hypersurface in RN is the envelope of its tangent hyper planes, each represented by (N-1) indexed points, providing (N-1) linked planar regions (see below) whose contours can be efficiently obtained. This is equivalent to representing the hyper surface by its normal vectors at each point. The resulting patterns reveal surface properties i.e. developable, ruled, cusps, twists, non-orientability, convexity which are hidden or distorted in other representations. Our 3-dimensional experience serves as a laboratory by visually discovering properties from the patterns of surfaces in R3 and conjecture higher dimensional generalizations i.e. dualities like cusp in RN -- (N-1) "swirls" in R2 and others. The patterns persist in the presence of errors which is good news for the applications.