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.
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