The plane with parallel coordinates

By means of Parallel Coordinates planar "graphs" of multivariate relations are obtained. Certain properties of the relationship correspond to the geometrical properties of its graph. On the plane a point <- ->. line duality with several interesting properties is induced. A new duality between bounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results in Computational Geometry. There is also a suprising "cusp" <- -> "inflection point" duality. The narrative ends with a preview of the corresponding results in R-N.