Duality of the QuickHull Algorithm

Duality is the concept that two numbers a and b can be represented in two ways: as a set of points (a,b) or as a line with the equation y = 2ax - b (this equation produces parabolic duality; other equations can be used for slope or polar duality.)

Duality of points and lines produces interesting correlations. An algorithm that finds the convex hull of a set of ponts corresponds exactly to an algorithm that finds the upper and lower envelopes of an arrangement of lines.