On a convex operator for finite sets

In this paper we introduce a convex operator which generalizes the familiar concepts of the convex hull and the affine hull of a finite set of points. We call this operator a convex interval hull. For example, this operator, with a special choice of intervals, assigns a regular dodecagon to the 4-element set consisting of the vertices and the orthocenter of an equilateral triangle. For another choice of intervals, the operator assigns an equilateral triangle to the same set of points. The transition from the triangle to the dodecagon, changing one interval at each step, is presented in the animation. The specific intervals are given in the paper on page 5.