Mathematical modeling of distance constraints on two-dimensional φ-objects

This paper introduces the concept of radical-free pseudonormalized Φ-functions, which allows one to describe constraints on minimum and maximum allowable distances between two-dimensional φ-objects. Translations and rotations of φ-objects in a two-dimensional Euclidean space are allowable. The theorem on the existence of a radical-free pseudonormalized Φ-function for a pair of arbitrary-shaped φ-objects whose frontiers are formed by the union of line segments and circular arcs is formulated. An efficient algorithm is proposed to derive pseudonormalized Φ-functions.