Smooth linear approximation of non-overlap constraints

Abstract

Constraint-based placement tools and their use in diagramming tools has been investigated for decades. One of the most important and natural placement constraints in diagrams is that their graphic elements do not overlap. However, non-overlap of objects, especially non-convex objects, is difficult to solve and, in particular, to solve sufficiently rapidly for direct manipulation. Here we present the first practical approach for solving non-overlap of possibly non-convex objects in conjunction with other placement constraints such as alignment and distribution. Our methods are based on approximating the non-overlap constraint by a smoothly changing linear approximation. We have found that thi..