Visualizing ordered sets using force-directed placement.

Abstract

The main aim of this thesis is to study and develop algorithms to visualise ordered sets and secondly to develop algorithms to visualise the faces of complicated ordered sets. To obtain a "pleasing" drawing for an order is an important issue and deserves attention. To this end, the ordered set may be drawn with minimum edge crossing, same edge length, and it may reflect geometrical symmetry (BaEaTaTo94). A leading problem is to visualise the faces of an ordered set with discrete structure; some ordered sets, like the projective plane, have a discrete structure that is difficult to visualise and understand. In this thesis we are extending to three dimensions the concept of Eades (Ea84). The ordered set is treated as a physical object and the vertices are considered as metal spheres with charges while the edges are considered as mechanical springs. The rules of physics are applied to the system and each vertex moves according to the net force applied to it until the system reaches its equilibrium position and the net force on each vertex is zero.