Minimal Representations of Order Types by Geometric Graphs

Abstract

In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unequivocally display the order type of S. We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices.

Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.

Keywords

• Geometric graph
• Straight-line drawing
• Order type
• Pseudoline arrangement
• Triangular cell