Prof. Dr. Benedikt Stufler

Simulations: Schnyder-wood-decorated triangulations


A Schnyder-wood decorated triangulation is a special type of planar triangulation - a maximal planar graph drawn in the plane without edge crossings - endowed with an additional combinatorial structure called a Schnyder wood. In this decoration, the interior edges of the triangulation are oriented and coloured using three colours (typically labelled 0, 1, and 2) in such a way that each interior vertex has exactly one outgoing edge of each color, and the edges follow specific local rules that organize the global embedding into a tree-like structure.

Schnyder-wood-decorated triangulation with 1M faces. The colours of the faces represent closeness centrality in the dual map.


Schnyder-wood-decorated triangulation with 2M faces. The colours of the faces represent closeness centrality in the dual map.


Schnyder-wood-decorated triangulation with 4M faces. The colours of the faces represent closeness centrality in the dual map.


Schnyder-wood-decorated triangulation with 8M faces. The colours of the faces represent closeness centrality in the dual map.