Morphing Schnyder Drawings of Planar Triangulations

摘要

We consider the problem of morphing between two planar drawings of the same triangulated graph, maintaining straight-line planarity. In How to morph planar graph drawings (SIAM Journal on Computing) the authors give a morph that consists of O(n) steps where each step is a linear morph that moves each of the n vertices in a straight line at uniform speed. However, their method imitates edge contractions so the grid size of the intermediate drawings is not bounded and the morphs are not good for visualization purposes. Using Schnyder embeddings, we are able to morph in O(n2) linear morphing steps and improve the grid size to O(n)xO(n) for a significant class of drawings of triangulations, namely the class of weighted Schnyder drawings. The morphs are visually attractive. Our method involves implementing the basic flip operations of Schnyder woods as linear morphs.