Betweenness in Polar Coordinates

Carroll, Jeremy J.

HP Development Company

关键词: betweenness;    geometry;    lines;    polar coordinates;    trilinear coordinates;   

RP-ID  :  HPL-2000-71

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

We consider straight line drawings. From a graph theoretic point of view these are plane graphs with a set of preferred paths. This graph is expressed in geometric terms through the consideration of the betweenness of the points of intersection along each of the lines. If we fix a reference system for polar coordinates, we can identify a number of equalities and inequalities over the complete set of polar coordinates satisfied by this particular drawing. We show that every solution to these inequalities describes a drawing that is equivalent under graph theoretic considerations, in particular betweenness. We show that this equivalence is independent of the polar reference system. Notes: 17 Pages