Upright-Quad Drawing of st-Planar Learning Spaces

TL;DR

This paper presents a method for drawing st-planar learning spaces as convex quadrilaterals with specific orientation, establishing a correspondence between these drawings and arrangements of translated quadrants.

Contribution

It introduces a novel drawing technique for st-planar learning spaces and characterizes their geometric representations, linking them to quadrant arrangements.

Findings

All internal faces are convex quadrilaterals with specified orientation.

Every such drawing corresponds to an st-planar learning space.

Connections to arrangements of translated quadrants are established.

Abstract

We consider graph drawing algorithms for learning spaces, a type of st-oriented partial cube derived from antimatroids and used to model states of knowledge of students. We show how to draw any st-planar learning space so all internal faces are convex quadrilaterals with the bottom side horizontal and the left side vertical, with one minimal and one maximal vertex. Conversely, every such drawing represents an st-planar learning space. We also describe connections between these graphs and arrangements of translates of a quadrant.