Offline Drawing of Dynamic Trees: Algorithmics and Document Integration

TL;DR

This paper introduces an extension to the exttt{TeX} system for embedding dynamic tree animations in documents, providing an algorithm that balances aesthetic criteria and produces SVG animations, despite some NP-completeness limitations.

Contribution

It presents a novel method for integrating animated dynamic trees into documents via exttt{TeX} and a new algorithm that considers aesthetic criteria for drawing animations.

Findings

The algorithm produces visually pleasing SVG animations.

Balancing multiple aesthetic criteria is NP-complete.

The extension simplifies creating animated trees in documents.

Abstract

While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not integrated into a document production workflow and algorithmic approaches only rarely take temporal information into consideration. During the production of a presentation or a paper, most users will visualize how, say, a search tree evolves over time by manually drawing a sequence of trees. We present an extension of the popular $\TeX$ typesetting system that allows users to specify dynamic trees inside their documents, together with a new algorithm for drawing them. Running $\TeX$ on the documents then results in documents in the SVG format with visually pleasing embedded animations. Our algorithm produces animations that satisfy a set of natural aesthetic criteria when possible. On the negative side, we show that one cannot always satisfy all criteria simultaneously and that minimizing their violations is NP-complete.