FreeForm: Flexibly Augmenting Formulas with Synchronized Markup and Graphical Edits

Authors of typeset formulas augment those formulas to make them easier to understand. When they do so, they trade off between using markup tools like LaTeX and formula-unaware graphical editors. In this paper, we explore how editing tools could combine the best affordances of both kinds of tools. We develop FreeForm, a projectional editor wherein authors can augment formulas—with color, labels, spacing, and more—across multiple synchronized representations. Augmentations are created graphically using direct selections and compact menus. Those augmentations propagate to LaTeX markup, which can itself be edited and easily exported. In two lab studies, we observe the value of our editor versus baselines of a widely-used LaTeX document editor and a state-of-the-art formula augmentation tool. Finally, we make recommendations for the design of projectional markup augmentation editors.