Math Augmentation: How Authors Enhance the Readability of Formulas using Novel Visual Design Practices

To find the light towards the viewer from a specific point, we sum the light emitted form such point plus the integral within the unit hemisphere of the light coming from a any given direction multiplied by the chances of such light rays bouncing towards the viewer and also by the irradiance factor over the normal at the point.

Note that incoming light is also computed by that very formula, which makes this exhaustingly recursive.

Figure 1: A formula from computer graphics, visually embellished to improve its readability, from [5] (CC BY-NC-SA 4.0). One author from our interview study created this formula and the accompanying colorized diagram and text to teach readers of his blog how to implement the formula in source code. Like many of the formulas analyzed in this paper, this one makes use of color to draw attention to conceptually important expressions in the formula, and to help a reader visually link those expressions to complementary diagrams and prose. Contents of the blog post (formula, prose, and diagram) have been rearranged in this fgure to emphasize the formula.