Breaking the Plane: Exploring Real-Time Visualization of 3D Surfaces in Augmented Reality with Handwritten Input

We introduce Breaking the Plane, an augmented reality (AR) application built for AR headsets that enables users to visualize 3D mathematical functions using handwritten input. Researchers have demonstrated overlaying 3D visualizations of mathematical concepts through AR enhances learning motivation and comprehension, and equation parsing makes the authoring of teaching materials more time-efficient for instructors. Previous works have developed AR systems that separately employ equation parsing and 3D mathematical visualizations, but work has yet to be done to combine those features by enabling real-time interactions and dynamic visualizations that help users learn in situ. We explore this by developing an AR system featuring handwritten equation parsing, graph manipulation, and a 3D function plotter. We found that our system significantly surpassed other systems in engagement, achieved comparable ease of use to a popular visualization tool, was considered the most effective in aiding problem-solving, and was highly preferred by participants for future use.