How to Turn Equations into Illustrations?

Monday, June 15, 2020 - 12:44

Carnegie Mellon University researchers have developed a tool that is able to turn the abstractions of mathematics into illustrations and diagrams through software.

The software turns ordinary mathematical expressions typed by the user into illustrations, UNITE.AI reports. The tool “Penrose”, inspired by the mathematician and physicist Roger Penrose, who is known for using complex mathematical and scientific ideas through diagrams and drawings.

One of the major developments in this project is that the expressions are not required to be basic functions, as in the case of a graphing calculator. Instead, they can be complex relationships coming from various different fields within mathematics.

Penrose will be presented by researchers at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques. The conference will take place virtually this year due to the COVID-19 pandemic.

Diagrams are not used as much in technical communication, due to the required amount of high-skill and tedious work required in order to produce them. To get around this, the Penrose tool allows experts to encode the steps in the system, and other users are then able to access this by using mathematical language. All of this means that the computer is doing most of the work.

The computer first learns how the user wants the mathematical objects visualized, such as an arrow or a dot, and it then draws up multiple diagrams. The user selects and edits one of those diagrams.

The team that developed Penrose also included Nimo Ni and Jenna Wise, who are Ph.D. students in CMU’s Institute for Software Research (ISR); Jonathan Aldrich, professor in ISR; Joshua Sunshine, ISR senior research fellow; Max Krieger, cognitive science undergraduate; and Dor Ma’ayan, former master’s student at the Technion-Israel Institute of Technology.

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