"The secret sauce of our system is to empower people to easily 'explain' this translation process to the computer, so the computer can do all the hard work of actually making the picture." Once the computer learns how the user wants to see mathematical objects visualized - a vector represented by a little arrow, for instance, or a point represented as a dot - it uses these rules to draw several candidate diagrams. student in the Computer Science Department. "We started off by asking: 'How do people translate mathematical ideas into pictures in their head?'" said Katherine Ye, a Ph.D. The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques, which will be held virtually this July because of the COVID-19 pandemic. Other users can then access this capability using familiar mathematical language, leaving the computer to do most of the grunt work. Penrose addresses these challenges by enabling diagram-drawing experts to encode how they would do it in the system. "We want to make this expressive power available to anyone." Diagrams are often underused in technical communication, since producing high-quality, digital illustrations is beyond the skill of many researchers and requires a lot of tedious work. "Some mathematicians have a talent for drawing beautiful diagrams by hand, but they vanish as soon as the chalkboard is erased," said Keenan Crane, an assistant professor of computer science and robotics. The researchers named it Penrose after the noted mathematician and physicist Roger Penrose, who is famous for using diagrams and other drawings to communicate complicated mathematical and scientific ideas. Unlike a graphing calculator, these expressions aren't limited to basic functions, but can be complex relationships from any area of mathematics.
The tool enables users to create diagrams simply by typing an ordinary mathematical expression and letting the software do the drawing.
Thanks to a new tool created at Carnegie Mellon University, anyone can now translate the abstractions of mathematics into beautiful and instructive illustrations.
Some people look at an equation and see a bunch of numbers and symbols others see beauty.