20/09/2024

Visgraf's work is the subject of an AMS book.

The development of algorithms for virtual reality simulations of Euclidean, spherical, and hyperbolic space, carried out by Visgraf (the Computer Graphics Laboratory of IMPA), is one of the topics in the recently released book "What's Happening in the Mathematical Sciences". Published every two years by the American Mathematical Society (AMS) , the book features an image of the laboratory on its cover, which used computers and virtual reality to bring to life the eight distinct geometries of three-dimensional "alternative universes" discovered more than 40 years ago by Bill Thurston.

Volume 13 of the publication, which will soon be available in the IMPA library, recalls that the exhibition "A Look at 3-Dimensional Spaces," which shows how light travels within Euclidean and non-Euclidean spaces, was the starting point for the new work. Organized by the French authors Pierre Berger and Pierre-Yves Fave, with the participation of scientists Luiz Velho (IMPA) and Alex Laier (UFF) and the artist Sergio Krakowski, the exhibition visited four cities in Brazil and remained on display for four years. However, Luiz Velho felt that something was missing from the project.

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"You feel the concept, it includes these visuals and sounds, but you're not really immersed. It was necessary to do this using virtual reality," said the lead researcher of Visgraf in an interview with journalist Leila Sloman.

It was at this time that mathematicians Vinicius Silva and Tiago Novello arrived at IMPA for a postdoctoral fellowship in Visgraf. While Silva had experience in developing simulations that could load images in real time, Novello had just completed a doctorate in geometry and programming. "This group is very special because we end up complementing each other," Velho recalled.

After much work, in 2020, the trio published several articles sharing algorithms for virtual reality simulations of Euclidean, spherical, and hyperbolic space, as well as the three twisted geometries. In 2023, they gave a course on the topic at the 33rd Brazilian Mathematics Colloquium, for which they published a book entitled "Visualizing Thurston's Geometries".

The results caught the attention of professionals from various fields. "I'm surprised by the number of people who are seeing our articles," Silva said in an interview. "On ResearchGate, you see many people who aren't from computer graphics looking at the work. There are many people from mathematics, people from physics, so people are trying to understand the geometry of this space," he concluded.

Currently, Novello is a researcher at IMPA and Silva is part of the Tecgraf team at PUC-Rio.

The book continues the theme and points to other works carried out in the area. One of them is the game HyperRogue, developed by researchers Eryk Kopezynski and Dorota Clisa Kopczynska from the University of Warsaw. The game's premise is that players jump from piece to piece in a Nomentidian space, escaping monsters and using geometry to their advantage.