GPU Ray Tracing in Non-Euclidean Spaces

Tiago Novello is a Postdoctoral Researcher at IMPA Vision and Graphics (VISGRAF) Laboratory. He obtained a D.Sc. in Applied Mathematics at Pontifícia Universidade Católica do Rio de Janeiro, an M.Sc. in Mathematics from the Universidade Federal de Alagoas, and a B.Sc. in Mathematics at Universidade Estadual do Paraná. Vinícius da Silva is a Postdoctoral Researcher at PUC-Rio. He obtained his D.Sc. and M.Sc in Computer Science from the Federal University of Rio de Janeiro. His research interests are Real-Time Computer Graphics, Virtual Reality, Games, and Machine Learning, with a current focus on Real-Time Ray Tracing. Luiz Velho is a Senior Researcher/Professor at IMPA and the leading scientist of the VISGRAF Laboratory. He received a B.E. in Industrial Design from ESDI, an M.S. in Computer Graphics from the MIT/Media Lab, and a Ph.D. in Computer Science from the University of Toronto. His experience spans the fields of modeling, rendering, imaging, and animation.

• List of Figures.- Introduction.- Mathematical Background.- Visualization of Three-Dimensional Spaces.- Immersive Visualization.- Riemannian Ray Tracing.- Classical \lowercase {non.- Nil, SL2, and Sol.- Curved 3D Spaces.- Photo-Realism.- Bibliography.- Authors' Biographies.