GPU Ray Tracing in Non-Euclidean Spaces

This book explores the visualization of three-dimensional non-Euclidean spaces using ray-tracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. Several conditions made this a special moment for such topic. On one hand, the development of mathematical research, computer graphics, and algorithms have provided the necessary theoretical framework. On the other hand, the evolution of the technologies and media allows us to be immersed in three-dimensional spaces using Virtual Reality. The content of this book serves both experts in the areas and students. Although this is a short book, it is self-contained since it considers all the ideas, motivations, references, and intuitive explanations of the required fundamental concepts.

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.

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.