GPU Ray Tracing in Non-Euclidean Spaces (2022) [Novello et al] [9781636393278].pdf

GPU Ray Tracing in Non-Euclidean Spaces (2022) [Novello et al] [9781636393278].pdf List of Figures Introduction Motivation Related Work OpenGL Visualization of Non-Euclidean Spaces Virtual Reality Ray Tracing Metric Neutral Visualization of Non-Euclidean Manifolds Structure of the Book Mathematical Background History Henri Poincaré William P. Thurston Grigori Perelman Topology Riemannian Geometry Manifold Metric Lie Groups Geodesics Exponential Map 2-Manifolds Classification of Compact Surfaces Geometrization of Compact Surfaces 3-Manifolds Classification of Compact 3-Manifolds Geometrization of Compact 3-Manifolds Eight Thurston Geometries Classical Geometries Product Geometries ``Twisted" Product Geometries Visualization of Three-Dimensional Spaces The Viewing Transformation Pipeline Inside Views in Non-Euclidean Spaces Types of Algorithms Rendering Acceleration Immersive Visualization GPU Ray Tracing RTX Ray Tracing Falcor 3.2.1 Ray Tracing VR Simple Ray Tracer PathTracing StereoRendering Integration Stereo Convergence Ray Tracing Overhead Riemannian Ray Tracing Core Concepts Geodesics and Fundamental Domain Non-Euclidean Ray Tracing Riemannian Manifolds and Lie Groups Visualization of Riemannian Manifolds Visualization Approaches Riemannian Ray Tracing Ray Tracing in Riemannian Manifolds Overview of the Method Algorithm in CPU Ray Marching RTX Pipeline GPU Implementation Classical non-Euclidean Spaces Flat Flat Torus Mirrored Cube Spherical Poincaré Sphere Hyperbolic Seifert–Weber Dodecahedral Space Mirrored Dodecahedron Analysis Performance Interaction Space Perception Nil, SL2, and Sol Visualizing Nil Space Visualizing Sol Space Visualizing SL2(R)0K0I0d"0365 SL2(R)0K0I0d"0365 SL2(R)0K0I0d"0365 SL2(R)0K0I0d"0365 Space Experiments and Comparisons Curved 3D Spaces Examples of Riemannian Metrics Graph of a Function Diffeomorphisms Deforming the Space Local Metric Deformations Using Graphs Using Diffeomorphism Accumulating Deformations Photo-Realism Illumination of Non-Euclidean Spaces Global Illumination in Non-Euclidean Spaces Path Tracing in Non-Euclidean Spaces Overview of the Method Algorithm in CPU Examples and Results Flat Torus Poincaré Sphere Mirrored Dodecahedron Web Resources Books Videos Lectures Researchers and Groups Working in the Area Activities at IMPA Lectures Events and Conferences Courses Bibliography Authors' Biographies

This book explores the visualization of three-dimensional non-Euclidean spaces using raytracing 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.