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