Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs

Table of Contents
Preface
Foreword
Contributors
Notation
Part I: Ray Tracing Basics
	Chapter 1: Ray Tracing Terminology
		1.1	 Historical Notes
		1.2	 Definitions
	Chapter 2: What is a Ray?
		2.1	 Mathematical Description of a Ray
		2.2	 Ray Intervals
		2.3	 Rays in DXR
		2.4	 Conclusion
	Chapter 3: Introduction to DirectX Raytracing
		3.1	 Introduction
		3.2	 Overview
		3.3	 Getting Started
		3.4	 The DirectX Raytracing Pipeline
		3.5	 New HLSL Support for DirectX Raytracing
			3.5.1	 Launching a New Ray in HLSL
			3.5.2	 Controlling Ray Traversal in HLSL
			3.5.3	 Additional HLSL Intrinsics
		3.6	 A Simple HLSL Ray Tracing Example
		3.7	 Overview of Host Initialization for DirectX Raytracing
			3.7.1	 Insight into the Mental Model
		3.8	 Basic DXR Initialization and Setup
			3.8.1	 Geometry and Acceleration Structures
				3.8.1.1	 Bottom-Level Acceleration Structure
				3.8.1.2	 Top-Level Acceleration Structure
			3.8.2	 Root Signatures
			3.8.3	 Shader Compilation
		3.9	 Ray Tracing Pipeline State Objects
		3.10	 Shader Tables
		3.11	 Dispatching Rays
		3.12	 Digging Deeper and Additional Resources
		3.13	 Conclusion
	Chapter 4: A Planetarium Dome Master Camera
		4.1	 Introduction
		4.2	 Methods
			4.2.1	 Computing Ray Directions from Viewport Coordinates
			4.2.2	 Circular Stereoscopic Projection
			4.2.3	 Depth of Field
			4.2.4	 Antialiasing
		4.3	 Planetarium Dome Master Projection Sample Code
	Chapter 5: Computing Minima and Maxima of Subarrays
		5.1	 Motivation
		5.2	 Naive Full Table Lookup
		5.3	 The Sparse Table Method
		5.4	 The (Recursive) Range Tree Method
		5.5	 Iterative Range Tree Queries
		5.6	 Results
		5.7	 Summary
Part II: Intersections and Efficiency
	Chapter 6: A Fast and Robust Method for Avoiding Self-Intersection
		6.1	 Introduction
		6.2	 Method
			6.2.1	 Calculating the Intersection Point on the Surface
			6.2.2	 Avoiding Self-Intersection
				6.2.2.1	 Exclusion Using the Primitive Identifier
				6.2.2.2	 Limiting the Ray Interval
				6.2.2.3	 Offsetting Along the Shading Normal or the Old Ray Direction
				6.2.2.4	 Adaptive Offsetting Along the Geometric Normal
		6.3	 Conclusion
	Chapter 7: Precision Improvements for  Ray/Sphere Intersection
		7.1	 Basic Ray/Sphere Intersection
		7.2	 Floating-Point Precision Considerations
		7.3	 Related Resources
	Chapter 8: Cool Patches: A Geometric Approach to Ray/Bilinear Patch Intersections
		8.1	 Introduction and Prior Art
			8.1.1	 Performance Measurements
			8.1.2	 Mesh Quadrangulation
		8.2	 GARP Details
		8.3	 Discussion of Results
		8.4	 Code
	Chapter 9: Multi-Hit Ray Tracing in DXR
		9.1	 Introduction
		9.2	 Implementation
			9.2.1	 Naive Multi-Hit Traversal
			9.2.2	 Node-Culling Multi-Hit BVH Traversal
		9.3	 Results
			9.3.1	 Performance Measurements
				9.3.1.1	 Find First Intersection
				9.3.1.2	 Find All Intersections
				9.3.1.3	 Find Some Intersections
			9.3.2	 Discussion
		9.4	 Conclusions
	Chapter 10: A Simple Load-Balancing Scheme with High Scaling Efficiency
		10.1	 Introduction
		10.2	 Requirements
		10.3	 Load Balancing
			10.3.1	 Naive Tiling
			10.3.2	 Task Size
			10.3.3	 Task Distribution
			10.3.4	 Image Assembly
		10.4	 Results
Part III: Reflections, Refractions, and Shadows
	Chapter 11: Automatic Handling of Materials in Nested Volumes
		11.1	 Modeling Volumes
			11.1.1	 Unique Borders
			11.1.2	 Additional Air Gap
			11.1.3	 Overlapping Hulls
		11.2	 Algorithm
			11.2.1	 Implementation
		11.3	 Limitations
	Chapter 12: A Microfacet-Based Shadowing Function to Solve the Bump Terminator Problem
		12.1	 Introduction
		12.2	 Previous Work
		12.3	 Method
			12.3.1	 The Normal Distribution
			12.3.2	 The Shadowing Function
		12.4	 Results
	Chapter 13: Ray Traced Shadows: Maintaining Real-Time Frame Rates
		13.1	 Introduction
		13.2	 Related Work
		13.3	 Ray Traced Shadows
		13.4	 Adaptive Sampling
			13.4.1	 Temporal Reprojection
			13.4.2	 Identifying Penumbra Regions
			13.4.3	 Computing the Number of Samples
			13.4.4	 Sampling Mask
			13.4.5	 Computing Visibility Values
				13.4.5.1 Temporal Filtering
				13.4.5.2 Spatial Filtering
		13.5	 Implementation
			13.5.1	 Sample-Set Generation
			13.5.2	 Distance-Based Light Culling
			13.5.3	 Limiting the Total Sample Count
			13.5.4	 Forward Rendering Pipeline Integration
		13.6	 Results
			13.6.1	 Comparison with Shadow Mapping
			13.6.2	 Soft Shadows versus Hard Shadows
			13.6.3	 Limitations
		13.7	 Conclusion and Future Work
			13.7.1	 Future Work
	Chapter 14: Ray-Guided Volumetric Water Caustics in Single Scattering Media with DXR
		14.1	 Introduction
		14.2	 Volumetric Lighting and Refracted Light
		14.3	 Algorithm
			14.3.1	 Compute Beam Compression Ratios
			14.3.2	 Render Caustics Map
			14.3.3	 Ray Trace Refracted Caustics Map and Accumulate Surface Caustics
			14.3.4	 Adaptively Tessellate the Triangles of the Water Surface
			14.3.5	 Build Triangular Beam Volumes
			14.3.6	 Render Volumetric Caustics Using Additive Blending
			14.3.7	 Combine Surface Caustics and Volumetric Caustics
		14.4	 Implementation Details
		14.5	 Results
		14.6	 Future Work
		14.7	 Demo
Part IV: Sampling
	Chapter 15: On the Importance of Sampling
		15.1	 Introduction
		15.2	 Example: Ambient Occlusion
		15.3	 Understanding Variance
		15.4	 Direct Illumination
		15.5	 Conclusion
	Chapter 16: Sampling Transformations Zoo
		16.1	 The Mechanics of Sampling
		16.2	 Introduction to Distributions
		16.3	 One-Dimensional Distributions
			16.3.1	 Linear
			16.3.2	 Tent
			16.3.3	 Normal Distribution
			16.3.4	 Sampling from a One-Dimensional Discrete Distribution
				16.3.4.1 Just Once
				16.3.4.2 Multiple Times
		16.4	 Two-Dimensional Distributions
			16.4.1	 Bilinear
			16.4.2	 A Distribution Given a Two-Dimensional Texture
				16.4.2.1 Rejection Sampling
				16.4.2.2 Multi-Dimensional Inversion Method
				16.4.2.3 Hierarchical Transformation
		16.5	 Uniformly Sampling Surfaces
			16.5.1	 Disk
				16.5.1.1 Polar Mapping
				16.5.1.2 Concentric Mapping
			16.5.2	 Triangle
				16.5.2.1 Warping
				16.5.2.2 Flipping
			16.5.3	 Triangle Mesh
			16.5.4	 Sphere
				16.5.4.1 Latitude-Longitude Mapping
				16.5.4.2 Octahedral Concentric (Uniform) Map
		16.6	 Sampling Directions
			16.6.1	 Cosine-Weighted Hemisphere Oriented to the z-Axis
			16.6.2	 Cosine-Weighted Hemisphere Oriented to a Vector
			16.6.3	 Directions in a Cone
			16.6.4	 Phong Distribution
			16.6.5	 GGX Distribution
		16.7	 Volume Scattering
			16.7.1	 Distances in a Volume
				16.7.1.1 Homogeneous Media
				16.7.1.2 Inhomogeneous Media
			16.7.2	 Henyey-Greenstein Phase Function
		16.8	 Adding to the Zoo Collection
	Chapter 17: Ignoring the Inconvenient When Tracing Rays
		17.1	 Introduction
		17.2	 Motivation
		17.3	 Clamping
		17.4	 Path Regularization
		17.5	 Conclusion
	Chapter 18: Importance Sampling of Many Lights on the GPU
		18.1	 Introduction
		18.2	 Review of Previous Algorithms
			18.2.1	 Real-Time Light Culling
			18.2.2	 Many-Light Algorithms
			18.2.3	 Light Importance Sampling
		18.3	 Foundations
			18.3.1	 Lighting Integrals
			18.3.2	 Importance Sampling
				18.3.2.1	 Monte Carlo Method
				18.3.2.2	 Light Selection Importance Sampling
				18.3.2.3	 Light Source Sampling
			18.3.3	 Ray Tracing of Lights
		18.4	 Algorithm
			18.4.1	 Light Preprocessing
			18.4.2	 Acceleration Structure
				18.4.2.1	 Building the BVH
				18.4.2.2	 Light Orientation Cone
				18.4.2.3	 Defining the Split Plane
			18.4.3	 Light Importance Sampling
				18.4.3.1	 Probabilistic BVH Traversal
				18.4.3.2	 Random Number Usage
				18.4.3.3	 Sampling the Leaf Node
				18.4.3.4	 Sampling the Light Source
		18.5	 Results
			18.5.1	 Performance
				18.5.1.1	 Acceleration Structure Construction
				18.5.1.2	 Render Time per Frame
			18.5.2	 Image Quality
				18.5.2.1	 Build Options
				18.5.2.2	 Triangle Amount per Leaf Node
				18.5.2.3	 Sampling Methods
		18.6	 Conclusion
Part V: Denoising and Filtering
	Chapter 19: Cinematic Rendering in UE4 with  Real-Time Ray Tracing and Denoising
		19.1	 Introduction
		19.2	 Integrating Ray Tracing in Unreal Engine 4
			19.2.1	 Phase 1: Experimental Integration
				19.2.1.1	 DirectX Raytracing Background on Acceleration Structures
				19.2.1.2	 Experimental Extensions to the UE4 RHI
				19.2.1.3	 Registering Geometry for a Variety of Engine Primitives
				19.2.1.4	 Updating the Ray Tracing Representation of the Scene
				19.2.1.5	 Iterating over All Objects
				19.2.1.6	 Customizing Shaders for Ray Traced Rendering
				19.2.1.7	 Batch Commit of Shader Parameters of Multiple Ray Types
				19.2.1.8	 Updating Instance Transformation
				19.2.1.9	 Building Acceleration Structures
				19.2.1.10	 Miss Shaders
			19.2.2	 Phase 2
				19.2.2.1	 Tier 1
				19.2.2.2	 Tier 2
				19.2.2.3	 Tier 3
		19.3	 Real-Time Ray Tracing and Denoising
			19.3.1	 Ray Traced Shadows
				19.3.1.1	 Lighting Evaluation
				19.3.1.2	 Shadow Denoising
			19.3.2	 Ray Traced Reflections
				19.3.2.1	 Simplified Reflection Shading
				19.3.2.2	 Denoising for Glossy Reflections
				19.3.2.3	 Specular Shading with Ray Traced Reflections
			19.3.3	 Ray Traced Diffuse Global Illumination
				19.3.3.1	 Ambient Occlusion
				19.3.3.2	 Indirect Diffuse from Light Maps
				19.3.3.3	 Real-Time Global Illumination
				19.3.3.4	 Denoising for Ambient Occlusion and Diffuse Global Illumination
			19.3.4	 Ray Traced Translucency
				19.3.4.1	 Ray Generation
		19.4	 Conclusions
	Chapter 20: Texture Level of Detail Strategies for Real-Time Ray Tracing
		20.1	 Introduction
		20.2	 Background
		20.3	 Texture Level of Detail Algorithms
			20.3.1	 Mip Level 0 with Bilinear Filtering
			20.3.2	 Ray Differentials
				20.3.2.1	 Eye Ray Setup
				20.3.2.2	 Optimized Differential Barycentric Coordinate Computation
			20.3.3	 Ray Differentials with the G-Buffer
			20.3.4	 Ray Cones
				20.3.4.1	 Screen Space
				20.3.4.2	 Reflection
				20.3.4.3	 Pixel Spread Angle
				20.3.4.4	 Surface Spread Angle for Reflections
				20.3.4.5	 Generalization
		20.4	 Implementation
		20.5	 Comparison and Results
		20.6	 Code
	Chapter 21: Simple Environment Map Filtering Using Ray Cones and Ray Differentials
		21.1	 Introduction
		21.2	 Ray Cones
		21.3	 Ray Differentials
		21.4	 Results
	Chapter 22: Improving Temporal Antialiasing with Adaptive Ray Tracing
		22.1	 Introduction
		22.2	 Previous Temporal Antialiasing
		22.3	 A New Algorithm
			22.3.1	 Segmentation Strategy
				22.3.1.1	 Automatic Segmentation
				22.3.1.2	 UE4 Automatic Segmentation Implementation
				22.3.1.3	 Manual Segmentation
			22.3.2	 Sparse Ray Traced Supersampling
				22.3.2.1	 Subpixel Sample Distribution and Reuse
		22.4	 Early Results
			22.4.1	 Image Quality
			22.4.2	 Performance
		22.5	 Limitations
		22.6	 The Future of Real-Time Ray Traced Antialiasing
		22.7	 Conclusion
Part VI: Hybrid Approaches and Systems
	Chapter 23: Interactive Light Map and Irradiance Volume Preview in Frostbite
		23.1	 Introduction
		23.2	 GI Solver Pipeline
			23.2.1	 Input and Output
				23.2.1.1	 Input
				23.2.1.2	 Output
			23.2.2	 GI Solver Pipeline Overview
			23.2.3	 Lighting Integration and Path Construction
			23.2.4	 Light Sources
			23.2.5	 Special Materials
			23.2.6	 Scheduling Texels
			23.2.7	 Performance Budgeting
			23.2.8	 Post-Process
		23.3	 Acceleration Techniques
			23.3.1	 View Prioritization
			23.3.2	 Light Acceleration Structure
			23.3.3	 Irradiance Caching
				23.3.3.1	 Direct Irradiance Cache Light Maps
				23.3.3.2	 Cache Update Process
				23.3.3.3	 Future Improvements
		23.4	 Live Update
			23.4.1	 Lighting Artist Workflow in Production
			23.4.2	 Scene Manipulation and Data Invalidation
		23.5	 Performance and Hardware
			23.5.1	 Method
			23.5.2	 Results
			23.5.3	 Hardware Setup
		23.6	 Conclusion
	Chapter 24: Real-Time Global Illumination with Photon Mapping
		24.1	 Introduction
		24.2	 Photon Tracing
			24.2.1	 RSM-Based First Bounce
			24.2.2	 Following Photon Paths
			24.2.3	 DXR Implementation
		24.3	 Screen-Space Irradiance Estimation
			24.3.1	 Defining the Splatting Kernel
				24.3.1.1 Uniform Scaling of the Kernel
				24.3.1.2 Adjusting the Kernel’s Shape
			24.3.2	 Photon Splatting
				24.3.2.1 Optimizing Splatting Using Reduced Resolution
		24.4	 Filtering
			24.4.1	 Temporal Filtering
			24.4.2	 Spatial Filtering
				24.4.2.1 Variance Clipping of Detail Coefficients
			24.4.3	 Incorporating the Effect of Shading Normals
		24.5	 Results
		24.6	 Future Work
			24.6.1	 Optimizing Irradiance Distribution by Skipping Splatting
			24.6.2	 Adaptive Constants for Variance Clipping of the Detail Coefficients
	Chapter 25: Hybrid Rendering for Real-Time Ray Tracing
		25.1	 Hybrid Rendering Pipeline Overview
		25.2	 Pipeline Breakdown
			25.2.1	 Shadows
			25.2.2	 Reflections
			25.2.3	 Ambient Occlusion
			25.2.4	 Transparency
			25.2.5	 Translucency
			25.2.6	 Global Illumination
		25.3	 Performance
		25.4	 Future
		25.5	 Code
	Chapter 26: Deferred Hybrid Path Tracing
		26.1	 Overview
		26.2	 Hybrid Approach
		26.3	 BVH Traversal
			26.3.1	 Geometry Selection
			26.3.2	 Vertex Preprocessing
			26.3.3	 Shading
		26.4	 Diffuse Light Transport
			26.4.1	 Ray Heuristic
			26.4.2	 Last Frame’s Reprojection
			26.4.3	 Temporal and Spatial Filtering via Optimized Multi-Pass
		26.5	 Specular Light Transport
			26.5.1	 Temporal Accumulation
			26.5.2	 Reuse of Diffuse Lobe
			26.5.3	 Path Traced Indirect Lighting
			26.5.4	 Lobe Footprint Estimation
		26.6	 Transparency
		26.7	 Performance
			26.7.1	 Stereo Rendering for Virtual Reality
			26.7.2	 Discussion
	Chapter 27: Interactive Ray Tracing Techniques for High-Fidelity Scientific Visualization
		27.1	 Introduction
		27.2	 Challenges Associated with Ray Tracing Large Scenes
			27.2.1	 Using the Right Geometric Primitive for the Job
			27.2.2	 Elimination of Redundancy, Compression, and Quantization
			27.2.3	 Considerations for Ray Tracing Acceleration Structures
		27.3	 Visualization Methods
			27.3.1	 Ambient Occlusion Lighting in Scientific Visualization
				27.3.1.1 AO with Limited Occlusion Distance
				27.3.1.2 Reducing Monte Carlo Sampling Noise
			27.3.2	 Edge-Enhanced Transparent Surfaces
			27.3.3	 Peeling Away Excess Transparent Surfaces
			27.3.4	 Edge Outlines
			27.3.5	 Clipping Planes and Spheres
		27.4	 Closing Thoughts
Part VII: Global Illumination
	Chapter 28: Ray Tracing Inhomogeneous Volumes
		28.1	 Light Transport in Volumes
		28.2	 Woodcock Tracking
		28.3	 Example: A Simple Volume Path Tracer
		28.4	 Further Reading
	Chapter 29: Efficient Particle Volume Splatting in a Ray Tracer
		29.1	 Motivation
		29.2	 Algorithm
		29.3	 Implementation
			29.3.1	 Ray Generation Program
			29.3.2	 Intersection and Any-Hit Programs
			29.3.3	 Sorting and Optimizations
		29.4	 Results
		29.5	 Summary
	Chapter 30: Caustics Using Screen-Space Photon Mapping
		30.1	 Introduction
		30.2	 Overview
		30.3	 Implementation
			30.3.1	 Photon Emission and Photon Tracing
				30.3.1.1	 Photon Emission
				30.3.1.2	 Photon Tracing
				30.3.1.3	 Storing Photons
			30.3.2	 Photon Gathering
			30.3.3	 Lighting
		30.4	 Results
			30.4.1	 Limitations and Future Works
			30.4.2	 Transparent Objects in the Depth Buffer
			30.4.3	 Practical Usage
		30.5	 Code
	Chapter 31: Variance Reduction via Footprint Estimation in the Presence of Path Reuse
		31.1	 Introduction
		31.2	 Why Assuming Full Reuse Causes a Broken MIS Weight
		31.3	 The Effective Reuse Factor
			31.3.1	 An Approximate Solution
			31.3.2	 Estimating the Footprint
		31.4	 Implementation Impacts
			31.4.1	 Performance Consequences
		31.5	 Results
	Chapter 32: Accurate Real-Time Specular Reflections with Radiance Caching
		32.1	 Introduction
		32.2	 Previous Work
			32.2.1	 Planar Reflections
			32.2.2	 Screen-Space Reflections
			32.2.3	 Image-Based Lighting
			32.2.4	 Hybrid Approaches
			32.2.5	 Miscellaneous
		32.3	 Algorithm
			32.3.1	 Radiance Cache
				32.3.1.1	 Rendering
				32.3.1.2	 Lighting
			32.3.2	 Ray Tracing
				32.3.2.1	 Sampling the Specular BRDF
				32.3.2.2	 Ray Generation and Hit Storage
			32.3.3	 Radiance Computation for Rays
				32.3.3.1	 Sampling the Radiance Cache and Screen-Space Illumination
				32.3.3.2	 Shading Cache-Missed Rays
		32.4	 Spatiotemporal Filtering
			32.4.1	 Spatial Filtering
				32.4.1.1	 Edge-Stopping Weight
				32.4.1.2	 Roughness Weight
				32.4.1.3	 Reflection-Direction Weight
				32.4.1.4	 Ray-Length Weight
			32.4.2	 Temporal Filtering
			32.4.3	 Reflection Motion Vectors
				32.4.3.1	 Understanding the Problem
				32.4.3.2	 Direct Solution
				32.4.3.3	 Geometrical Optics Approach
				32.4.3.4	 Obtaining Optical Parameters
				32.4.3.5	 Velocity Transformation for Dynamic Objects
		32.5	 Results
			32.5.1	 Performance
			32.5.2	 Quality
		32.6	 Conclusion
		32.7	 Future Work