Prerequisites — Educational Goals — Topics Covered — Structure — Projects and Code — Primary Sources — Feedback

Images and Light — Physically Based Rendering — The Rendering EquationRadiometry Photometry light ray primary ray Rendering Equation

An Example — Header and Source Files — Memory Model — Types — Plain Old Data — Pointer Types — Stack and Heap Allocation — References — const References — Reference-Counted Pointers — Copying and Assignment — Pre- and Post-Increment — Conclusion: The C++ Programmer Mindsetheader source translation units linker variable value address type pointer dereference dangling pointers memory leak reference reference-counted pointer shared pointer

What is a Surface? — The Speeds of Light — Surfaces are Interfaces — Modeling a 1D Surface in 2D Space — A Surface is a Set of Points — Implicit Form — Explicit Form — Triangle Meshes — A Triangle — Triangle List — Indexed Triangle Listobject implicit explicit homogeneous optical interface boundary oriented implicit explicit simplex front mesh triangle list tetrahedron indexed triangle list vertex array index array

Digital Images are Measurements — Rays of Light — Transport Paths — Vectors — Unit Vectors — Geometric Rays — The Light Field — Light is Conserved Along a Ray — Assumptions and Simplificationslight field crepuscular rays ray line segment line segment path emitter luminaire light source vector magnitude length unit vector normalizing unit sphere light field plenoptic function 4D light field light slab Lumigraph time phase Polarization frequencies

Radiometric Units — Photon Energy — Power — Irradiance and Radiosity — The Measure of a Set — Radiance — Measurements in Different Frames — Lambert's Projected Area — Vector Dot Product — The Rendering Equation — Rendering is Very Hardradiometry energy photons power flux Irradiance radiosity measure angle solid angle steradians Radiance Lambert's cosine law dot product inner product integral equation

Systems — Advantages — Repository Model — An Example — Concurrent Changes — Typical Workflow — Starting a Project — Pull into the Workspace — Merge Conflicts — Adding and Removing Files — Push to the Remote Repository — Leveraging Versions — Checking the Log — Inspecting Old Versions — Workspace Undo — Local Repository Undo — Remote Repository Undo — Best PracticesSubversion git Perforce server client bridges remote repository workspace revision history distributed version control systems local repository local snapshot pulls commits pushes conflict resolved log message log git perforce p4 svn subversion mercurial hg cvs rcs source control source management revision control

Images — Images are Everywhere — An Aperture Selects an Image — A 16ᵗʰ Century Mechanical Renderer — A Modern Computational Renderer — Primary Rays from a Pinhole Camera — Dynamic Range — Gamma Encoding — Bloom — Desaturationpinhole aperture virtual image real image data driven ray casting surface element (surfel) direct illumination dynamic range tone mapping gamma encoding Bloom

Ray Casting Algorithm  ray trace  — Ray-Sphere Intersection — Ray-Plane Intersection — Ray-Triangle Intersection — Unit Triangle — Barycentric Coordinates — Arbitrary Triangle — Vector Cross Product — Triangle Mesh — Some Performance Considerations — Visualization for Debugging — Texture Coordinates — Stepping Into One Pixelray casting surface element surfel unit triangle barycentric coordinate barycenter signed area cross product cross product procedural early out spatial data structure Visualization texture coordinate texture map ray trace

Radiance is Conserved Along a Ray — Direct Illumination — Scattered Radiance — Biradiance — Implementing Point Lights — Shadows — The Visibility Function — Ambient Illuminationdirect illumination ambient term direct illumination point light biradiance shadow visibility function ambient environment mapping irradiance mapping

Probability Density — The BSDF brdf btdf shading  — Lambert's Law — Scattering Functions — Common Terms — Mirror Reflection — Implementing Impulses — Transmission and Refraction — Microfacets — Subsurface Scattering — Lambertian Reflection — The Fresnel Effect — Partial Coverage — Compositing — Alpha Cutout — Perceived Colorbidirectional scattering distribution function material scattering function bump partial coverage probability mass probability density differential probability probability mass bidirectional scattering distribution function reflective bidirectional reflectance distribution function transmission non-negative energy conserving reciprocal passive Lambert's Law scattering distribution photon distribution impulse transmits refraction microfacets diffuse half vector Lambertian reflectivity normal incidence partial coverage over composite brdf btdf shading

The Transport Graph metropolis radiosity  — Path Notation — Node Types — Operators — Notable Phenomena — Direct and Ambient Illumination — Whitted Ray Tracing — Path Tracing — Bidirectional Path Tracing — Photon Mapping — Radiositytransport graph Path notation Luminaire Specular Diffuse Eye Caustics Mirror reflections perfect refraction Diffuse interreflection color bleeding shadow Highlights ambient Whitted ray tracing backwards ray tracing ray tracing path tracing Bidirectional path tracing photon mapping consistent biased radiosity algorithm form factor metropolis radiosity

Definition of a Derivative — Numerical Differentiation — Definition of an Integral — Analytic Integration — Numerical Integration — A Tale of Two Cities — Las Vegas — Monte Carlo — Monte Carlo Integration — An Energy Examplederivative differentiable analytically power rule antiderivative symbolic analytic Numerical (definite) integration samples randomized algorithms nondeterministic stochastic deterministic algorithms Las Vegas Monte Carlo Monte Carlo (definite) Integral estimator probability density function converged

A Simple Implementation — Algorithmic Complexity — The Transport Graph — Elements of Path Tracing — Applying Monte Carlo Integration — The Camera Integrals — Distributed Sampling — The Transport Integral — Terminal Cases  direct resampling  — Importance SamplingReverse, recursive ray tracing Distributed sampling Markov chain Monte Carlo Importance sampling spatial data structures SIMD SPMD stream processing Fixed-function hardware distributed sampling Russian roulette shadow rays material importance sampling bidirectional scattering distribution function (BSDF) importance sampling direct resampling

Intersection Algorithms GPU implicit signed distance  — Marching — Distance Estimators — Sphere Tracing — Some Distance Estimators — Sphere — Plane — Box — Rounded Box — Torus — Wheel — Cylinder — Computing Normals — A Simple GLSL Ray Caster — C++ Shader Launch — GLSL Ray Setup — GLSL Intersection — Operations on Distance Estimators — Some Useful Operators — Union — Intersection — Subtraction — Repetition — Transformation — Blending — Increasing Performance — Over-Relaxation — Bounding Spheres — Reintroducing Analytic Roots — Other Optimization Strategies — Some Online Examples in GLSL — Educational — Aspirational — Further Readingimplicit surface Analytic ray-surface intersection explicit equation Ray marching Rasterization depth buffer signed distance estimators isosurface level set sphere tracing gradient surface normal point-based graphics GPU implicit signed distance

SIMD GPU CPU SIMT AVX SSE warp CUDA  — Coherence — Memory Coalescing — Cores — Thread Pools and Megakernels — Occupancy — Synchronization — Pipelines — Physics Revisited — Super-Linear Speedups — Intra-core Utilization — Memory — Physics Revisited — Structures and ArraysSIMD SIMT lane masked coherent divergent coalesce virtual cores physical cores Stream Processor CUDA Core thread pooling Megakernel occupancy concurrent strict parallel race condition deadlock atomic operations mutexes spinlocks semaphores lockless datastructures barrier pipelining bubble array of structures (AOS) structure of arrays (SOA) GPU CPU SIMT AVX SSE warp CUDA

Photoreceptors — Photoreceptor Response — Photopic Vision — Scotopic Visioncones rods punctum caecum