782 Schedule & Notes

Tentative schedule - subject to change at a moment's notice. This is only a guide and not meant to be a strict schedule of how fast the material will be taught. The order of material is fairly set for the early part of the course, but becomes more fluid as the quarter progresses.

Dates Topic Chapters Assignments
W: Sept 20 Introduction 1
F: Sept 22 Basic ray tracing review 1

M: Sept 25 Preview course topics 1
W: Sept. 27 Intersections 2-4 read about PBRT
F: Sept. 29 Bounding volumes 4 Lab 0

M: Oct. 2 Spatially based acceleration 4
W: Oct. 4 Color and radiometry 5
F: Oct. 6 Tone mapping 8

M: Oct. 9 Adaptation Luminance 8
W: Oct. 11 Photographic Tone Reproduction 8
F: Oct. 13 Color Systems 8

M: Oct. 16 Reflection models 9 Lab 1
W: Oct. 18 Reflection models 9
F: Oct. 20 Reflection models 9

M: Oct. 23 Sampling 7
W: Oct. 25 Sampling 7 Lab 2
F: Oct. 27 Review homework and
review for midterm Homework

M: Oct. 30 Midterm Midterm
W: Nov. 1 Sampling 7
F: Nov. 3 Sampling 7

M: Nov. 6 Review midterm and
start Monte Carlo Fundamentals 14
W: Nov. 8 Monte Carlo Fundamentals 14
F: Nov. 10 No Class Lab 3

M: Nov. 13 Monte Carlo Fundamentals 14
W: Nov. 15 Monte Carlo Integration 15
F: Nov. 17 Monte Carlo Integration 15 Project description

M: Nov. 20 Light Transport - unbiased 16-17
W: Nov. 22 Light Transport - unbiased 16-17
F: Nov. 14 No Class

M: Nov. 27 Light Transport - biased 16-17
W: Nov. 29 Light Transport - biased 16-17
F: Dec. 1 Sub-surface scattering 18.2.3 Final Project (programming part)

R: Dec. 7 exam time: 7:30-9:18 (need to reschedule?) Project presentations

Dates	Topic	Chapters	Assignments
W: Sept 20	Introduction	1
F: Sept 22	Basic ray tracing review	1

M: Sept 25	Preview course topics	1
W: Sept. 27	Intersections	2-4	read about PBRT
F: Sept. 29	Bounding volumes	4	Lab 0

M: Oct. 2	Spatially based acceleration	4
W: Oct. 4	Color and radiometry	5
F: Oct. 6	Tone mapping	8

M: Oct. 9	Adaptation Luminance	8
W: Oct. 11	Photographic Tone Reproduction	8
F: Oct. 13	Color Systems	8

M: Oct. 16	Reflection models	9	Lab 1
W: Oct. 18	Reflection models	9
F: Oct. 20	Reflection models	9

M: Oct. 23	Sampling	7
W: Oct. 25	Sampling	7	Lab 2
F: Oct. 27	Review homework and review for midterm		Homework

M: Oct. 30	Midterm		Midterm
W: Nov. 1	Sampling	7
F: Nov. 3	Sampling	7

M: Nov. 6	Review midterm and start Monte Carlo Fundamentals	14
W: Nov. 8	Monte Carlo Fundamentals	14
F: Nov. 10	No Class		Lab 3

M: Nov. 13	Monte Carlo Fundamentals	14
W: Nov. 15	Monte Carlo Integration	15
F: Nov. 17	Monte Carlo Integration	15	Project description

M: Nov. 20	Light Transport - unbiased	16-17
W: Nov. 22	Light Transport - unbiased	16-17
F: Nov. 14	No Class

M: Nov. 27	Light Transport - biased	16-17
W: Nov. 29	Light Transport - biased	16-17
F: Dec. 1	Sub-surface scattering	18.2.3	Final Project (programming part)

R: Dec. 7	exam time: 7:30-9:18 (need to reschedule?)	Project presentations

Introduction

Reading: Syllabus; Section 1.1, pp. 1-4; Section 1.5, pp. 38-39;
         Lab  0 Assignment; pbrt setup; 
Lectures: 1

Introduction to class
- instructor, grader
- overview of course
Roster
Syllabus
- course description
- prereqs
- Book
- grade components
- Course software - pbrt
- grading
- academic misconduct
Course software - pbrt
- Read 1.1: Literate programming
- look at installation notes: pbrtsetup.html
Labs
- overview
- Lab 0 - specifics
- getting started with course software

Basic Ray Tracing

Reading: Section 1.2, pp. 4-16
Lectures: 1

Basic idea of ray tracing

perspective by projecting rays through virtual pixels
bounce rays around environment
recursive ray tracing
- initial ray spawns other rays
- SHADE(origin,ray)
photorealistic rendering

Steps of basic ray tracing

camera model
- set up camera coordinate system
- pinhole camera: plane in-front or behind camera
- view volume
- establish virtual frame buffer: position pixel plane on view plane
- sample frame buffer: generate rays
intersection objects
- parametric form of ray: origin + t*direction
- spheres: algebraic v. geometric
- polygon intersection
illuminate point of intersection
- point lights
- area lights
- light energy
- distance falloff
- tilted surface
- shadows: shadow rays
surface scattering
- Bidirectional Reflectance Distribution Function (BRDF)
- Bidirectional Transmission Distribution Function (BTDF)
- Bidirectional Scattering Distribution Function (BSDF)
Recursive Ray Tracing
- Light Transport Equation (aka rendering equation
- Whitted's algorithm
- Reflection ray
- Refraction ray
Ray propagation
- participating medium
- volume light transport equation

Refine ray tracing

speed up intersection testing
- bounding volumes
- partition space
sample pixel: pixel as an area of screen
sample area light source: how much is visible from light source?
surface scattering: interaction of ray and material

PBRT

Reading: Section 1.3, pp. 16-36
Lectures: 2

NOTE: refer to the book for actual code segments; the ones here are condensed versions

The PBRT implementation of ray tracing

Phases of execution
- parse -> instance of the Scene class
- rendering: Scene::Render() determines light at film plane using rays
- postprocessing

Scene representation

  int main() {
    pbrtInit()
    process scene description
    pbrtCleanup()
  }

Process scene file
- geometric objects, Scene::aggregate
- lights
- camera
- participating media: Volume region
- Surface integrator
- volume integrator
- sampler: choose points on image planes to trace through

Main rendering loop

  Render() {
    allocate and initialize sample
    allow integrators to pre-process scene
    trace rays: main loop
    clean-up
  }
<

Scene Methods
- Render - holds variables that represent the scene; forwards requests to methods of Scene's member variables
- Intersect - traces the given ray; return boolean of whether intersection and fills in Intersection structure with info
- IntersectP - checks for existence of intersection only
- WorldBound - returns 3D bounding box of Scene:aggregate
- Li - compute radiance along a ray
- Transmittance - returns attenuation due to participating media
Integrator for Whitted-style ray tracing (1.3.5, pp. 30-36)
See Figure 1.16,, p. 32

Intersection acceleration

Reading: Chapter 2 as needed to review geometry and transformations
         Sections 3.0-3.6; pp. 89-133
         Sections 4.0-4.2 pp. 169-180
Lectures: 3

Primitives:
- Basic Shape Interface
  - ObjectBound, WorldBound
  - CanIntersect()
  - Intersect()
  - IntersectP()
  - Refine()
  - GetShadingGeometry()
  - Area()
- Spheres
- Cylinders
- Disks
- Other Quadrics
- Triangles and Meshes
GeometricPrimitive class: represents a single shape and combines shape with material properties
- also holds AreaLight if it emits light
- Intersect ()- pass on to shape:intersect
- GetBSDF(): forwarded to Material
InstancePrimitive provides instances; each has its own transform
- Intersect(): forwarded on to the shared primitive
- WorldBound(): transformed shared primitive's WorldBound
Bounding volumes
- bounding boxes: axis aligned, oriented bounding boxes
- bounding spheres
- slabs
- convex hull
- hierarchical
- Aggregate class - container for acceleration structures
  - spatial enumeration
  - octree
  - K-D tree
  - BSP
Color and Radiometry
```
Reading: Chapter 5
Lectures: 2
```
- radiometry - propagation of EM radiation; wavelengths 370-730 nm visible
  SPD - spectral power distribution - amount of light at each wavelength
- Spectral Representation
  - Spectrum class
  - XYZ Color
  - tristimulus theory of color perception
- Basic Radiometry
radiation transfer
geometric optics

Basic Quantities

Flux - power
Irradiance - area density of flux
Solid Angle & Intensity: steradians, flux energy / solid angle
Radiance flux per unit area per solid angle
incident & exident radiance functions

Radiance Integrals

projected solid angle
integrate over area

Surface Reflectance & BDRF >

Tone Reproduction

Reading: Chapter 8
Lectures: 3

Perceptual issues and tone mapping
- uniform scale
  - mapping to white
  - perceptually based
- adaptation luminance
  - JND
  - blurred images
- photographic tone reproduction for digital images
  - difference of gaussians
  - center-surround function
Final imaging pipeline states
- Color theory
  - SPD
  - tristimulus theory of color
  - metamers,
- Color systmes
  - CIE color matching functions, CIE Color Space, XYZ, xyY, chromaticity diagram
  - color gamut, line of purple
  - RGB,
  - CMY(K),
  - YUV
  - HSV
  - linear v. non-linear transformations
  - perceptual metric spaces
- Gamma correction
- Dithering

Reflection Models

Reading: Chapter 9
Lectures: 1

Basic interface
Specular reflection and transmission
Lambertian reflection
Microfacet models
Lafortune model
Fresnel incidence effects

Sampling

Reading: Chapter 7.1, 7.3-7.6 covered in class, read 7.2 on your own
Lectures: 2

Sampling theory
- frequency domaiin, fourier transform
- ideal sampling and reconstruction
- typical sampling in c.g., reconstruction in graphics sytems
- aliasing, anti-aliasing
- prefiltering, adaptive sampling, non-uniform sampling
Sampling interface - read 7.2 on your own
Various sampling strategies effect on the sampling statistics

Monte Carlo Fundamentals

Reading: Chapter 13-14
Lectures: 2

Monte Carlo algorithms
probability distribution function
cumulative distribution function
conditional probability
Expected value
Variance
Uniform Monte Carlo Estimator
General Monte Carlo Estimator
Expected value of MC
Variance of MC
Uniform random variable
non-uniform distribution from uniform random variable
- Inversion method
- Rejection method
- Transforming between distributions
Multiple dimensions
- sampling hemisphere
- sampling disk

Monte Carlo Integration

Reading: Chapter 15.1-15.6
Lectures: 2

Efficiency
Russian Roulette
Stratified sampling
Bias
Importance sampling
Monte Carlo for global illumination
Sampling light sources

Light Transport

Reading: Chapter 16-17
Lectures: 4

Light Transport Equation
unbiased
- Path Tracing
- Bidirectional Path Tracing
- Metropolis Light Transport
biased
- Irradiance Caching
- Photon Mapping

Sub-Surface Scattering

Reading: Chapter 18.2.3
Lectures: 1

Volume Rendering

Reading: Chapter 12, 15.7
Lectures: 3

Radiosity

Reading: Chapter 17, Cohen & Wallace
Lectures:  2