CS 534 Vector Graphics

Spring 2008

MW 1:00-2:15

Dane Smith 331

Instructor:

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Recommended Text

Ray Tracing from the Ground Up

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Realistic Ray Tracing

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Description

This course covers the basic mathematics of ray-based graphics. Topics include ray tracing implicit surfaces and meshes, high dynamic range images, high quality sampling, material modeling, and effects. Students will write a complete working raytracer and produce realistic images. Students will also be encouraged to pursue high performance, parallel implementations and well engineered software. The course is currently listed as a 500 level graphics course, but future versions will serve as an introductory class for undergraduates and graduates, undergraduates are invited to take this course.

Deliverables

Assignments must be delivered electronically. Only 1 late assignment will be accepted with full credit (must be in before the next assignment is due). Any other late assignments will incur a 10% penelty per day. Students must solve 3-4 extra credit parts to achieve an A in the class.

Content

Week 1
- Introduction
- Assignment 1: Viewer, due Jan 30.
  - Use OpenGL and Glut to produce a simple image viewer.
  - Viewer must accept command-line parameters for size, camera, lights, etc...
  - Viewer must report pixel values under mouse when image is clicked on...
  - Viewer must report current state (size, camera...) in command line form when 'C' key is pressed
  - Viewer must display an image either read from file or generated by the program.
  - Extra credit 1: measure speed of image updates. (how fast can images be loaded?)
  - Extra credit 2: identify fastest method for image updates. (use GL extensions)
- Basic math
- Software design issues.
Week 2
- Basic math continued
- Viewer, Tracer, Scene design
Week 3
- Barycentric Coordinates and intro to lighting.
- Viewing parameters (eye, at, and up)
- Assignment 2: Math Review, due Feb 11
  1. Describe the basic properties (Associativity, Commutativity, and ~~Transitivity~~ Distributivity) of:
    - The inner (dot) product
    - The outer product
    - The cross product
  2. What other properties do these operators have?
  3. Derive the ray-plane intersection (set up and solve for t)
  4. Derive the ray-sphere intersection (set up and solve for t)
  5. Derive the ray-triangle intersection (set up and solve for t)
  6. Extra Credit: Derive:
    - the ray-cone intersection
    - the ray-disk intersection
    - the ray-cylinder (with cap) intersection
Week 4

Shading and tone mapping
Assignment 3: Vanilla Ray Tracer, due Feb 18
1. Please make a web page for this assignment and discuss your results there.
2. Implement a basic ray-tracer.
3. Objects should be shaded using the Phong model.
4. Render these objects (z is up) (all in one scene):
  - Plane at [0,0,0], normal [0,0,1], diffuse color [.05, .05, 1], specular color [.2, .3, 1], specular power 3
  - Sphere at [0,0,1] radius 1, diffuse color [1, .05, .05], specular color [1, .9, .9], specular power 10
  - Sphere at [2,2,0.2] radius 1, diffuse color [.05, 1, .05], specular color [.9, 1, .9], specular power 30
  - Triangle [-1, -1, .02][2,-2,.02][-1.5,-1.5,1.5], diffuse color [1, 1, .05], specular color [1,1,.9], specular power 100
5. Light is at [4,4,4], color [1,1,1]
6. Eye [0,5,2], Look-at [0,0,0], Up [0,0,1]
7. Image plane is at [0,4,2] (distance of 1 from eye), Dimensions 2x2 (width and height)
8. Rendered image should be 512x512 pixels
9. Indicate runtime and computer specs with each rendered image.
10. Extra Credit
  - Implement shadows (test if light is blocked by other objects)
  - Implement reflective bounce (3 bounces)
  - Implement and discuss an optimization (with runtimes before and after)
Intro to texture mapping.

Week 5

BRDFs
Assignment 4: Texture and Antialiasing, due Mar 3
1. Texture the plane with a checkerboard pattern.
2. Texture the red sphere with a map of the earth.
3. Render the scene with 4, 16, 32, and 128 samples per-pixel.
4. Discuss the method you use to sample the pixels
5. Identify and illustrate the artifacts or improvements that anti-aliasing provides.
6. Extra Credit 1 render the scene with new view points
7. Extra Credit 2 make a movie of the the scene (moving through it) and compare different anti-aliasing methods

Week 6

More BRDFs and Shader Models
Assignment 5: Acceleration Datastructures, due Mar 12
1. Implement a log(n) acceleration data structure for triangle intersections. (KD, BVH, or Octree)
2. You must be able to load a .obj model.
3. Provide timings before and after acceleration.
4. Provide a detailed analysis of your ray-tracer's performance.

Weeks 7,8,& 9
- Spectroscopy
- Units and terms of light transport
- Transparency
- Glass and dielectrics
Week 10
- More dielectrics
- Fresnel terms
- Snell's Law
- Beer's Law
- Assignment 6: Dielectrics, due Apr 16
  1. Implement glass in your raytracer
  2. Glass must support a Fresnel term
  3. Glass must support different indexes of refraction
  4. Glass must support different absorption terms
  5. Produce a sequence of 7 glass spheres (all in one scene), each with a different index of refraction. Make sure the background you choose makes the differences clearly visible.
  6. Render a model of your choosing as glass.
  7. Extra Credit Render a scene with nested glass objects, each with a different index of refraction.
  8. Extra Credit Experiment with different absorption terms for your glass, try to simulate a real-world object (such as different colored glass bottles).
  9. Discuss how you implemented the reflection/refraction ray pairs, and provide performance statistics with and without dielectrics.
Week 11

Procedural Methods
Splines
Noise
Hacking!

Resources

Code
- A Basic C++ vector class
Data
- High Dynamic Range images.
- HDRShop is a tool for manipulating HDR images.
- Earth Texture Map
- CUReT BRDF Database
- Cornell BRDF Database
- Bonn BTF Database
Papers & Maths