Insu Yu (Research Fellow)

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Monte Carlo Path Tracing Coursework Notes

• Insu Yu (Research Fellow)
• i.yu_at_cs.ucl.ac.uk
• James Tompkin (Research Engineer T.A.)
• j.tompkin_at_cs.ucl.ac.uk (email me with questions)

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What you need to do (in brief)

1. Shoot many rays through each pixel with
   stratified, jittered sampling.
2. Modify the direct lighting calculations to add
   support for area light sources.
3. Add support for sampling a BRDF.
4. Add support for evaluating the BRDFs at a surface
   point.
5. Put it all together to form paths that sample all
   the integrals pixels, direct lighting and BRDFs.
6. Add importance sampling OR unbiased path
   termination (Russian roulette).
7. Make your own scenes.

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Path Tracing

• Review

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Simple Stochastic Path Tracing

• Radiance for each ray (eye to pixel in view
  plane) is calculated by
• The integral cam be evaluated using Monte Carlo
  integration by generating N random direction ?i
  on hemisphere Ox distributed according to some
  probability density function P(x)

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Monte Carlo Path Tracing

• Rendering Equation

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Monte Carlo Path Tracing
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The Coursework

• Notes for each part

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Part 1 Stratified Jittered sampling Function
LitScenerenderPixel, SimpleCameraStratifiedRan
domRay

• Generate N x N stratified Sample per pixel at
  (i,j)
• Generate random variable ?1 ?2 to index
  stratified sample
• Generate Ray COP to sampled position at (i
  ?1,j ?2)
• Radiance Total Radiance / N_RAYS_PER_PIXEL
• Remember to change N_RAYS_PER_PIXEL 1 to 1,
  64, 256, 1024 rays, etc.

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Part 2 Direct Lighting Area light source
sampling
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Part 2 Direct Lighting Example Spherical Light
sampling

• Samples the sphere over the solid angle as seen
  from a point
• Find direction toward sphere in polar coordinates
  
• Transform local to world coordinates with U,V,N.
• Find intersection point (x)
• Reference Section 3.2 'Sampling Spherical
  Luminaries in "Monte Carlo Techniques for Direct
  Lighting Calculations," ACM Transactions on
  Graphics, 1996

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Part 2 Direct Lighting Polygon Light sampling
Function PolygonTriangularSampling,
PolygonRectangularSampling

• Sampling Rectangular Luminaries
• The uniform random sampled are given by
• Sampling Triangular Luminaries
• Use barycentric coordinates of triangles.
• The uniform random sampled are given by
• Sampling Polygon Luminaries
• Up to you!
• Reference Section 3.3 'Sampling Planar
  Luminaires in "Monte Carlo Techniques for Direct
  Lighting Calculations," ACM Transactions on
  Graphics, 1996

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Part 3,4,5 Lambertian Reflection
Model Function lambertianBRDFreflection,
lambertianBRDFbrdf
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Part 3,4,5 Modified Phong Reflection Model
Function phongBRDFreflection, phongBRDFbrdf
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Part 3,4,5 Modified Phong Reflection Model
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Part 3,4,5 Modified Phong Reflection
Model Function phongBRDFreflection,
phongBRDFbrdf
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Part 3,4,5 Modified Phong Reflection Model
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Part 3,4,5 Modified Phong Reflection Model

• Reading Lafortune and Willems Using the Modified
  Phong Reflectance Model for Physically-based
  Rendering will help.

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Part 6 Importance Sampling/Russian Roulette

• Look up the references on the webpage for these
  techniques to read more about them.
• Reading Avro and Kirks Particle Transport and
  Image Synthesis is a good place to start.

Part 7 D.I.Y. scenes

• Try to demonstrate advantages and disadvantages
  of path tracing in your scenes.
• What limitations exist? Which types of scene
  require more sampling to reduce noise?

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General Tips

• Use the paper references!
• They contain valuable background information
  which will help you understand the problem.
• Dutres Global Illumination Compendium is named
  precisely.
• A simple screenshot function exists in
  mainray.cpp for automating capture to .bmp. You
  can use it for your documentation.
• screenshot(int windowWidth, int windowHeight,
  char filename)
• Any other questions, e-mail j.tompkin_at_cs.ucl.ac.uk