
Week 
Topic 
Exercises 
Readings 
14.04.2011 
Introduction: Motivation, Examples, Challenges. 
First class, no exercises or readings. 

21.04.2011 
Color, Radiometry, and Images. 
pbrt gymnastics: download, install, and compile pbrt and render some of the example scenes; also experiment with the scene descriptions. 
Jensen, H.
W., and T. AkenineMöller. The Race for RealTime Photorealism. American
Scientist 98, no. 2 (2010): 132139. Greenberg, D. P. et al. A Framework for Realistic Image Synthesis. In Proceedings of SIGGRAPH '97, 477494. New York, New York, USA: ACM Press, 1997. 
28.04.2011 
Signals and their Representation. 
1. Color representation and radiometry. 2. Look at pbrt's spectrum.h / spectrum.cpp
and understand the color representation used. Think about possible
advantages and disadvantages, with our discussion in class in mind. 
Hanrahan, P. Rendering Concepts. In Radiosity and Realistic Image Synthesis, edited by M. F. Cohen and J. Wallace. San Diego, CA, USA: Academic Press Professional, Inc., 1993. Mallat, S. G. Wavelets for Compressing Images. In L'explosion des mathematiques. Societe Mathematique de France, 2007. 
05.05.2011 
Using signal representations for rendering. 
Exercises on signal representation and approximation using the starter code. Code containing the solution to your exercise and the Monte Carlo integration example presented in class. 
Cook, R. L. Stochastic Sampling in Computer Graphics. ACM Trans. Graph. 5 (1986): 5172. Green, R. Spherical Harmonic Lighting: The Gritty Details, p. 121. 
12.05.2011 
The rendering equation and the operator formulation. 
Image sampling and reconstruction in pbrt has three parameters: the sampling pattern used (Sampler), the number of samples per pixel (pixelsamples), and the reconstruction filter (PixelFilter). Use spheresdifferentialstexfilt.pbrt, which is available in pbrt's extended scene set,
to explore the effect of the different parameters, try to understand
the advantages and disadvantages, and connect your observations to our
discussions in class. Please make sure the images you generate are
available in class. 
No reading but the project proposals are due this week. 
19.05.2011 
The Neumann series: solving the rendering equation. 
Compute
the generalized GaussLegendre quadrature weights for the space H_5
spanned by all Legendre polynomials up to L=5 for node locations: [0.9311,0.3658,0.2369, 0.1225,0.3897,0.9004] and [0.6748,0.6263,0.4479, 0.1088,0.0205,0.2926, 0.3102,0.3594,0.4187, 0.5094,0.5310,0.5904], and verify your result. You might find the discussion in the Numerical Recipes book useful. Matlab script computing generalized GaussLegendre quadrature for arbitrary nodes. Code used in class to demonstrate the power series and the effectiveness of finite approximations for the Neumann series. 
Kajiya, J. T. The Rendering Equation. ACM SIGGRAPH Computer Graphics 20, no. 4 (1986). He, X. D., K. E. Torrance, F. X. Sillion, and D. P. Greenberg. A Comprehensive Physical Model for Light Reflection. ACM SIGGRAPH Computer Graphics 25, no. 4 (1991). 
26.05.2011 
Finite element methods for light transport simulation: Galerkin projection of the rendering equation. 
In class we talked about the matrix representation of operators. Derive an explicit
representation for the projection operator of an arbitrary function
onto the space spanned by all spherical harmonics up to band L for finite L. Slepian functions
are an alternative to spherical harmonics that provide many advantages
for computer graphics applications. Derive also an explicit
representation for the projection operator of an arbitrary input
function onto the first k Slepian functions for some finite L. 
Kajiya, J. T. The Rendering Equation. ACM SIGGRAPH Computer Graphics 20, no. 4 (1986). Arvo, J. The Role of Functional Analysis in Global Illumination. In Rendering Techniques '95, edited by P. M. Hanrahan and W. Purgathofer, 115126. New York: SpringerVerlag, 1995. 
02.06.2011 
No class this week (legal holiday). 

09.06.2011 
Monte Carlo integration. 
Derive Galerkin projection
for the shading equation, using either an abstract basis or spherical
harmonics, and simplify the resulting expression as much as possible.
What additional simplifications arise in the case of purely diffuse
shading? Also consider how the obtained formulas could be implented and
what aspects would most likely be challenging to attain high
performance. 
Arvo, J., K. Torrance, and B. Smits. A Framework for the Analysis of Error in Global Illumination Algorithms.
In SIGGRAPH '94: Proceedings of the 21st annual conference on computer
graphics and interactive techniques, 7584. New York, NY, USA: ACM,
1994. 
16.06.2011 
The path integral formulation + interim presentations. 
No exercise. In class project interim presentations (15 min. presentation + 5 min. discussion). 
Hanrahan, P., E. Veach, and D. Zorin. Mathematical Models for Computer Graphics Lecture Notes, 1997, Chapter 6. The complete lecture notes are worth a look for those interested in the subject. 
23.06.2011 
Path tracing and bidirectional path tracing. 
There will be a more comprehensive exercise due to next week. 
Lafortune, E. P., and Y. D. Willems. A Theoretical Framework for Physically Based Rendering. Comput. Graph. Forum 13 (1994): 97107. 
30.06.2011 
Interpolation methods: irradiance caching and photon mapping. 
Monte Carlo estimators and Monte Carlo integration on the sphere (combined with last week's exercise).  Veach, E., and L. Guibas. Bidirectional Estimators for Light Transport. In Fifth Eurographics Workshop on Rendering, 147162, 1994. 
07.07.2011 
Volume transport: media with varying refractive index and scattering media. 
Same exercise as last week. Here is some Matlab helper code. 
Hachisuka, T., S. Ogaki, and H. W. Jensen. Progressive Photon Mapping. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2008) 27, no. 5 (2008). 
14.07.2011 
Final presentations. 
Final presentations (20
min. talk + 5 min. discussion). The project reports should in their
structure follow a conference publications in computer graphics (e.g. the SIGGRAPH style), possibly with a longer implementation section. The reports are due 5th August 2011. 
No reading this week. 
©
christian (dot) lessig (at) tu (minus) berlin (dot) de 
June 2011 