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ECE 3610 Lifelong Learning Project The Rendering Equation Philip Dutr - K. Leuven, Belgium, SIGGRAPH 2004 Movie:55 [Click to download] Rendering...

“The definition of the BRDF is the starting point for the
RE… the BRDF is going to transform this equation into an"

ECE 3610 Lifelong Learning Project The Rendering Equation Philip Dutr é K. U. Leuven, Belgium, SIGGRAPH 2004 Movie: 0:55 [Click to download] Rendering Equation Derivation 1. “I am going to talk a little bit about the rendering equation (RE). The RE is a fundamental equation that derives all global ___________________ algorithms.” 2. “The RE describes ______________________ in a scene.” 3. “The definition of the BRDF is the starting point f or the RE… the BRDF is going to transform this equation into an ________________ equation.” 4. “So what we really want to do is consider all possible incoming directions Ψ … and we are going to integrate it over the entire _____________________.” d x L x f x dE x f x dL ) cos( ) , ( ) , , ( ) , ( ) , , ( ) , ( thus, what is the total L, including light sources? hemi e x L x L ? ) , ( ) , ( “…This is an equation that derives all global illumination algorithms.” 5. “And so the problem of finding the ______________ radiance at point x in a specific direction Ψ now has been transformed to finding the exit radiance from that point on the wooden block there in the direction of point x… and so the RE is a ___________________ equation because it expresses radiance in terms of other radiance values.” 6. “We have to c onsider all possible paths [from the light source] in order to find the correct value of radiance… through which light can be __________________… in the algorithm we will have to make a specific selection [of paths] and that’s what global illumination (GI ) algorithms do… they find ___________________ techniques to search for the most important [paths].”
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Direct and Indirect Paths 7. “How can we go to different paths there? Suppose we are just interested in paths of length 1, which basically gives us __________________ illumination, a path which starts at the light source and hits a surface and will just reflect back to the camera. .. Paths of length 2 [indirect illumination with one bounce] are actually substituting the integral part of the RE into the ________________ itself… What this equation now expresses really is all the radiance that is collected at all points Y that are visible from X… is reflected to X and is reflected toward the pixel [camera] we are interested in.” 8. “Suppose we have a poin t at a light source for which Le 0 and then we will have some sort of __________________ function that says something about the energy once light leaves point Y in direction Ψ … to ward the final point X, Ø .” 9. “Any GI problem has… to detect what paths are ____________________ and what paths are __________________________ for a specific scene.” 10. “If we can transform a differential ______________angle to a differential surface and then we can write these as an integral over surfaces instead of solid angle.” 11. Direct Path Generators Le: Vis check: __________________ sampling ___ ___ __________________ sampling ___ ___ __________________ sampling ___ ___ 12. Indirect Paths Vis check: _______________________________ ___ _______________________________ ___ _______________________________ ___ 13. Classic ray tracing ignores many ____________ and does not solve the RE. 14. “There are many, many ways of generating paths and what GI is all about is to design different types of path generation that work in ______ ___________ scenes.” 15. Future: There will be different ______________________ for different areas of the [same] scene.
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