Last Time

1. Last Time • Ray-tracing implementation • Recall the light paths that ray-tracing captures • Technically, we are talking about “eye ray tracing,” which traces rays originating at the eye • Some people use the terms forward or backward ray-tracing, but there is no agreement in which direction is forward! (c) 2002 University of Wisconsin

2. Which paths are present? Which paths are missing? Ray-traced Cornell box, due to Henrik Jensen, http://www.gk.dtu.dk/~hwj (c) 2002 University of Wisconsin

3. (c) 2002 University of Wisconsin

4. Today • Rendering algorithms that capture other light paths • Distribution ray-tracing • Radiosity • Bi-directional ray tracing (c) 2002 University of Wisconsin

5. Ray-Tracing and Sampling • Basic ray-tracing casts one ray through each pixel, sends one ray for each reflection, one ray for each point light, etc • This represents a single sample for each point, and for an animation, a single sample for each frame • Many important effects require more samples: • Motion blur: A photograph of a moving object smears the object across the film (longer exposure, more motion blur) • Depth of Field: Objects not located at the focal distance appear blurred when viewed through a real lens system • Rough reflections: Reflections in a rough surface appear blurred (c) 2002 University of Wisconsin

6. Distribution Raytracing • Distribution raytracing casts more than one ray for each sample • Originally called distributed raytracing, but the name’s confusing • How would you sample to get motion blur? • How would you sample to get rough reflections? • How would you sample to get depth of field? (c) 2002 University of Wisconsin

7. Distribution Raytracing Depth of Field From Alan Watt, “3D Computer Graphics” (c) 2002 University of Wisconsin

8. Missing Paths • Basic recursive raytracing cannot do: • LS*D+E: Light bouncing off a shiny surface like a mirror and illuminating a diffuse surface • LD+E: Light bouncing off one diffuse surface to illuminate others • Basic problem: The raytracer doesn’t know where to send rays out of the diffuse surface to capture the incoming light • Also a problem for rough specular reflection • Fuzzy reflections in rough shiny objects (c) 2002 University of Wisconsin

9. Bi-directional Raytracing • Cast rays from the light sources out into the scene • When a ray hits a diffuse surface, accumulate some light there • Surfaces record the amount of light that hits them • Store the light in texture maps • Store the light in quadtrees • Store the light in photon maps • Cast rays from the eye out into the scene • When a ray hits a diffuse surface, look up the amount of light that hit it in the light-ray phase • What paths does it capture? • What sort of visual effects do you see? (c) 2002 University of Wisconsin

10. Caustics Standard raytracer: Diffuse table and blue ball, mirrors left, right and back, transparent red ball Bi-directional raytracer More rays in the light pass Note the LS*DS*E paths From Alan Watt, “3D Computer Graphics” (c) 2002 University of Wisconsin

11. Refraction caustic Henrik wann Jensen, http://www.gk.dtu.dk/~hwj (c) 2002 University of Wisconsin

12. Refraction caustics Henrik wann Jensen, http://www.gk.dtu.dk/~hwj (c) 2002 University of Wisconsin

13. Still Missing… • LD*E paths – Diffuse-diffuse transport • Formulated and solved with radiosity methods • L(S|D)*E paths • Solved with Monte-Carlo renderers – very very inefficient • Also solvable with multi-pass methods, but also very very inefficient, and subject to aliasing • An unsolved (unsolvable?) problem (c) 2002 University of Wisconsin

14. Real World LD*E Paths From Alan Watt, “3D Computer Graphics” (c) 2002 University of Wisconsin

15. Radiosity Assumptions • All surfaces are perfectly diffuse • Means that is doesn’t matter which way light hits or leaves a surface • Illumination is constant over a patch • Can break the world up into a discrete number of pieces • Problems at sharp illumination boundaries - shadows • Ways around these problems, but less efficient and less able to manage scene complexity • Assumptions allow us to solve for LD*E paths (c) 2002 University of Wisconsin

16. Radiosity Equation • Derived from the global illumination equation using radiosity assumptions • Bi is the radiosity (brightness) of patch i • i is the diffuse reflection coefficient • Fij is the form factor, which quantifies how much light patch j contributes to patch i • The brightness of each patch depends on how much light it gets from all the others, and its diffuse reflection (c) 2002 University of Wisconsin

17. Solving the Radiosity Eqn • Radiosity algorithms use one of several methods to solve the radiosity equation • Basically a very large linear system, so techniques can all be mapped onto linear system solvers • A large part of the computation is in finding form factors • Describe how much light gets from each patch to every other patch • Geometric in nature - do not depend on the illumination, just the layout of the scene • Another key factor is finding good meshing strategies - ways of laying out the patches (c) 2002 University of Wisconsin

18. Radiosity Example • Color bleeding is extreme in this example • Textures are applied after solving for illumination • Some meshing artifacts are visible - note the banding around the pictures on the wall From Alan Watt, “3D Computer Graphics” (c) 2002 University of Wisconsin

19. Radiosity Meshing • Each patch is colored with its illumination • Note the discrete nature of the solution • The previous image was obtained by pushing color to vertices and then Gourand shading From Alan Watt, “3D Computer Graphics” (c) 2002 University of Wisconsin