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  1. Week 10 - Thursday CS361

  2. Last time • What did we talk about last time? • Reflections • Transmittance • Refractions • Caustics • Global subsurface scattering

  3. Questions?

  4. Project 3

  5. Assignment 4

  6. Radiosity • To create a realistic scene, it is necessary for light to bounce between surfaces many times • This causes subtle effects in how light and shadow interact • This also causes certain lighting effects such as color bleeding (where the color of an object is projected onto nearby surfaces)

  7. Radiosity • Radiosity was the first graphics technique designed to simulate radiance transfer • Turn on the light sources and allow the environmental light to reach equilibrium • While the light is in stable state, each surface may be treated a light source • A general simplification is to assume that all indirect light is emitted from a diffuse surface • Radiosity doesn't do specular reflection

  8. Radiosity • The outgoing radiance of a diffuse surface is: where r and E are the reflectance and irradiance • Each surface is represented by a number of patches • To get even lighting and soft shadows, it may be necessary to break polygons down into smaller patches • It's even possible to have fewer patches than polygons

  9. Form factors • To create a radiosity solution, we need to create a matrix of form factors • These are geometric values saying what proportion of light travels directly from one surface to another • The form factor between a surface point with differential area dai and another surface point with daj is • These differentials have to be (numerically) integrated for each patch

  10. Visibility • If the receiving patch faces away from the viewed patch, the form factor is zero • hij is the visibility factor, which ranges from either 0 (not visible) to 1 (visible) • It is scaled if the view between the surfaces is fully or partially blocked

  11. Solving radiosity • A common way to solve for the equilibrium is to form a square matrix with each row formed by the form factors for a given patch times the patch’s reflectivity • Performing Gaussian elimination on the resulting matrix gives the exitance of the patch in question • Much research has focused on how to do this better • Though radiosity is no longer a sexy research topic since it doesn't allow for specular effects

  12. Ray tracing • Radiosity is a great technique for getting soft shadows and many other effects characteristic of diffuse lighting • Specular highlights and reflections are not present • An alternative global illumination model is ray tracing which shoots single rays through the scene and computes their colors

  13. Classical ray tracing • Rays are traced from the camera through the screen to the closest object, called the intersection point • For each intersection point: • Trace a ray to each light source • If the object is shiny, trace a reflection ray • If the object is not opaque, trace a refraction ray • Opaque objects can block the rays, while transparent objects attenuate the light

  14. Pros and cons • Pros • Classical ray tracing is relatively fast (only a few rays are traced per pixel) • Good for direct lighting and specular surfaces • Cons • Not good for environmental lighting • Does not handle glossy and diffuse interreflections

  15. Monte Carlo ray tracing

  16. Monte Carlo ray tracing • Ray directions are randomly chosen, weighted by the BRDF • Called importance sampling • Usually it means tracing more rays along the specular reflection path • There are two main types of Monte Carlo ray tracing: • Path tracing • Distribution ray tracing

  17. Ray tracing • Path tracing • A single ray is reflected or refracted throughout the scene, changing direction at each surface intersection • Good sampling requires millions of rays or more per pixel • Distribution ray tracing • Spawns random rays from every surface intersection • Starts with fewer rays through each pixel than path tracing, but ends up with lots at each surface

  18. Pros and cons • Pros • Very realistic • Cons • Tons of computational power is necessary • Not good for real-time rendering with many objects

  19. Precomputed lighting • Full global illumination algorithms are expensive • Some results can be pre-computed • Those results can be used in real-time rendering • Scene and light sources must remain static • The majority of scenes are only partially static

  20. Simple surface prelighting • Lighting on smooth, Lambertian surfaces is simple • Single RGB value giving irradiance • Dynamic lights can simply be added on top • Irradiance can be stored in vertices if there is a lot of geometric detail • Or texture maps (which could change depending on situation) • Cannot be used with glossy or specular surfaces • Irradiance maps have no directionality • Can’t be used with high frequency normal maps

  21. Directional surface prelighting • Can be used with specular and glossy surfaces, and high frequency normal maps • Additional directional data must be stored • How irradiance changes with surface normal • Storing irradiance environment map at each surface location

  22. Volume prelighting • Indirect light illuminates dynamic objects • Multiple methods: • Interpolate irradiance values from closest environment maps (Valve) • Use the prelighting on adjacent surfaces (Racing games) • Store average irradiances at each point (Little Big Planet) • Little has been done for specular and glossy surfaces

  23. Precomputed occlusion • Global illumination algorithms precompute quantities other than lighting • Often, a measure of how much parts of a scene block light are computed • Bent normal, occlusion factor • These precomputed occlusion quantities can be applied to changing light in a scene • Creates a more realistic appearance than precomputing lighting alone

  24. Precomputed ambient occlusion • Cast rays over hemisphere around each surface location or vertex • Cast rays may be restricted to a set distance • Usually involves a cosine weighting factor • Most efficient way is importance sampling • Instead of casting rays uniformly over hemisphere, distribution of ray directions is cosine-weighted around surface normal

  25. Precomputed ambient occlusion • Precomputed ambient occlusion factors are only valid on stationary objects • Example: a racetrack • For moving objects (like a car), ambient occlusion can be computed on a large flat plane • This works for rigid objects, but deformable objects would need many precomputed poses • Like a human

  26. Precomputed directional occlusion Horizon mapping is used to determine self-occlusion on a height field surface For each point of the surface, the altitude angle of the horizon is determined Soft shadowing can be supported by tracking the angular extents of the light source

  27. Precomputed directional occlusion • An alternative technique is to use volume textures to store horizon angles • This is useful for a light source that travels along some predetermined path • Like the sun • Multiple occluded angle intervals are stored, rather than one horizon angle • This enables modeling non-height field geometry

  28. Precomputed directional occlusion

  29. Spherical harmonics • Spherical harmonics are the angular portion of a set of solutions to Laplace's equation • The spherical harmonics that we're interested in form an orthogonal system that gives us an organized way to refer to more and more complicated coverage of an object from different directions

  30. Precomputed radiance transfer • We can record the effects on a point from many different sources of irradiance • These effects can be stored as spherical harmonics coefficients • The final result gets the dynamic irradiance from the same spherical harmonics directions and combines the effects • Wavelets can be used instead of spherical harmonics with better effects • These techniques are best suited for diffuse (low frequency) lighting

  31. Upcoming

  32. Next time… • Image based effects • Skyboxes • Sprites • Billboarding • Particle systems

  33. Reminders • Assignment 4 is due tonight by midnight • Keep working on Project 3 • Read Chapter 10