05/07/02 (c) 2002 University of Wisconsin

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!

05/07/02 (c) 2002 University of Wisconsin

Ray-traced Cornell box, due to Henrik Jensen,http://www.gk.dtu.dk/~hwj

Which paths are present?Which paths are missing?

05/07/02 (c) 2002 University of Wisconsin

05/07/02 (c) 2002 University of Wisconsin

Today

• Rendering algorithms that capture other light paths– Distribution ray-tracing– Radiosity– Bi-directional ray tracing

05/07/02 (c) 2002 University of Wisconsin

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

05/07/02 (c) 2002 University of Wisconsin

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?

05/07/02 (c) 2002 University of Wisconsin

Distribution RaytracingDepth of Field

From Alan Watt, “3D Computer Graphics”

05/07/02 (c) 2002 University of Wisconsin

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

05/07/02 (c) 2002 University of Wisconsin

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?

05/07/02 (c) 2002 University of Wisconsin

Caustics

From Alan Watt, “3D Computer Graphics”

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

05/07/02 (c) 2002 University of Wisconsin

Refraction caustic

Henrik wann Jensen, http://www.gk.dtu.dk/~hwj

05/07/02 (c) 2002 University of Wisconsin

Refraction caustics

Henrik wann Jensen, http://www.gk.dtu.dk/~hwj

05/07/02 (c) 2002 University of Wisconsin

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

05/07/02 (c) 2002 University of Wisconsin

Real World LD*E Paths

From Alan Watt, “3D Computer Graphics”

05/07/02 (c) 2002 University of Wisconsin

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

05/07/02 (c) 2002 University of Wisconsin

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

j

N

jijiii BFEB

1

05/07/02 (c) 2002 University of Wisconsin

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

05/07/02 (c) 2002 University of Wisconsin

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”

05/07/02 (c) 2002 University of Wisconsin

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”