Radiosity
Jian Huang, CS594, Fall 2002
This set of slides reference the text book and slides
used at Ohio State.
Radiosity
• Radiosity is a global illumination model that
– assumes all surfaces are diffuse and computes view
independent illumination.
• Radiosity computes the intensity reflected from each small
surface region ( differential area ) equally in all directions
(including the eye...). This intensity includes energy
emitted by the surface itself and reflected energy from
other objects.
• Following an (expensive) preprocessing to compute
radiosity, the model is shaded and can be rendered
interactively.
Basic Definitions
• Radiosity: (B) Energy per unit area per unit time.
• Emission: (E) Energy per unit area per unit time
that the surface emits itself (e. g., light source).
• Reflectivity: (r) The fraction of light which is
reflected from a surface. (0 <= r <=1)
• Form- Factor: (F) The fraction of the light leaving
one surface which arrives to another. (0<=F<=1)
The Basic Radiosity Equation
• We will compute the light emitted from a single
differential surface area dAi.
• It consists of:
• 1. Light emitted by dAi.
• 2. Light reflected by dAi.
– depends on light emitted by other dAj, fraction of it
reaches dAi.
• The fraction depends on the geometric relationship
between dAi and dAj: the formfactor .
The Basic Radiosity Equation
• The relationship between a single differential area’s
radiosity and the radiosities of the rest of the environment:
The Discrete Radiosity
Equation
• We can’t operate in continuous space. We need a finite
problem!
• We divide the surfaces into small discrete areas called
patches. We assume that radiosity and emission do no vary
across the patch area.
• The radiosity of a patch is then:
• Or, more conveniently:
The Reciprocity Relationship
• If we had equal sized emitters and receivers, the fraction of
energy emitted by one and received by the other would be
identical to the fraction of energy going the other way.
• Thus, the formfactors from Ai to Aj and from Aj to Ai are
related by the ratios of their areas:
• Thus:
• The radiosity equation is now:
Matrix Formulation
• For an environment of N patches:
• Because the sum of formfactor along a lines is less then 1, this matrix
is diagonally dominant and therefore iterative Gauss- Siedel is
guaranteed to (quickly) converge to a solution!
The Formfactor
• The formfactor is purely a function of geometric
relationship between patches and thus does not depend on
viewer position or surface reflectivity attributes.
• Between differential areas:
Computation Hurdles
• Computation of the formfactors
– Solutions: hemicube, elements.
• Solution of the matrix in time O(N2).
– Solution: progressive shooting.
Nusselt’s Analog
• The inner integral in the previous double integral
represents the formfactor from a differential area to a finite
patch. This quantity can also be computed by the fraction
of the base of the hemisphere covered by the projection:
The Hemi-cube
• Any patch which covers the same projected area on the
hemisphere has the same formfactor.
• Any surface can be used to project the patches onto,
without changing the formfactor.
The Hemi-cube
• Compute the delta formfactor of each grid cells DF and
store in a table (next slide...).
• Project all patches onto the ‘ hemi- cube ’ screen (use Zbuffer rendering hardware?), drawing a patch- id instead of
color.
• Sum the delta form factors of all grid cells covered by the
patch’s id.
Computing the delta formfactor
Problems with the Hemi-cube
• Because we compute only the inner integral
serious inaccuracies can occur if the size of the
patch is large relative to the distance.
• Because the hemisphere is divided into discrete
solid angles, a number of aliasing problems may
occur.
Patches and Elements
• Patches are used for emitting light. Some patches are
divided into elements, which are used to more accurately
compute the received light after the patch solution have
been computed.
Progressive Radiosity
• The problem: we need to solve a set of N
equations – O(N2) time.
• In the conventional radiosity we gather the
contribution of other patches to patch i.
Shooting Radiosity
• Shoot the radiosity of patch i and update the
radiosity of all other patches.
Visual Comparison
• Assume the scene is displayed after each update:
• In the ‘row solution’ (gather), every image will show
another element being fully illuminated.
• In the ‘column solution’ (shoot), every image will show the
whole image change due to the contribution by one
element. The magnitude of this change depends on the
amount of energy BiAi sent out from the ‘shooting’ patch.
• Therefore, the image will converge faster to the final
solution if the patches with highest added energy DBiAi
shoot first!
The Total Process
Comparing Radiosity and Raytracing
• Radiosity:
– Object space
– Only diffuse (specular is too expensive to do, why?)
– View independent
• Ray-tracing:
– Image space
– Only specular (why?)
– View dependent
• Which is more realistic?
• Are we stuck on techniques towards realism?
– Distributed Ray Tracing and Photon mapping!!
More Issues...
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Specular illumination
Reflections (ray tracing)
Participating media
Adaptive subdivision
Dynamic models
View dependent radiosity
...