The
Radiosity
Method
Donald Fong
February 10, 2004
Why?

Ray tracing has a visual
signature


Only models perfect
specular reflection and
transmission
Interaction between diffusely
reflecting surfaces

Interiors, matte surfaces,
indirect lighting
Basic idea

Divide surfaces into discrete patches

Object space algorithm
Model light transfer between patches
as system of linear equations
 Solve matrix equation for radiosity of
each patch



Do it for R,G,B
Render patches as colored polygons
Simplifying assumptions

All surfaces are perfectly diffuse


Does not matter which way light
enters or leaves a surface
Radiosity is constant over a patch
Radiosity Equation

Bi is radiosity of patch i




Ei is non-zero for emitters
Ri is reflectivity of the patch


energy per unit area leaving a surface patch
per unit time
rate energy emitted + rate energy reflected
Wavelength dependent
Fij is the form factor – how much light patch
j contributes to patch i

Depends on geometric relationship –
distance and relative orientation
Radiosity solution

Finding form factors

Hemicube method
Meshing strategies
 Solving set of linear equations to get
radiosity for each patch

Form factor example

Almost 100%
Hemicube method

Efficient


Fq can be precomputed
Approximate

Aliasing
Gauss-Siedel method
Iterative
 Generates sequence of vectors that
converges to the solution
 Slow

Gathering vs. Shooting

Gathering


One iteration updates a
single patch by gathering
contributions from all other
patches
Shooting (and sorting)


Single iteration updates all
receiving patches with
unshot energy
Process patches
according to amount of
energy they are likely to
radiate
Progressive radiosity
Another example
Problems

Aliasing from hemicube method

Uniform pixel size
Using bilinear interpolation to
reconstruct radiosity function
 Using meshing of scene independent
of variations in radiosity function

Hemicube aliasing
Limited resolution of the hemicube
pixels
 Patches of same size map to different
number of cells

Reconstruction artifacts
Meshing artifacts
Shadow
leakage
 Light
leakage

Meshing strategies

Discontinuity meshing
Completed before radiosity solution
 Predict where discontinuities will occur


Adaptive meshing

Refine a “start” mesh as the solution
progresses
Discontinuity meshing

Mesh around expected
discontinuities


Sharp boundaries from point
light source or object
contact
Derivative discontinuities
from area light sources and
multi-object shadows
Hierarchical radiosity

Use different resolution depending on
who is emitting and who is receiving
Remeshing example
Summary

Diffuse only


Costly to add
specular
Not efficient
Meshing
 Memory intensive

Two pass solution