Radiosity

@article{goral1984modeling,
  title={Modeling the interaction of light between diffuse surfaces},
  author={Goral, Cindy M and Torrance, Kenneth E and Greenberg, Donald P and Battaile, Bennett},
  journal={ACM SIGGRAPH computer graphics},
  volume={18},
  number={3},
  pages={213--222},
  year={1984},
  publisher={ACM New York, NY, USA}
}

with

See Lambertian BRDF

Nusselt-Analog #

For two patches in the radiosity method:
For all two points on the two surfaces:
The geometry factor accounting to the Area Foreshortening can be assumed as a constant.

Discrete Radiosity Equation #

<img src="/ltximg/radiosity_b33b28740c911682aeb0410c79f6ff76b6912d9c.svg" alt="radiosity_b33b28740c911682aeb0410c79f6ff76b6912d9c.svg" class="org-svg" />

with:

= The average fraction of energy that leaves finite element i and directly arrives at element j

Form Factors #

Idea: Double Projection

Properties #

Planar patch:
Energy conservation:
Reciprocity:

Computation #

Formular to compute the form factor to some Area at to :

Hemicube Algorithm #

Use the Nusselt Analog
precompute formfactors for hemicube
When rendering, project other patches onto the cube (respect visibility)

Using hardware acceleration #

Put camera in the center of the hemicube
Render cube maps
Each fragment just writes some unique per patch ID, no color
Standard depth test takes care of visibility
After that, sum up the contributions of the objects by their ID

Rendering the scene #

Render per patch radiosity values
Color the vertices according to their neighboring patch colors and use Gouraud shading .

Comparison to raytracing #

Raytracing is good at specular reflection and refraction, but bad at diffuse interactions
Radiosity is good at diffuse lighting but bad at other stuff

Both methods are global, use them both at the same time!