The Radiosity Method Donald Fong February 10, 2004.

The

RadiosityMethod

Donald FongFebruary 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 patchesObject space algorithm

Model light transfer between patches as system of linear equations

Solve matrix equation for radiosity of each patchDo it for R,G,B

Render patches as colored polygons

Simplifying assumptions

All surfaces are perfectly diffuseDoes not matter which way light

enters or leaves a surface Radiosity is constant over a patch

Radiosity Equation

Bi is radiosity of patch i energy per unit area leaving a surface patch

per unit time rate energy emitted + rate energy reflected

Ei is non-zero for emitters Ri is reflectivity of the patch

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

EfficientFq can be precomputed

ApproximateAliasing

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 methodUniform 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 meshingCompleted before radiosity solutionPredict where discontinuities will occur

Adaptive meshingRefine 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 onlyCostly to add

specular Not efficient

MeshingMemory intensive

Two pass solution