Practice

Basis functions for Radiosity

• Piecewise constant
• Piecewise linear
• Higher order polynomials
• Wavelets

Piecewise constant make computation easier because of their simplicity. Linear are much better for display purposes. Higher order polynomials tend to have problems with discontinuities due to larger support[38,35,21]. Wavelets [15,13] tend to be similar to piecewise constant in practice (although I'm sure some people would disagree with this), however in theory they should have the advantages of higher order polynomials and still have the locality of piecewise constant.

Radiosity Data Structures: The Mesh

Properties for the mesh

Basis functions need to be associated with the geometry. This is the function of the mesh. A radiosity mesh is the geometry chopped up into regions over which one or several basis functions live. It is important that it be possible to subdivide the mesh. This will allow the creation of a hierarchy. It should be possible to get geometry from a mesh element. It should also be possible to get reflectance information. You will be storing either the radiance or the irradiance for each basis function.

Mesh domains

The most common mesh elements are quads and triangles. Usually polygonal objects are tessellated into quads and tris before radiosity processing begins. Meshing can also be done for parametric objects. It is important that the mapping between parameter space be described well enough that normals, points, and areas can all be estimated reasonably accurately.

Projection onto the basis functions

The projection onto the basis function is an inner product with the dual of the basis function. As the integration cannot be done analytically in most cases, the integral must be estimated by sampling the value over the surface.

• Sample over surface
• Sample at corners
• Sample at quadrature points

Remember to sample the full integral equation

$$L(x) = L_e(x) + \rho(x) \int_{\cal E} L(x') {\rm vis}(x,x')\f... ...{ \left\vert \left\vert x - x' \right\vert \right\vert ^2}dA.$$

including emission.