Following a finite element approach, an appropriate set of functions can be defined having broken down the surface into , ,..., surface elements:

If the emission *E* and the diffuse coefficient are
assumed to be constant on the elemental surface and equal to
and respectively,
equation 1.79 will have the
following form:

According to the definition of basis function
,
the radiosity of patch *k* is:

Substituting this into equation 1.81 and using the definition of
*g*(*p*,*p*') in equation 1.70, we get:

Let us introduce the **patch-to-patch form factor** as follows:

Note that this is the usual definition taking into account the
interpretation of *f*(*p*,*p*') in equation 1.59.

Dividing both sides by , the linear equation is then:

This is exactly the well known linear equation of original radiosity method (equation 1.10). Now let us begin to discuss how to define and use other, more effective function bases.

Mon Oct 21 14:07:41 METDST 1996