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Piecewise constant radiosity approximation

Following a finite element approach, an appropriate set of tex2html_wrap_inline2639 functions can be defined having broken down the surface into tex2html_wrap_inline2641 , tex2html_wrap_inline2643 ,..., tex2html_wrap_inline2645 surface elements:


If the emission E and the diffuse coefficient tex2html_wrap_inline2653 are assumed to be constant on the elemental surface tex2html_wrap_inline2655 and equal to tex2html_wrap_inline2657 and tex2html_wrap_inline2659 respectively, equation 1.79 will have the following form:


According to the definition of basis function tex2html_wrap_inline2639 , 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 tex2html_wrap_inline2655 , 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.

Szirmay-Kalos Laszlo
Mon Oct 21 14:07:41 METDST 1996