Join / Forgotten your password?
 
HomeFeaturesStoreForumsWikiWorkshopsJobsPortfolioGalleryEvents Members
 
> CGWiki Home       > Community Portal       > Current Events      > Recent Changes     > Random Page       > Join       > Support Forum       > Help     
 

Form factor

(Redirected from Form Factor)
[edit]

Brief Description

The term form factor is used in global illumination literature, specifically when discussing finite element techniques or radiosity, to describe the geometrical relationship between two patches in the scene. This terminology was inherited from physics and is used to determine how much of the energy leaving a patch i arrives at a second patch j given their sizes, orientations and positions. A visibility term is also included to account for cases when two patches are occluded by a third.

Because of the immense number of form factors that have to be computed when using radiosity (originally n2 where n is the number of surface patches in the scene), it is important that they are calculated as quickly as possible to keep render times down. However, accurately determining form factors is extremely expensive in terms of render time, and there is a definite trade off between speed and visual fidelity.

[edit]

Form Factor Determination

The form factor Fij is formulated

F_{ij} = \frac{1}{A_i}\int_{A_i}{\int_{A_j}{ \frac{\cos{\theta_i}\cos{\theta_j}}{\pi r_{ij}^2}V_{ij} dA_i dA_j }}

where:

  • Ai and Aj are the areas of patches i and j respectively.
  • θi and θj are the angles between the surface normal at patch i and j respectively, and the line connecting the two.
  • rij is the distance between the two patches.
  • Vij is the visibility term denoting the visibility between the two patches, ranging from 0 when the patches are completely occluded, to 1 when completely unoccluded.

While the concept of form factors is a deceptively simple one, the above equation cannot be solved directly. Instead we normally assume that the patch i has a differential (infinitesimally small) area. By making this assumption we can reduce the problem from one where we have to consider the relationship between every single point of patch i and every single point on patch j, to one where we consider the relationship between one point on the patch i and every point on the patch j.

Even with the above assumption solving the equation analytically is far too expensive to be practically usable. Additionally, analytical solutions cannot account for the visibility term at all. Instead the form factor is normally calculated using numerical methods, such as the hemi-cube where the form factor is discretised into cells on a hemi cube centred at the differential area i, or other methods such as stochastic sampling, where rays are from i in random directions and checked for intersections with with the given surface.

Retrieved from "http://wiki.cgsociety.org/index.php/Form_factor"