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Application of vertex-surface form factors

   

In the traditional radiosity and the discussed progressive refinement methods, the radiosity distributions of the elemental surfaces were assumed to be constant, as were the normal vectors. This is obviously far from accurate, and the effects need to be reduced by a bilinear interpolation of Gouraud shading at the last step of the image generation. In progressive refinement, however, the linear radiosity approximation can be introduced earlier, even during the phase of the calculation of radiosities. Besides, the real surface normals in the vertices of the approximating polygons can be used resulting in a more accurate computation.

This method is based on the examination of energy transfer between a differential area ( tex2html_wrap_inline1812 ) around a vertex of a surface and another finite surface ( tex2html_wrap_inline1824 ), and concentrates on the radiosity of vertices of polygons instead of the radiosities of the polygons themselves. The normal of tex2html_wrap_inline1812 is assumed to be equal to the normal of the real surface in this point. The portion of the energy landing on the finite surface and the energy radiated by the differential surface element is called the vertex-surface form factor (or vertex-patch form factor).   

The vertex-surface form factor, based on equation 1.6, is:

equation641

This expression can either be evaluated by any discussed method or by simply firing several rays from tex2html_wrap_inline1812 towards the centers of the patches generated by the subdivision of surface element tex2html_wrap_inline1824 . Each ray results in a visibility factor of either 0 or 1, and an area-weighted summation has to be carried out for those patches which have visibility 1 associated with them.

Suppose that in progressive refinement total and unshot radiosity estimates are available for all vertices of surface elements. Unshot surface radiosities can be approximated as the average of their unshot vertex radiosities. Having selected the surface element with the highest unshot radiosity ( tex2html_wrap_inline2400 ), and having also determined the vertex-surface form factors from all the vertices to the selected surface (note that this is the reverse direction), the new contributions to the total and unshot radiosities of vertices are:

equation654

This has modified the total and unshot radiosities of the vertices. Thus, estimating the surface radiosities, the last step can be repeated until convergence, when the unshot radiosities of vertices become negligible. The radiosity of the vertices can be directly turned to intensity and color information, enabling Gouraud's algorithm to complete the shading for the internal pixels of the polygons.


next up previous index
Next: Probabilistic progressive refinement Up: Progressive refinement Previous: Progressive refinement

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