Lecture 13 - Radiosity I

Lecture 13 Radiosity I

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Unformatted text preview: tion •  The equation can be simplified if we assume that Ai is small compared with r. ! • Thethis is the case, then wewe assume that A is small If equation can be simplified if can treat the inner integral as i constant over compared with r. the surface of Ai. ! If this is the case, then we can treat the inner integral as constant over the surface of Ai . Fij = 1 |Ai | Z Ai Z cos Aj cos ⇡r2 i j dAj dAi Graphics Lecture 13: Slide 22! . Simplifying form factors " Simplifying form factors •  With this assumption the outer integral evaluates to |Ai| (i.e. the area of Ai). ! With this assumption the outer integral evaluates to |Ai | (ie the •  Hence we area of Ai ). can write the integral as: ! Hence we can write the integral as: Z cos i cos Fij = ⇡r2 Aj Graphics Lecture 13: Slide 23! j dAj Further simplifying Further simplifying Further simplifying " We assumed that the radius is large compared with patch Ai We assumed that the radius is large compared with patch Ai . . Shouldalso be reasonable to assume it is large compared tothe also be to assume it is the Shouldassumedreasonableradius is largelarge compared topatch We that the compared with size of A. size .of Aj j . also be reasonable to assume it is large A Should i compared to the size of Aj. ! Hence the integrand of Hence the integrand of Hence the integrand ofZ ! Z cos cos cos i icos j j dA ! F= Fijij= dAj j 2 ⇡r2 A ⇡r Aj j ! can similarly considered constant over can similarly be be considered constantAj can similarly be considered constant over Aover Aj j ! So weget the approximation So wewe get the approximation ! So get the approximation cos cos | |A | cos i icos j jAj j | F= Fijij= ⇡ 22 ⇡ rr Graphics Lecture 13: Slide 24! . 20 29 20 / / 29 . Thehe Hemicube method " T Hemicube method Using bounding hemisphere it it can shown that all patches that Using a a bounding hemisphere can bebe shown that all patches that p...
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This document was uploaded on 03/26/2014.

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