Lecture 13 - Radiosity I

We canlecture 13 slide 11 fii 0 graphics assume that

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Unformatted text preview: sent the energy leaving all the The Bj in the sum represent the energy leaving all the other patches in the scene other patches in the scene ! F i a constant that links surface patch i with patch j and is Fij ijiss a constant that links surface patch i with patch j and is called the factor called the form form factor " We can assume that Fii = 0 ! We canLecture 13: Slide 11! Fii = 0 Graphics assume that Final formulation " Final formulation We can substitute this expression for incident light into We• can substitute this expression for incident light into Equation 1 the previous equation ! We obtain a discrete approximation for the energy We• obtain a discrete approximation for the energy leaving the ith patch: leaving the i-th patch: ! Bi = Ei + Ri Ii becomes Bi = Ei + Ri •  The form factors Fij take into account ! X Bj Fij j –  Patch areas ! The form factors Fat whichinto account other ! –  The angle ij take they ‘face’ each I •  Patch areas the amount of energy leaving patch i that They control I The anglepatch i they ‘face’ each other reaches at which They control the amount of energy leaving patch i that reaches patch i Lecture 13: Slide 12! Graphics In matrix form In matrix form In matrix form" Re-write the equation for the ith patch th Re-write the equation for thefor the i-th patch
 •  Re-write the equation i patch X ! Bi XRi Bj Fij = Ei Bi Ri Bj Fij = Ei j j •  Joining the equations for all patches, we can the matrix Joining the equations for all patches, we can formulate formulate Joining the equations for all patches, we can formulate the matrix the matrix equation: ! equation: equation: 0 1 0B 1 0E 1 1 1 R1 F12 R1 F13 . . R 1 F1 n 1 0 B 1 0 E 1 01 1 R1 F12 R F13 . . R 1F 1nC B B21C B E21C RF B R2 F21 1 R21F23 . . 2 2n C B B C BCBC B RF B CB . 2C B E2C 1 R2 F23 .. .. R 2F 2nC B . C = B . C RF C BC 21 B R32F31 B R3 F32 1 B .. C 3 3n C B .. C B RF...
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This document was uploaded on 03/26/2014.

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