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 ith 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"
Rewrite the equation for the ith patch
th
Rewrite the equation for thefor the ith patch
• Rewrite 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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 Spring '14
 Energy, Light, form factor, Rendering

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