講義資料

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2
3
(Ambient Occlusion)
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0.5s
1.4s
5
1.4s
37.2s
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E (p, n) =
∫
Ω
LA cosθi dωi = π LA
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E (p, n) = LA ∫ v (p, l) cosθi dωi
Ω
{
0
1
1
kA (p) =
π
∫
v (p, l) =
Ω
v (p, l) cosθi dωi
E (p, n) = kA (p) π LA
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p0
p2
p0
p2
p1
p0
p1
p1
kA
(bent normal)
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n
&
cdiff #
Lo (v) =
⊗ %kA π LA + ∑ v (lk ) ELk cosθik (
π
$
'
k=1
•  BRDF
n
camb
Lo (v) = kA
π LA + ∑ v (lk ) f (lk , v) ⊗ ELk cosθik
π
k=1
•  bent normal
nbent =
∫
∫
Ω
v (l) l cosθi dωi
Ω
v (l) l cosθi dωi
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•  Eind
kind
n
& n
camb #
Lo (v) = kA
⊗ %Eind + kind ∑ ELk ( + ∑ v (lk ) f (lk , v) ⊗ ELk cosθik
π
$
' k=1
k=1
•  bent normal nbent
n
' n
camb $
Lo (v) = kA
⊗ &Eind + kind ∑ ELk cosθi"k ) + ∑ v (lk ) f (lk , v) ⊗ ELk cosθik
π
%
( k=1
k=1
•  θ’ik bent normal nbent
lk
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(Visibility)
(Obscurance)
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d
ρ(l) = d
max
(Obscurance)
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ρ(l)
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1
kA =
π
∫ Ω ρ (l) cosθi dωi
dmax
l
d
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Li
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kA
kA! =
1− camb (1− kA)
Lo
Li
Lo
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kA
bent normal nbent
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kA
bent normal nbent
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• 
[Bunnell, GPU Gems 2, 2005]
•  ILM
Pirates of the Caribbean
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Bunnel
R
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1−
E
r cosθE max (1, 4 cosθR)
4 2
+r
π
E
E
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kA
R
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•  Crytek
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Crysis
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Crytek
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kA
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kA =1
P
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Crytek
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Crytek
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Volumetric
Obscurance
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Luft
•  Image Enhancement
z
by Unsharp Masking
the Depth Buffer
y
•  SIGGRAPH 2006
x
z
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x
z
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x
z
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x
x
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Luft
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Luft
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n
p
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•  n:
•  p:
•  R(u, v):
u
v
•  T(p): p
•  S(x, y, z):
x, y, z
F = R (n, (0,1, 0)) T (−p)
M = F−1S (1, −1,1) F
n = (0,1, 0)
⇓
M = T (p) S (1, −1,1) T (−p)
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Environment Map Bump Mapping
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n1 sin (θ1) = n2 sin (θ2)
i
θ1
n
t = ri + (w − k) n
r = n1 n2
w = − (i ⋅ n) n
surface
k = 1+ (w − r) (w + r)
t = −cn + i
c ≈ 1.0
θ2
t
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•  Whitted [1980]
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Cook[1984]
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Precomputed Radiance Transfer
•  Sloan[2002]
•  Microsoft
•  Direct X9.0c
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→2011
Disney
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DirectX
PRT
PRT
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DirectX
PRT
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PRT
Precomputed Local Radiance Transfer for Real-Time Lighting Design
Kristensen[2005]
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PRT
Local, Deformable Precomputed Radiance Transfer
Sloan [2005]
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All-Frequency Shadows Using Non-linear Wavelet Lighting Approximation
Ng[2003]
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Instant Radiosity
光源の配置
光源から光を放射して
各点の陰影付け
各点を点光源にして
陰影計算
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SiliconStudio YEBIS
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• 
•  https://github.com/tokoik/ggsample12
•  mirror.vert
simple.vert
• 
main.cpp
mirror.vert
n = (0, 1, 0)
p = (0, 0, 0)
• 
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mirror.vert
•  main.cpp
• 
mirror.vert
[email protected]
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