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Reflection Models III
Previous lectures
￭ Ideal materials: mirrors, glass, matte
￭ Glossy materials
Today
￭ Anisotropic materials
￭ Translucent materials; subsurface reflection
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Anisotropic Reflection Models
VANGUARD
Bruce Beasley
Stainless Steel, 1980
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Anisotropic Reflection
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Quarterhorse
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Reflection from a Cylinder
ˆ
T
ˆ
L
ˆ)
R Nˆ ( L
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Anisotropic Reflection
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Shape of Anisotropic Highlights
Fibers tangent to the plane defined by the halfway
vector reflect light
From Lu, Koenderink, Kappers
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Shape of Anisotropic Highlights
From Lu, Koenderink, Kappers
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Kajiya-Kay Model
ˆ
T
ˆ
L
Diffuse
(
ˆ
sin θ L = 1 − Tˆ • L
2
)
ˆ)
R Nˆ ( L
Specular
s
ˆ
E
s
cos (θ E − θ L ) = (cos θ E cos θ L + sin θ E sin θ L )
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Herbert the Teddy Bear
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Hair Fibers
Measurements for cosmetics industry
￭
[Stamm 1977; Bustard & Smith 1994]
Structure of hair fiber
[Robbins ’94]
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Fiber Model
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Fiber Model
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Fiber Model
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Caustics
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Hair Appearance
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Hair Appearance
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Sasquatch: Hair Modeling System
www.worley.com
CS348b Lecture 16
Stuart Aitken
Pat Hanrahan, Spring 2015
Subsurface Reflection
Traditional Reflection Models: BRDF
BRDF:
CS348b Lecture 16
dLr ( x, ωo )
f r ( x, ωi , ωo ) ≡
dEi ( x, ωi )
Pat Hanrahan, Spring 2015
Subsurface Scattering: BSSRDF
dLr ( xo , ωo )
BSSRDF: S ( xi , ωi ; xo , ωo ) ≡
d Φ i ( xi , ωi )
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Translucent Materials: Jade
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Translucent Materials: Marble
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Translucent Materials: Skin
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Translucent Materials: Leaves
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Subsurface Scattering
Skin
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Single Scattering
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Semi-Infinite Homogenous Media
Reduced Intensity
L ( z, ω i ) = e
−τ ( z ,ωi )
L (0, ωi )
cosθ i
cosθ o
Effective source term
S( z, ω o ) = σ s p(ωi → ω o )e −τ ( z ,ωi ) L (0, ωi )
Volume rendering equation
∂L ( z, ω o )
cos θ o
= −σ t L ( z, ω o ) + S( z, ω o )
∂z
z = s cosθ
dz = ds cos θ
Integrating over depths
∞
cos θ o L (ω o ) = ∫ e −σ t z / cosθoσ s p(ωi , ω o )e −σ t z / cosθi L (ωi ) dz
0
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Semi-Infinite Homogenous Media
Integrating over depths
cosθ i
cosθ o
∞
cos θ o L (ω o ) = ∫ e −σ t z / cosθoσ s p(ωi , ω o )e −σ t z / cosθi L (ωi ) dz
0
∞
= σ s p(ωi , ω o ) L (ωi ) ∫ e
& 1
1 '
−σ t (
+
)z
cos
θ
cos
θ
i
o+
*
dz
0
= σ s p(ωi , ω o ) L (ωi )
1
& 1
1 '
σt (
+
)
cos
θ
cos
θ
i
o+
*
cos θ i cos θ o
= W p(ωi , ω o ) L (ωi )
cos θ i + cos θ o
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Seeliger’s Law
BRDF
cos θ i cos θ o
L (ωi , ω o )
dL
fr (ωi , ω o ) =
=
dE L (ωi ) cos θ i
1
= W p(ωi , ω o )
cos θ i + cos θ o
Seeliger’s Law or The Law of Diffuse Reflection
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Multiple Scattering
BSSRDF:
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Pat Hanrahan, Spring 2015
Highly Scattering Media
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Pat Hanrahan, Spring 2015
Highly Scattering Media
Random Walk
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Pat Hanrahan, Spring 2015
Diffusion Approximation
φ (r ) = Φ
CS348b Lecture 16
e
− kr
r
Pat Hanrahan, Spring 2015
Dipole Diffusion Approximation
CS348b Lecture 16
!
N • (∇φ1 (r ) − ∇φ2 (r ))
Rd (r ) = −
Φi
Pat Hanrahan, Spring 2015
Evaluating the BSSRDF
Diffusion approximation
Lr ( xo , ωo ) = ∫ ∫ S ( xi , ωi ; xo , ωo ) Li ( xi , ωi ) cos θi d ωi dA
AΩ
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Marble: BDRF versus BSSDRF
BRDF
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BSSRDF
Pat Hanrahan, Spring 2015
Marble: MCRT vs BSSRDF
MCRT
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BSSRDF
Pat Hanrahan, Spring 2015
Skim Milk
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Pat Hanrahan, Spring 2015
Whole Milk
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Pat Hanrahan, Spring 2015
Diffuse Milk
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Pat Hanrahan, Spring 2015
A Face (BSSRDF Model)
Modeled by Stephen Stahlberg
CS348b Lecture 16
Pat Hanrahan, Spring 2015
A Face (BRDF Approximation)
Modeled by Stephen Stahlberg
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Wrap-Up
The Goals of Rendering
Goals
￭ Accurate physical simulation (perfect duplicate)
￭ Artistic or expressive (tell a story)
￭ Informative or useful (visualize some data)
CS348b Lecture 16
Pat Hanrahan, Spring 2015
Measured
Simulated
Ralph Goings
Snap the Whip, Winslow Homer
Visualizing Anatomy
A photographic depiction captures
the exact appearance of the
object as we actually see it
Subtle, complex details of
coloration and texture are fully
represented, with great accuracy
Photograph of the right hip bone (lateral aspect).
Johannes W. Rohen and Chihiro Yokochi.
Color Atlas of Anatomy:
A Photographic Study of the Human Body,
Igaku-Shoin, 1993.
A drawing offers the possibility to
clarify structural or conceptual
information that may be difficult to
perceive in even a very good photo.
Color drawing of the same subject.
Sobotta Atlas of Human Anatomy,
11th English edition, vol. 2, edited
by Jochen Staubesand, translated
and edited by Anna N. Taylor,
Urban & Schwarzenberg, 1990.
Fun and Interdisciplinary
Understand
￭ Appreciate and notice how the world appears
￭ Simulation techniques
Interdisciplinary
￭ Physical simulation of light
￭ Perception and cognition
￭ Graphics design and art
CS348b Lecture 16
Pat Hanrahan, Spring 2015