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
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Anisotropic Reflection
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Quarterhorse
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Reflection from a Cylinder
ˆ
T
ˆ
L
ˆ)
R Nˆ ( L
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Anisotropic Reflection
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Shape of Anisotropic Highlights
Fibers tangent to the plane defined by the halfway
vector reflect light
From Lu, Koenderink, Kappers
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Shape of Anisotropic Highlights
From Lu, Koenderink, Kappers
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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 )
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Herbert the Teddy Bear
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Hair Fibers
Measurements for cosmetics industry
￭
[Stamm 1977; Bustard & Smith 1994]
Structure of hair fiber
[Robbins ’94]
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Fiber Model
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Fiber Model
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Fiber Model
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Caustics
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Hair Appearance
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Hair Appearance
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Sasquatch: Hair Modeling System
www.worley.com
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Stuart Aitken
Pat Hanrahan, Spring 2015
Subsurface Reflection
Traditional Reflection Models: BRDF
BRDF:
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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 )
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Translucent Materials: Jade
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Translucent Materials: Marble
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Translucent Materials: Skin
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Translucent Materials: Leaves
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Subsurface Scattering
Skin
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Single Scattering
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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
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Multiple Scattering
BSSRDF:
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Highly Scattering Media
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Highly Scattering Media
Random Walk
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Diffusion Approximation
φ (r ) = Φ
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e
− kr
r
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Dipole Diffusion Approximation
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!
N • (∇φ1 (r ) − ∇φ2 (r ))
Rd (r ) = −
Φi
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Evaluating the BSSRDF
Diffusion approximation
Lr ( xo , ωo ) = ∫ ∫ S ( xi , ωi ; xo , ωo ) Li ( xi , ωi ) cos θi d ωi dA
AΩ
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Marble: BDRF versus BSSDRF
BRDF
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BSSRDF
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Marble: MCRT vs BSSRDF
MCRT
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BSSRDF
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Skim Milk
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Whole Milk
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Diffuse Milk
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A Face (BSSRDF Model)
Modeled by Stephen Stahlberg
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A Face (BRDF Approximation)
Modeled by Stephen Stahlberg
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Wrap-Up
The Goals of Rendering
Goals
￭ Accurate physical simulation (perfect duplicate)
￭ Artistic or expressive (tell a story)
￭ Informative or useful (visualize some data)
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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