Lesson 10 – Physically-based rendering
PV227 – GPU Rendering
Jiˇrí Chmelík, Jan ˇCejka
Fakulta informatiky Masarykovy univerzity
21. 11. 2016
PV227 – GPU Rendering (FI MUNI) Lesson 10 – PBR 21. 11. 2016 1 / 34
Physically-based rendering (PBR)
Think about the physics behind everything:
Light
Lights
Materials
Sensors / Eyes
In practice, still approximations
More and more popular in real-time rendering, in rendering
engines
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Light propagation – Homogeneous media
Light interacts with the material it travels through
In homogeneous materials, the light is absorbed
Loses some of its energy
Clean water, glass, air, oil, . . .
Low Absorbtion High Absorbtion
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Light propagation – Heterogeneous media
Light interacts with the material it travels through
In heterogeneous materials, the light is scattered
Scatters the energy without losses
Milk, skin, wood, (dirty water, air with fog), . . .
Low Scattering High Scattering
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Light propagation – Absorbtion vs. Scattering
Absorbtion vs. Scattering
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Light interaction – Materials
Light changes its direction at the boundary between two materials
Reflection
Refraction
Without losses of energy
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Reflection
Perfect reflection: θi = θo
Amount of reflected light depends on θi and on the wavelength
Described by Fresnel equations
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Fresnel reflection
Depends on the wavelength, reflection has a color (!)
Metals have usually higher values
Dielectrics have usually lower values
Mostly without any change until 50◦, then goes straight to one
In practice: Schlick’s approximation:
FSchlick (F0, L, N) = F0 + (1 − F0)(1 − L · N)5
where F0 is Fresnel reflection at 0◦, L is direction to light, N is
surface normal
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Fresnel reflection at 0◦
Fresnel reflections at 0◦ for some materials
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Refraction
Snell’s law
sin θi
sin θt
=
v1
v2
In metals, all energy is absorbed
In homogeneous materials, the light continues in different direction
In heterogeneous materials (including skin, wood, plastic, . . . ), the
light is scattered and absorbed
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Refraction – diffuse light
Diffuse lighting
When all the (non-absorbed) light exits the surface at approximately
the same point as the light enters.
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Refraction – sub-surface scattering
Sub-surface scattering (SSS)
When all the (non-absorbed) light exits the surface at different
places.
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Ambient lighting?
“Does not exist in PBR”
Average of lighting coming from all directions.
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Microfacets
Only some objects are flat (mirrors, water surface, . . . ), others are
not
With microfacets, the surface is represented with very small facets
Smaller then ‘pixel’, not for displacement in geometry, not for
normal mapping
(Larger than light’s wavelength)
Each mifrofacet is a flat surface
Many microfacets models, for different materials
Different distribution of orientation of facets
Different shadowing between facets
Different approximation of the model
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Microfacets
Top: smooth surface, Bottom: rough surface
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Distribution of microfacets
We are usually interested in facets which are oriented in the
proper direction to give us perfect reflection.
i.e. facets that are oriented in the half-vector direction
Gaussian distribution, . . .
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Geometrical attenuation
Shadowing: Facets occlude the light for other facets
Masking: Facets cannot be seen due to other facets
Interreflection: Facets reflect the light to other facets, and then the
light is reflected to the viewer
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Task: Implement microfacets models
Cook-Torrance (1982)
Oren-Nayar (1994)
Ashikhmin-Shirley (2000)
Normalized Blinn-Phong (2008)
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Legend to the following equations
N, T, B are surface normal, tangent, and bitangent
L is direction to the light, V is direction to the viewer
H is half-vector, vector between the light and the viewer
All dot products are non-negative, e.g.: max(0, N · L)
All vectors are normalized
All results must be multiplied by light’s intensity and color
Fresnel(V · H) = F0 + (1 − F0)(1 − V · H)5
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Cook-Torrance
Useful for most surfaces, metals,
All microfacets are perfect mirrors
Single parameter m (roughness), usually in range (0, 1)
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Cook-Torrance cont.
Diffuse:
Idiff = Colordiff · (N · L)
Specular:
Ispe =
F · G · D
4 · (N · V)
where
Fresnel F = Fresnel(V · H)
Geom. atten. G = min(1, 2·(N·H)·(N·V)
(V·H)
, 2·(N·H)·(N·L)
(V·H)
)
Beckmann distribution D = e
(N·H)2−1
m2·(N·H)2
m2·(N·H)4
(m is roughness of the material)
Diffuse is energy-conserving, specular is energy-conserving, but
not together
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Oren-Nayar
For non-shiny objects like concrete, flowerpots, bricks, Moon
All microfacets are Lambertian (diffuse) surfaces
No specular highlights
Retroreflections at boundaries
Single parameter m (roughness)
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Oren-Nayar cont.
Diffuse:
Idiff = Colordiff · (N · L) · (A + B · max(0, cos(φ)) · C)
where
θi = arccos(N · L)
θo = arccos(N · V)
α = max(θi , θo)
β = min(θi , θo)
cos(φ) = norm V − N · (V · N) · norm L − N · (L · N)
A = 1.0 − 0.5 · m2
m2+0.57
B = 0.45 · m2
m2+0.09
C = sin(α) · tan(β)
Diffuse is energy-conserving
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Ashikhmin-Shirley
For brushed objects (metal) with anisotropic reflections
All microfacets are perfect mirrors
Two parameters shinT , shinB: shininess exponents in tangent and
bitangent directions, usually greater than 1
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Ashikhmin-Shirley cont.
Diffuse (not energy-conserving with specular):
Idiff = Colordiff · (N · L)
or diffuse (energy-conserving with specular):
Idiff =Colordiff · (N · L) ·
·
28
23
(1 − F0)

1 − 1 −
(N · L)
2
5



1 − 1 −
(N · V)
2
5


where
F0 is Fresnel reflection at 0◦
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Ashikhmin-Shirley cont.
Specular:
Ispe =Fresnel(V · H) · (N · L) ·
·
(shinT + 1)(shinB + 1)
8
·
(N · H)
shinT ·(T·H)2+shinT ·(B·H)2
1−(N·H)2
(V · H) · max((N · L), (N · V))
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Normalized Blinn-Phong
Improvement of the original Blinn-Phong (1977)
Specular is energy conserving, without creating or losing energy
Diffuse is the same
Idiff = Colordiff · (N · L)
Original specular
Ispe = (N · L) · Colorspe · (N · H)shin
Normalized specular
Ispe = (N · L) · Colorspe ·
shin + 8
8
(N · H)shin
where shin is shininess exponent
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Normalized Blinn-Phong cont.
Original Blinn-Phong, Colorspe = 120/255
shin = 25 shin = 50 shin = 75 shin = 100
Normalized Blinn-Phong, Colorspe = 32/255
shin = 25 shin = 50 shin = 75 shin = 100
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Task: Implement microfacets models
Task 1: Implement Normalized Blinn-Phong
Fragment shader BlinnPhongNormalized_fragment.glsl
Parameters in variables:
Colordiff in material_diffuse
Colorspe in material_specular
shin in material_shininess
Compare with the original Blinn-Phong
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Task: Implement microfacets models
Task 2: Implement Cook-Torrance
Fragment shader CookTorrance_fragment.glsl
Parameters in variables:
Colordiff in material_diffuse
F0 in material_fresnel
m in material_roughness
Notice the highlight when looking from near surface angles
Comparative with Blinn-Phong. To get approx. the same result:
Set Specular color and Fresnel color to the same value
Set roughness = 2
2+shininess
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Task: Implement microfacets models
Task 3: Implement Oren-Nayar
Fragment shader OrenNayar_fragment.glsl
Parameters in variables:
Colordiff in material_diffuse
m in material_roughness
Set roughness to 0.5 and compare with Blinn-Phong with black
specular
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Task: Implement microfacets models
Task 4: Implement Ashikhmin-Shirley
Fragment shader AshikhminShirley_fragment.glsl
Parameters in variables:
Colordiff in material_diffuse
F0 in material_fresnel
shinT in material_shininess_tangent
shinB in material_shininess_bitangent
Test on cylinder or teapot, set different shininess in tangent and
bitangent directions (e.g. 20 and 500)
When using simple computation for diffuse color, and setting
shininess to the same values, the result should be compatible with
Blinn-Phong.
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Further reading
SIGGRAPH cources on PBR:
http://renderwonk.com/publications/
s2010-shading-course/
http://blog.selfshadow.com/publications/
s2012-shading-course/
http://blog.selfshadow.com/publications/
s2013-shading-course/
http://blog.selfshadow.com/publications/
s2014-shading-course/
http://blog.selfshadow.com/publications/
s2015-shading-course/
http://blog.selfshadow.com/publications/
s2016-shading-course/
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Further reading
Cook, R., Torrance, K.: A Reflectance Model for Computer
Graphics
Oren, M., Nayar, S.: Generalization of Lambert’s Reflectance
Model
Ashikhmin, M., Shirley, P.: An Anisotropic Phong BRDF Model
Akenine-Möller, T., et al.: Real-Time Rendering
Pharr, M., et al.: Physically Based Rendering, From Theory to
Practice
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