Lesson 11 – Physically-based rendering
Image-based lighting
PV227 – GPU Rendering
Jiˇrí Chmelík, Jan ˇCejka
Fakulta informatiky Masarykovy univerzity
26. 11. 2019
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Physically-based rendering (PBR)
Physically-based rendering: Theory (cont.)
Light & Lights
BRDF
Sensors (cameras, eyes)
Image-based lighting
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Light – quantities and units
Quantities and units
Radiant energy
Radiant flux
Irradiance
Intensity
Radiance
Different equations use different quantities
Convertible between each other
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Light – quantities and units (cont.)
Radiant energy (Q)
“Energy of one photon”
Joule: J
Radiant flux, radiant power (Φ)
“Energy per second”
dQ/dt
Watt: W = J/s
Great to describe the power of lights like light bulb, area lights, . . .
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Light – quantities and units (cont.)
Irradiance (E)
“Flux through area”
dΦ/dA
Watt per square meter: W/m2
Drops with the square of the distance
Great to describe the power of strong distant lights like the sun
Intensity (I)
“Flux through a cone of directions”
dΦ/dω
Watt per steradian: W/sr
Does not drop with the distance
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Light – quantities and units (cont.)
Radiance (L)
“Flux through a cone of directions from an area” or “Flux through an
area from a cone of directions”
d2
Φ/dAproj dω
Watt per square meter: W/m2
sr
This is what sensors measure
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BRDF
Bidirectional Reflectance Distribution Function
Describes the relation between the incoming and outcoming light
f(l, v) =
dLo(v)
dE(l)
Surface is illuminated from direction l with irradiance dE(l)
It is reflected in various directions
dLo(v) is the outcoming radiance in direction v
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Properties of BRDF
For non-area lights:
f(l, v) =
Lo(v)
EL cos(θi)
Energy conservation (for each incoming direction l :
Ω
f(l, v) cos θodωo < 1
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BRDF – Examples
BRDF of diffuse light:
f(l, v) =
Cdiff
π
Note: this is what we use in shaders:
dif = max(0.0, dot(N, L)) * Cdiff;
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BRDF – Examples
BRDF in the Cook-Torrance paper
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BRDF – Examples
BRDF in TriAce (presented at SIGGRAPH 2010 course)
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BRDF – Examples
BRDF in Frostbite (presented at SIGGRAPH 2014 course)
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Sensors
Many small sensors, each measure irradiance (flux through an
area) over time
System of lences and aperatures, which define the cone
Lences in camera or eye, aperature of a camera, pupil in an eye
So instead of irradiance, the system measures radiance
Remember Depth-of-field techniques
The result is the energy
Conversion to the output signal (logarithmic etc.)
Linear color space (RGB) vs. non-linear spaces (sRGB)
Remember HDR, gamma correction
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Image-based lighting
Image-based lighting
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Image-based lighting
Use the light from a texture
Environment textures, light probes
Usually HDR cubemap textures
Evaluate the integral using the BRDF to obtain the final color
Sampling the directions
Uniform sampling
Non-uniform importance sampling
Precomputation
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Task: Implement image-based lighting
Based on Real Shading in Unreal Engine 4 (presented at
SIGGRAPH 2013 Course)
With some changes, we use:
Uniform sampling for diffuse light
Importance sampling for specular light
Cook-Torrance based material
Fresnel as at the previous lecture
Geometry attenuation as at the previous lecture
Microfacet distribution is not important (according to the paper)
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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)
For better result, clamp them to be non-zero, e.g. not less than
0.001, to avoid divisions by zero
All vectors are normalized
Fresnel(V · H) = F0 + (1 − F0)(1 − V · H)5
Geom. atten. G = min(1, 2·(N·H)·(N·V)
(V·H)
, 2·(N·H)·(N·L)
(V·H)
)
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Uniform sampling for diffuse lighting
Output: Random direction r on a hemisphere (in the direction of z)
Input: Two random numbers R.x and R.y, uniformly distributed in
(0, 1)
begin
φ ← 2π · R.x
cos(θ) ← R.y
sin(θ) ← 1 − cos2(θ)
r.x ← sin(θ) cos(φ)
r.y ← sin(θ) sin(φ)
r.z ← cos(θ)
return r
end
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Computation of diffuse lighting
Output: Diffuse color color
begin
color ← (0, 0, 0)
forall diffuse samples i do
R.x, R.y ← i-th pair of random numbers
r ← random direction from R.x, R.y
L ← r.x · T + r.y · B + r.z · N
light ← SampleCubeTexture(L)/#samples
color ← color + Cdiff · (N · L) · light
end
return color
end
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Non-uniform importance sampling for specular lighting
Output: Random direction r on a hemisphere (in the direction of z)
Input: Two random numbers R.x and R.y, uniformly distributed in
(0, 1), roughtness m
begin
φ ← 2π · R.x
cos(θ) ← 1−R.y
1+(m2−1)R.y
sin(θ) ← 1 − cos2(θ)
r.x ← sin(θ) cos(φ)
r.y ← sin(θ) sin(φ)
r.z ← cos(θ)
return r
end
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Computation of specular lighting
Output: Specular color color
begin
color ← (0, 0, 0)
forall specular samples i do
R.x, R.y ← another i-th pair of random numbers
r ← random direction from R.x, R.y
H ← r.x · T + r.y · B + r.z · N
L ← reflect(−V, H)
light ← SampleCubeTexture(L)/#samples
F ← Fresnel(. . .)
G ← GeometricAttenuation(. . .)
color ← color + F · G · (V · H)/((N · H) · (N · V)) · light
end
return color
end
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Task: Test scene
Test scene
Materials: red/green/blue plastics, iron, copper, gold, alluminium,
silver
Roughness: 0.0, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5
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Task: IBL with diffuse lighting
Task 1: Implement diffuse lighting
Fragment shader object_fragment.glsl
Try higher number of samples
Try sampling higher mipmap-levels of cube map texture
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Task: IBL with diffuse lighting
Result, metals have zero diffuse light
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Task: IBL with specular lighting
Task 2: Implement specular lighting
Try higher number of samples
Try sampling higher mipmap-levels of cube map texture
Try using a mask texture to change the roughness
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Task: IBL with specular lighting
Result, with masked roughness
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Task: Layered material
Task 3: Create a thin shiny layer
The layer is completely transparent (except for the perfect
reflection)
Set its base Fresnel reflectance to 0.04 (it is a dielectric material)
Try using a mask texture to create parts of semitransparent white
areas.
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Task: Layered material
Result, with masked semitransparent areas
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Things we used
Depth-prepass
Some graphic cards reorder evaluation of fragment shaders and
evaluation of the depth test (when safe)
Depth test is first, skipping FS when the fragment is hidden
Sometimes, it is benefical to render the whole scene very simply
into depth buffer first, and then into the color buffer
Each fragment is evaluated only once
Rendering the objects from the closest also helps
Early depth tests
Fragment shader: layout (early_fragment_tests) in;
Forces the above behaviour
Stencil test is also performed before running the fragment shader
Do not use this when you change the fragment depth or when you
discard the fragment
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