Transcript Practical logarithmic rasterization for low error shadow maps

Logarithmic perspective
shadow maps
Brandon Lloyd1,2
Naga Govindaraju2
Cory Quammen1
Steve Molnar3
Dinesh Manocha1
1University
of North Carolina
– Chapel Hill
2Microsoft
3NVIDIA
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Goal
Low error shadows for
real-time applications
Emphasis on performance
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Standard Shadow Map
aliasing
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undersampled
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Perspective Warping
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Logarithmic Perspective
Warping
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Outline
Related work
Logarithmic perspective warping
Error analysis
Experimental results
Conclusion
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Single shadow map warping
Perspective shadow maps
(PSMs)
[Stamminger and Drettakis 2002]
Light-space perspective
shadow maps (LiSPSMs)
[Wimmer et al. 2004]
Trapezoidal shadow maps
[Martin and Tan 2004]
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Single shadow map warping
Warping cannot be used
for all light directions
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Face partitioning
Perspective warped
cube maps
[Kozlov 2004]
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z-partitioning
Cascaded shadow maps
[Engel 2007]
Parallel split shadow
maps [Zhang et al. 2006]
Separating-plane
shadow maps
z
[Mikkelsen 2007]
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z-partitioning
Cascaded shadow maps
[Engel 2007]
Parallel split shadow
maps [Zhang et al. 2006]
Separating-plane
shadow maps
z
[Mikkelsen 2007]
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Adaptive partitioning
Adaptive shadow maps
[Fernando et al. 2001]
Queried virtual shadow maps
[Geigl and Wimmer 2007]
Fitted virtual shadow maps
[Geigl and Wimmer 2007]
Resolution matched shadow maps
[Lefohn et al. 2007]
Tiled shadow maps
[Arvo 2004]
Multiple shadow frusta
[Forsyth 2006]
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Irregular z-buffer
[Aila and Laine 2004;
Johnson et al. 2004]
GPU implementations
[Arvo 2006; Sintorn et al. 2008]
Hardware architecture
[Johnson et al. 2005]
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Methods for better sampling
Scene-independent
Single SM warping + Lower, nearly constant cost
Face partitioning
– Higher error
z-partitioning
Scene-dependent
Adaptive
Irregular
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+ Lower error
– Higher, variable cost
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Filtering
Percentage closer filtering
[Reeves et al. 1987]
Variance shadow maps
[Donnely and Lauritzen 2006;
Lauritzen and McCool 2008]
Convolution shadow maps
[Annen et al. 2007]
Exponential shadow maps
[Salvi 2008; Annen et al. 2008]
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Standard Shadow Map
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Standard Shadow Map
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Perspective Warping
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Logarithmic Perspective
Warping
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Logarithmic perspective
shadow maps (LogPSMs)
Replace perspective warping in
scene-independent
single shadow map
z-partitioning
face partitioning
Similar performance with less error
Similar error with less texture
resolution
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Outline
Related work
Logarithmic perspective warping
Error analysis
Experimental results
Conclusion
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Perspective warping
Not necessarily the best fit to required
sampling distribution
PSM
high error
moderate error
LiSPSM
y
x
low error
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moderate error
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y
x
Perspective
projection
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low error
high error
Logarithmic+perspective
warping
Logarithmic
transform
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Logarithmic rasterization
Brute-force rasterization
use a fragment program
Slower than standard
rasterization
disables optimizations
• z-culling
• double-speed z-only rendering
breaks linear depth compression schemes
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Logarithmic rasterization
Hardware rasterization
[Lloyd et al. 2007]
equivalent to rasterizing on non-uniform grid
requires incremental modifications
Software rasterization
Larrabee [Seiler et al. 2008]
Performance comparable to standard
rasterization
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Outline
Related work
Logarithmic perspective warping
Error analysis
Experimental results
Conclusion
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Error analysis
Need more analysis for previous
methods
little analysis for point lights
limited analysis for lights in general position
[Tadamura et al. 1999; Zhang et al. 2006]
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Combinations of algorithms
P
LogP
ZP
FP
single SM
Standard
P
LogP
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-
Perspective warping
Logarithmic perspective warping
z-partitioning
face partitioning
z-partitioning
ZP
ZP+P
ZP+LogP
face-partitioning
FP+P
FP+LogP
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Combinations of algorithms
P
LogP
ZP
FP
single SM
Standard
P for the
LogP
-
Perspective warping
Logarithmic perspective warping
z-partitioning
face partitioning
z-partitioning
ZP
ZP+P
fewest
shadow
ZP+LogP
face-partitioning
Which algorithm gives the least error
maps?FP+P
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FP+LogP
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Quantifying aliasing error
shadow map
light
light image
plane
eye
eye image
plane
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Quantifying aliasing error
shadow map
light
light image
plane
eye
eye image
plane
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Quantifying aliasing error
shadow map
light
light image
plane
Maximum error:
eye
eye image
plane
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over a light ray
over the frustum
over all light positions
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Near optimal, sceneindependent warping
Minimizes maximum error over a face
Too complicated for practical use
Used as a baseline
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Maximum error
over all light positions
Param.
End face
Side face - s
Side face - t
Side face combined
Uniform
Perspective
Log+Persp.
Near optimal
Logarithmic perspective warping is about the best
we can do for scene-independent algorithms
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Error distribution along a face
Uniform
LiSPSM
PSM
LogPSM
15
10
5
0
0near
0.5
v
Uniform
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20
eerror
p;t
in t
maxM
e
error
maxM
p;s in s
20
far1
LiSPSM
15
10
5
0
0near
PSM
0.5
v
far1
LogPSM
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Maximum error
for varying light directions
max error (log2 scale)
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Standard
Perspective
Log+perspective
20
15
direction
to light
10
5
0
20
37
40
60
80
view
direction
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Maximum error
for varying light directions
max error (log2 scale)
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Standard
Perspective
Log+perspective
FP+LogP
20
15
direction
to light
10
5
0
20
38
40
60
80
view
direction
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k= 1
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k= 2
25
20
20
15
15
10
10
10
5
5
5
0
0
0
20
40
60
80
20
error reduction
20
15
60
80
20
k= 7
25
15
15
15
error reduction
10
10
10
5
5
5
0
0
0
°
60
80
20
40
°
60
80
60
k = 16
25
20
error reduction
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ZPk
ZPk+P
ZPk+LogP
FPcs+LogP
FPc+LogP
°
20
40
error reduction
°
k= 5
20
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40
20
2
max error
(log2 scale)
log S
°
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k= 3
25
2
max error
(log2 scale)
log S
z-partitioning
80
error reduction
20
40
60
FP uses 1-7
partitions
(3.8 average)
80
°
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k= 1
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k= 2
25
k= 3
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
0
ZPk
ZPk+P
ZPk+LogP
FPcs+LogP
FPc+LogP
2
max error
(log2 scale)
log S
Least error for
fewest shadow maps?
20
40
60
80
20
60
80
20
°
k= 5
25
40
60
80
°
k= 7
25
40
k = 16
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
0
FP uses 1-7
partitions
(3.8 average)
2
max error
(log2 scale)
log S
°
20
40
°
40
60
80
20
40
°
60
80
20
40
60
80
°
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Outline
Related work
Logarithmic perspective warping
Error analysis
Experimental results
Conclusion
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Single shadow map LogPSM
LogPSMs have
lower maximum error
more uniform error
LiSPSM
LogPSM
LiSPSM
LogPSM
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Image resolution:
5122
Shadow map resolution:
10242
f/n = 300
Grid lines for every 10 shadow map
texels
Color coding for maximum texel extent
in image
<
1
1
10 7.75
1
3.25
1
3.25
7.75
>10
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Partitioning schemes
Standard
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FP+P
ZP5+P
FP+LogP
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Comparison video
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PSM = LiSPSM with PSM
parameter
Cascaded = ZP5
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LogPSM
= FP+LogP
Point lights
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Point lights
<
1
1
10 7.75
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1
3.25
1
3.25
7.75
>10
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Limitations of LogPSMs
Not currently supported in hardware
Share problems as other warping
algorithms:
do not handle aliasing error due to surface
orientation
face partitioning needed for most benefit
• not as simple as z-partitioning
• can exhibit shearing artifacts
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Conclusion
LogPSMs
Single shadow map
z-partitioning
face partitioning
Error analysis
LogPSMs are close to optimal for sceneindependent algorithms
LogPSMs achieve low error with few shadow
maps
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Future work
Other error metrics [Zhang et al. 2007]
Combine with scene-dependent
algorithms
LiSPSM + adaptive [Giegl and Wimmer 2007]
LiSPSM + irregular [Sintorn et al. 2008]
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Acknowledgements
Aaron Lefohn and Taylor Holliday for town model
Ben Cloward for robot model
David Feng and Nico Galoppo
Funding agencies
NVIDIA University Fellowship
NSF Graduate Fellowship
ARO, NSF, DARPA/RDECOM, Disruptive Technology Office
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Questions
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Face partitioning
Low error over all light positions
Omnidirectional lights
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z-partitioning
In effect reduces f/n
f
n
0
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z-partitioning
In effect reduces f/n
Costly for omnidirectional lights
f
n
0
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Future work
Incorporate rough scene information
use a ‘pseudo-near plane’ [Lloyd 2007]
higher
error
low error
pseudo-near
plane
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Scene-independent
maximum error
Standard
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FP+P
ZP5+P
FP+LogP
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Handling shear
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Handling shear
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