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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
ECE 595 / CS 491 / CS 591
Real-Time Rendering &
Graphics Hardware
Pradeep Sen Advanced Graphics Lab
Class 18April 2, 2007
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Pop-quiz 1.
What is “radiance”? Define & give the units.
Suppose you integrate the incident radianceover the hemisphere. What do you get?Name and give the units.
What if you integrate the unit from #2 overthe area of the surface? What do you get?Name and give the units.
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Announcements ^
GFX Café this Friday will be given by MikeBispeck on the professional gamedevelopment process
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Last time ^
Spherical harmonics, irradiance maps
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Today ^
Pre-computed radiance transfer
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Problem ^
The irradiance maps we talked about lastweek ^
They only work for convex objects ^
Many objects are concave
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Need to account for visibility
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Example
unshadowed irradiance
irradiance accounting for
self-shadowingimages Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
PRT introduced by Sloan et al. ^
Sloan et al. “Precomputed RadianceTransfer for Real-time rendering in Dynamic,Low-frequency Lighting Environments”SIGGRAPH 2002
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
slide courtesy Peter-Pike Sloan
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Basic Idea
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Glossy Rendering
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slide courtesy Peter-Pike Sloan
Lookup Lookupat Rat R
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Glossy Rendering
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slide courtesy Peter-Pike Sloan
Lookup Lookupat Rat R
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Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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Glossy Rendering
slide courtesy Peter-Pike Sloan
Lookup Lookupat Rat R
Freeze the Light
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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Glossy Rendering
slide courtesy Peter-Pike Sloan
LookupLookupat Rat R
Freeze the Light
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Glossy Transfer Results No Shadows/Inter
Shadows
No Shadows/Inter
Shadows
Shadows+InterShadows+Inter
-^
Glossy object, 50K mesh
-^
Runs at 3.6/16/125fps on
2.2Ghz P4, ATI Radeon 8500
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Interreflections and Caustics
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interreflectionsinterreflections
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Transport PathsTransport Paths
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Runtime is independentRuntime is independentof transport complexityof transport complexity
Interreflections and Caustics
nonenone
1 bounce1 bounce
2 bounces2 bounces
causticscaustics
interreflectionsinterreflections
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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Arbitrary BRDFs [Kautz02]
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BRDF CoefficientsBRDF Coefficients
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
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slide courtesy Peter-Pike Sloan
==
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Arbitrary BRDF Results
Other BRDFs
Spatially Varying
Anisotropic BRDFs
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Neighborhood Transfer^ ^
Allows to cast shadows/caustics onto arbitrary receivers ^ Store how object scatters/blocks light around itself(transfer matrices on grid)
transfer matricestransfer matrices
transferred radiancetransferred radiance
receiverreceiver
lightinglighting
receiverreceiver
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Neighborhood Transfer Results ^ 64x64x8 neighborhood ^ diffuse receiver ^ timings on 2.2Ghz P4,
ATI Radeon 8500 ^
4fps if light changes ^
120fps for constant light
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Volumes ^
Diffuse volume: 32x32x32 grid ^
Runs at 40fps on 2.2Ghz P4, ATI 8500 ^
Here: dynamic lighting
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Local Lighting using Radiance Sampling Sample incident radiance at
multiple
points
^
Choose sample points over object using ICP from VQ ^
single samplesingle sampleCorrect for shadows but not interreflections (at center = light at(at center = light at
∞∞ ))
multimulti-
-samplesampleresultresult
multimulti-
-samplesample locationslocations
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Light Size vs. SH Order 0 0°° 20 20°° 40 40°°
n=2n=2linearlinear
n=3n=3quadraticquadratic
n=4n=4cubiccubic
n=5n=5quarticquartic
n=6n=6quinticquintic
n=26n=
n=26n=26windowedwindowed
RTRT
slide courtesy Peter-Pike Sloan
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
PRT ^
Now shipping in DirectX!
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Light-Transport Matrix Rows
11
12
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2
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1
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slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Light-Transport Matrix Rows
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slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Light-Transport Matrix Rows
11
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slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Rasterizing Matrix Rows
Pre-computing rows: ^ Rasterize visibilityhemicubes with graphicshardware ^ Read back pixels andweight by reflectionfunction
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Matrix Multiplication is Enormous ^
Dimension– 512 x 512 pixel images– 6 x 64 x 64 cubemap environments ^
Full matrix-vector multiplication is intractable– On the order of 10
10
operations
per frame
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Sparse Matrix-Vector Multiplication
Choose data representations with mostly zeroesVector: Use
non-linear wavelet approximation on lighting
Matrix:
Wavelet-encode transport rows^11
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slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Non-linear Wavelet Light Approximation
^
WaveletTransform
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Non-linear Wavelet Light Approximation
^
WaveletTransform
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Non-linear Wavelet Light Approximation
^
WaveletTransform
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Non-linear Wavelet Light Approximation
^
WaveletTransform
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Non-linear Wavelet Light Approximation
^
WaveletTransform
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
L^1 L^2 L^3 L^4 L^5 L^6 L^ N
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Non-linear Wavelet Light Approximation
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
L^1 L^2 L^3 L^4 L^5 L^6 L^ N
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Non-linear Wavelet Light Approximation
Non-linearApproximation
Retain 0.1% – 1% terms
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Why Non-linear Approximation? ^
Linear– Use a fixed set of approximating functions– Precomputed radiance transfer uses 25 - 100 of
the lowest frequency spherical harmonics ^
Non-linear– Use a dynamic set of approximating functions
( depends on each frame’s lighting
)
- In our case: choose 10’s - 100’s from a basis of 24,576 wavelets ^
Idea: Compress lighting by considering input data
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Why Wavelets?
^
Wavelets provide dual space / frequencylocality– Large wavelets capture low frequency,
area lighting
- Small wavelets capture high frequency, compact features ^
In contrast– Spherical harmonics
- Perform poorly on compact lights
- Pixel basis
- Perform poorly on large area lights
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Error in Lighting: St Peter’s Basilica
Approximation Terms
Error (%) 2 L Relative
Sph. Harmonics Non-linear Wavelets
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Error in Output Image: Plant Scene
Approximation Terms
Error (%) 2 L Relative
Sph. Harmonics Non-linear Wavelets
slide courtesy Ren Ng
Real-time Rendering & Graphics Hardware Pradeep Sen
Class 17 – March 28, 2007
Output Image Comparison^ Top:
Linear Spherical Harmonic Approximation
Bottom:
Non-linear Wavelet Approximation
25
slide courtesy Ren Ng
