All-Frequency Rendering with Dynamic, Spatially-Varying ...
Transcript of All-Frequency Rendering with Dynamic, Spatially-Varying ...
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All-Frequency Rendering with Dynamic, Spatially-Varying
Reflectance
CHOI WON YOUNG PARK HWANG PIL
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Complex, detailed reflectance
• Spatial/temporal variation
• All BRDF types: – parametric ↔ measured
– isotropic ↔ anisotropic
– glossy ↔ mirror-like
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Previous work
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Rendering Equation
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Precomputed Radiance Transfer
• A way to shade objects under different illumination
– Any kind of light transport is possible
– Real-time, allowing lighting to change
• Objects have to be static
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Rendering Equation
SVBRDF light visibility cosine
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Outline
• Reflectance Representation
– Microfacet Model with SGs
• Visibility Representation
– Signed Spherical Distance Function
• Lighting & Rendering
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Outline
• Reflectance Representation
– Microfacet Model with SGs
• Visibility Representation
– Signed Spherical Distance Function
• Lighting & Rendering
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– trivial rotation
– all-frequency signals
intensity sharpness
center
Spherical Gaussian (SG)
inner product:
vector product:
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SG Mixtures
Sum of Multiple SGs:
Original SG, N = 7 SG, N = 3 SG, N = 1
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Microfacet BRDF Model
• surface modeled by tiny mirror facets
Normal distribution function
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Microfacet BRDF Model
• surface modeled by tiny mirror facets
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• single-lobe, analytic approximation
–Cook-Torrance [Cook et al. 1981]
Parametric Models
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• single-lobe, analytic approximation
–Ward [Ward 1992]
Parametric Models
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• single-lobe, analytic approximation
–Blinn-Phong [Blinn 1977]
Parametric Models
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Parametric BRDFs
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7-l
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Anisotropic Parametric Models
• multi-lobe, analytic approximation
– Ashikhmin-Shirley anisotropic model
[Ashikhmin and Shirley 2000]
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nu=8, nv=128 nu=25, nv=400 nu=75, nv=1200
7-l
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M
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d t
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Anisotropic Parametric Models
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Measured BRDFs
• Isotropic BRDF
– Using Levenberg-Marquardt optimization
[Nocedal and Wright 1999]
• anisotropic BRDF
– Using L-BFGS-B solver [Zhu et al. 1997]
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Measured BRDFs
BRDF from [Matusik03] svBRDF from [Wang08] & [Lawance06]
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Representation Efficiency
- Parametric BRDF Texturing of original BRDF parameters isotropic : 7 float/texel: diffuse, specular, shininess Anisotropic: 8 float/texel: diffuse, specular, shininess u/v
- Measured BRDF Texturing of SGs
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Rendering Equation
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Normal Distribution in Half-vector Domain
BRDF Slice in light-vector
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BRDF Slices
Half-vector Domain
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SG Warping
- SG not closed under -1
- approx. by per-SG warp of D*
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SG Scaling
• Shadowing and Fresnel terms
– Assume low-frequency [Ashkmin01, Ngan05]
– approx. by per-SG scale
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Parametric svBRDF Painting
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Outline
• Reflectance Representation
– Microfacet Model with SGs
• Visibility Representation
– Signed Spherical Distance Function
• Lighting & Rendering
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Visibility Representation
• Instead of binary visibility function, using Spherical Signed Distance Function
• Stores signed angular distance
• Why?
– Ghost-free!
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Binary Visibility Function
scene binary visibility function
x V(x,i)
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Spherical Signed Distance Function
binary visibility, V(i)
i0
i1
SSDF, Vd (i)
Vd(i1)
Vd(i0)
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Ghosting artifact in Interpolation
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Ghosting-Free Interpolation
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Procedure
Sampling
Visibility
Per-vertex
Construct
SSDF and
Compression
Reconstruct
Visibility
per-pixel
Pre-compute Run-time
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Detailed Procedure
1. Sample binary visibility the hemisphere
2. Calculate SSDF
3. Re-parameterize to a square image
4. Compress using PCA
PCA:
Eigenvector (stored in texture)
PCA coefficients (vertex attributes)
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Detailed Procedure(Cont’d)
• Reconstruct
– Calculate inner, vector product with SG
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Detailed Procedure(Cont’d)
• Reconstruct
– Calculate inner, vector product with SG
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Detailed Procedure(Cont’d)
• inner product
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Detailed Procedure(Cont’d)
• Vector Product
– Is a SG
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SSDF-SG Product
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SSDF-SG product with Compression
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Outline
• Reflectance Representation
– Microfacet Model with SGs
• Visibility Representation
– Signed Spherical Distance Function
• Lighting & Rendering
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Lighting
• Local light Source
– Represented by a single SG
• Environment Light
– SGs for diffuse shading
– MIPMAP for specular shading
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Local Light Source
• Point light
• Directional light
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Environment Light
prefiltered MIPMAP [Kautz et al. 2000]
SGs (<10 lobes) [Tsai and Shih 2006]
for diffuse shading for specular shading
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Run-time Rendering
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Run-time Rendering
• Environment light
BRDF Slice in SGs
Cosine Term in SGs
Visibility in SSDF
Prefiltered Environment
●
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Run-time Rendering
• Local point light
Visibility in SSDF
●
BRDF Slice in SGs
Cosine Term in SGs
Point light in SGs
SG, N = 1
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Result
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Result
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Conclusion - Pros
• SG mixtures for microfacet-based reflectance
– Highly specular
– Speed up rendering
• Compressed SSDFs
– Ghost-free
– Per-pixel interpolation
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Conclusion - Cons
• Pre-computed visibility – Limited static scenes
– Maybe solve this problem by combining other methods.
• Consider only direct shadowing effects
• Many SG lobes are required for anisotropic BRDFs.
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Thank you!