jiaping wang 1 peiran ren 1,3 minmin gong 1 john snyder 2 baining guo 1,3 1 microsoft research asia...
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All-Frequency Rendering with Dynamic, Spatially-Varying Reflectance
Jiaping Wang1 Peiran Ren1,3 Minmin Gong1 John Snyder2 Baining Guo1,3
1 Microsoft Research Asia 2 Microsoft Research 3 Tsinghua University
Complex, detailed reflectance Spatial/temporal variation All BRDF types:
parametric ↔ measuredisotropic ↔ anisotropicglossy ↔ mirror-like
Previous work
TemporalVariation
SpatialVariation
static
singleBRDF
SVBRDF
dynamic
Previous work
[Wang04]
[Ng03][Wang04][Liu04][Wang06][Tsai06][Krivanek08]
TemporalVariation
SpatialVariation
static
singleBRDF
SVBRDF
dynamic
Previous work
[Wang04]
[Green06][Green07]
[Green06]
TemporalVariation
SpatialVariation
static
singleBRDF
SVBRDF
dynamic
Previous work
[Wang04]
[Ben-Artzi06][Sun07][Ben-Artzi08]
[Green06]
[Ben-Artzi06]
TemporalVariation
SpatialVariation
static
singleBRDF
SVBRDF
dynamic
Previous work
[Wang04]
[Green06]
[Ben-Artzi06]
Our method:
- per-pixel SVBRDF- dynamic SVBRDF- all BRDF types- all-frequency
[Wang09]
TemporalVariation
SpatialVariation
static
singleBRDF
SVBRDF
dynamic
Rendering Equation 2D lighting 4D visibility 6D reflectance (SVBRDF)
iinioiio d )max(0,),( ),,()(),( xVxLxR SVBRDFlight visibility cosine
o in
x
Precomputed Radiance Transfer
Dot product[Sloan et al. 2002]
iinoiiio d )max(0, ),,(),()(),( xxVLxR
light transferlight
Precomputed Radiance Transfer
Dot product[Sloan et al. 2002]
Triple product [Ng et al. 2004]
light transferlight
Light Transport & Precomputed
BRDF × cosinelight visibility
iinoiiio d )max(0, ),,(),()(),( xxVLxR
Precomputed Radiance Transfer
Dot product[Sloan et al. 2002]
Triple product [Ng et al. 2004]
Ours method
light transferlight
BRDF × cosinelight visibility
iinoiiio d )max(0, ),,(),()(),( xxVLxR
light BRDFvisibility cosine
LT & P LT & P
Precomputed Radiance Transfer
Dot product[Sloan et al. 2002]
Triple product [Ng et al. 2004]
Ours method
light transferlight
BRDF × cosinelight visibility
light BRDFvisibility cosine
LT & P LT & P LT & P
iinoiiio d )max(0, ),,(),()(),( xxVLxR
Algorithm Overview
Spherical Gaussians
o
Spherical Gaussians
Algorithm Overview
Spherical Gaussians SSDF
o
Environment
Dynamic, spatial varying BRDF
oOutline Reflectance Representation
Microfacet Model with SGs
Visibility Representation Signed Spherical Distance Function
Lighting & Rendering
oOutline Reflectance Representation
Microfacet Model with SGs
Visibility Representation Signed Spherical Distance Function
Lighting & Rendering
)1(),,;( pvpv eG
trivial rotationall-frequency signals
intensitysharpness
center
Spherical Gaussian (SG)
trivial rotationall-frequency signals
)1(),,;( pvpv eG
intensitysharpness
center
Spherical Gaussian (SG)
inner product: m
m
d
d
eGGGG
sinh4d)()(
21
212121
vvv
vector product:
)1(
212121m,;)()( pp
p
pvvv meGGGGG mm
m
m
SG Mixtures
Sum of Multiple SGs:
Original SG, N = 7 SG, N = 3 SG, N = 1
),,;()(1
*iii
N
i
GF pvv
Microfacet BRDF Model
[Cook 82]
surface modeled by tiny mirror facets
Microfacet BRDF Model
[Cook 82]
surface modeled by tiny mirror facets
shadow term fresnel termnormal distribution
Represented by SG
single-lobe, analytic approximationCook-Torrance [Cook et al. 1981]
Ward [Ward 1992]
Blinn-Phong [Blinn 1977]
)1,2,;()( 2))(arccos( 2
mGeD m nhh nh
)1,2,;()( 2)()))(1( 222
nhh nhnh GeD
)1,,;()()( nGD n nhnhh
Parametric Models
Parametric BRDFs
nu=8, nv=128 nu=25, nv=400 nu=75, nv=1200
7-lo
be S
GM
grou
nd t
ruth
Anisotropic Parametric Models
Measured BRDFs
BRDF from [Matusik03] svBRDF from [Wang08] & [Lawance06]
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 BRDFTexturing of SGs number
of SGsFloatsper SG
floats per texel
isotropic 1-3 4 4~12 + 3
anisotropic 2-7 6 12~42 + 3
)(hD
Normal Distributionin Half-vector Domain
ohhoh )(2)(
)()( 1 ii DW
)(iW
BRDF Slicein light-vector
o
BRDF Slices
Half-vector Domain
oi
oih
SG Warping
SG not closed under -1
approx. by per-SG warp of D*
))(()( 1** ii DW
DW
DDDDW
DDDW
opp
oppopp
4)(
)(2)(
)(* hD
))(( 1* iD
)(* iW
SG Warping
SG not closed under -1
approx. by per-SG warp of D*
)(* hD
))(( 1* iD
)(* iW
))(()( 1** ii DW
DW
DDDDW
DDDW
opp
oppopp
4)(
)(2)(
Parametric svBRDF Painting
oOutline Reflectance Representation
Microfacet Model with SGs
Visibility Representation Signed Spherical Distance Function
Lighting & Rendering
Visibility at one point
scene binary visibility function
x V(x,i)
Visibility Prerequisite Preserve sharp visibility boundary
inner product for Diffuse Term
vector product for Specular Term
iiinio d ),()max(0,)(),( xVLxRd
SGs ?
iiiinoio d )(),()max(0, ),,(),( LxVxxRs SGs ?
0)(if),arccos(min
1)(if),arccos(min)(
1)(
0)(
iit
iiti
t
t
V
VV
V
Vd
binary visibility, V(i)
i0
i1
SSDF, Vd (i)
Vd(i1)
Vd(i0)
Spherical Signed Distance Function
SSDF-SG Product
SSDF Visibility
SSDF-SG Product
p p
p
SG centered at p
SSDF Visibility
p≈
Approx. Visibility for p
p
Approx. Visibility for p
SSDF-SG Product
p p
p
SG centered at p
SSDF Visibility
p≈
Approx. Visibility for p
=0.329
Inner product vector product
Per-pixel Shading & Shadowing
oOutline Reflectance Representation
Microfacet Model with SGs
Visibility Representation Signed Spherical Distance Function
Lighting & Rendering
Point light
directional light
sr
GL ,ln
,;)(2
* pii
22
2
* ,ln
,;),(xp
s
r
xp
xp
xpGxL
ii
Local Light Source
prefiltered MIPMAP[Kautz et al. 2000]
SGs (10 lobes)[Tsai and Shih 2006]
for diffuse shading for specular shading
Environment Light
prefiltered MIPMAP[Kautz et al. 2000]
SGs (10 lobes)[Tsai and Shih 2006]
for diffuse shading for specular shading
Environment Light
Environment + Local Lighting
Rendering Summary: Diffuse
Microfacet Model Environment Light
Rendering Summary: Diffuse
Microfacet Model Environment Light
Visibilityin SSDF
●
BRDF Slicein SGs
Cosine Termin SGs
Environmentin SGs
Rendering Summary: Specular
Microfacet Model Environment Light
BRDF Slicein SGs
Cosine Termin SGs
Visibilityin SSDF
PrefilteredEnvironment
●
Performance SummaryScene BRDF Type
svBRDFResolusion
svBRDFSize
Env. FPS
Pt. FPS
Teapot CT (iso. 1 SG) 1024×1024 7.2MB 171 250
Dragon Ward (iso. 1 SG) 512×512 1.8MB 165 231
DishBall AS (aniso. 7 SGs) 512×1024 4.1MB 55 30
DishCardcard(iso. 2 SGs) 512×512 4.2MB
satin(aniso. 5 SGs) 850×850 22.4MB 48 35
velvet (aniso. 2SGs) 850×850 9.4MB 168 145
Testing MachineIntel Core2 Duo 3.2G CPU, 4GB memorynVidia Geforce 8800 Ultra graphics card
Performance SummaryScene BRDF Type
svBRDFResolusion
svBRDFSize
Env. FPS
Pt. FPS
Teapot CT (iso. 1 SG) 1024×1024 7.2MB 171 250
Dragon Ward (iso. 1 SG) 512×512 1.8MB 165 231
DishBall AS (aniso. 7 SGs) 512×1024 4.1MB 55 30
DishCardcard(iso. 2 SGs) 512×512 4.2MB
satin(aniso. 5 SGs) 850×850 22.4MB 48 35
velvet (aniso. 2SGs) 850×850 9.4MB 168 145
Testing MachineIntel Core2 Duo 3.2G CPU, 4GB memorynVidia Geforce 8800 Ultra graphics card
bump mapsdynamic BRDFs
anisotropic BRDFs
measured BRDFs
All-Frequency Visual Effects
parametric BRDFs
measured SVBRDFs
Reflectance Painting
Conclusion Overall method:
glossy to mirror-like, detailed, dynamic reflectanceall-frequency shadowsreal-time per-pixel shading
SG mixtures for microfacet-based reflectancecompact yet accuratefast rotation, warping, products
SSDFs for visibilityfast products with SG mixturesnon-ghosting spatial interpolation
Conclusion Overall method:
glossy to mirror-like, detailed, dynamic reflectanceall-frequency shadowsreal-time per-pixel shading
SG mixtures for microfacet-based reflectancecompact yet accuratefast rotation, warping, products
SSDFs for visibilityfast products with SG mixturesnon-ghosting spatial interpolation
Future work dynamic visibility inter-reflection anisotropic spherical Gaussian SSDF compression simpler SVBRDF acquisition
Future work dynamic visibility inter-reflection anisotropic spherical Gaussian SSDF compression simpler SVBRDF acquisition
Thank you for your attention.
Visibility Cuts [Cheslack-Postava et al.2008]
Light-cut frameworkNo highly glossy reflectanceHighly tessellationNot real-time
SG Scaling Shadowing and Fresnel terms
Assume low-frequency [Ashkmin01, Ngan05]
approx. by per-SG scale
))((4
),()()(
nn
FSSW
WWW
W
W
op
opop
pp
SSDF Compression
PCA:
M
jj
dj
d xwVxV1
)()(),( ii
binary visibility SSDF compressed SSDF
Error sources BRDF fitting error diffuse light fitting error SG warping error SSDF-SG product error SSDF compression error
SSDF-SG product errorvisibility function is approximateproduct is approximateinner product error typically less than 2%vector product error larger, but not visually
significanterror decreases as λ increases
SG mixtures
N-lobe approximation
violet-acrylic NDF [Ngan et al. 2005]
original SG, N = 3L2 = 6.2%
SG, N = 2L2 = 8.2%
SG, N = 1L2 = 25%
),,;()(1
*iii
N
i
GF pvv
SG representation of lighting distant light → environment map (EM)
diffuse shading: ○ fit EM with SG mixture (10 lobes) [Tsai and Shih 2006]
specular shading: ○ prefilter EM with SGs of various λ [Kautz et al. 2000]
EM Prefiltering with SGs
……
MIPMAP of prefiltered cubemapsλ reduced by 1/4 per level
λ=21000,level 1
λ =329, level 4 λ =5.1,
level 7
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