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Computer-Generated Watercolor. Cassidy J. Curtis Sean E. Anderson Joshua E. Seims Kurt W. Fleischer David H. Salesin. Outline. Introduction Related work Background Overview Watercolor simulation Rendering Applications Results Conclusion. Introduction. - PowerPoint PPT Presentation
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Computer-Generated Watercolor
Cassidy J. CurtisSean E. AndersonJoshua E. SeimsKurt W. FleischerDavid H. Salesin
Outline
• Introduction
• Related work
• Background
• Overview
• Watercolor simulation
• Rendering
• Applications
• Results
• Conclusion
Introduction
• Various artistic effects of watercolor
Related work
• Simulating artists’ traditional media and tools– Watercolor : [David Small 1991]– Sumie : [Guo and Kunii 1991]
• Commercial package– Fractal Design Painter
Background
• Properties of watercolor– Watercolor paper– Pigment– Binder– Surfactant
Background• Watercolor Effects
• a) dry-brush• b) Edge darkening• c) Backruns• d) granulation and separation of pigments• e) Flow patterns• f) color glazing
Overview
• Computer-generated watercolor
1. Fluid (and pigment) simulation for each glaze
2. Rendering
Glaze: physical properties, area
Fluid simulation
• Three-layer model
Fluid simulation
• Paper Generation
– Height field model ( 0 < h < 1 )– Based on pseudo-random process– Fluid capacity c: proportional to h
minminmax )( ccchc
Fluid simulation
• Main loop
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For e
ach
time
step
Fluid simulation
• Main loop
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For e
ach
time
step
Moving water• conditions of water
1. To remain within the wet-area mask
2. To flow outward into nearby region
3. To be damped to minimize oscillating waves
4. To be perturbed by the texture of the paper
5. To be affected by local changes
6. To present the edge-darkening effect
Navier-Stoke Eq.
Viscous drag k
Paper slope h
Mass conserv.
Flow outward
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Configuration– Staggered grid
),5.0(),( jivu ),5.0(),( jivu
)5.0,(),( jivu
)5.0,(),( jivu
...),,( dgp
i,j
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Updating the water velocities– Governing Equation (2D Navier-Stoke Eqn.)
y
pv
y
vv
x
vu
t
v
x
pu
y
uv
x
uu
t
u
2
2
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Derivation of Navier-Stoke Eqn.(1/5)
– Basic Eqn.:
– For unit volume:
dt
dmmFV
x
dt
dF
V
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Derivation of Navier-Stoke Eqn.(2/5)
– Two kind of measurements
fluid
solid
)(tVControl volume
,(tV ),, zyx
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Derivation of Navier-Stoke Eqn.(3/5)
– Eulerian view
dt
zyxtd ),,,(V
t
z
zt
y
yt
x
xt
VVVV
wz
vy
uxt
VVVV
VVV
)(
t
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Derivation of Navier-Stoke Eqn.(4/5)
– Governing Eq.:
– Forces:• Gravity:
• Viscosity:
• Pressure:
dt
dF
V
g
V2
p
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Derivation of Navier-Stoke Eqn.(5/5)– Navier-Stoke Eqn.
– For 2D case,
y
pv
y
vv
x
vu
t
v
x
pu
y
uv
x
uu
t
u
2
2
pVVVV
2)(
t
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Updating the water velocities– Numerical integration for u
x
pu
y
uv
x
uu
t
u
2
t
uu jiji
,5.,5.
)()( ,1,,5.,,1,5. jijijijijiji uuvuuu
jiji pp ,,1
jijijijiji uuuuu ,5.1,5.1,5.,5.1,5.1 4
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Updating the water velocities– Applying paper slope effect:
– Applying Drag Force:
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
h VV
VF
Fluid simulation
• Mass conservation (1/3)– Divergence free condition
0
y
v
x
u
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Mass conservation (2/3)– Relaxation (iterative procedure)
y
v
x
u
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Mass conservation (3/3)– Relaxation (iterative procedure)
y
v
x
u
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
jivu ,),(
)(y
v
x
u
Fluid simulation
• Edge darkening – To flow outward
• Remove some water at the boundary
MM )1( pp
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
coeff. Darkening :
mask BlurredGaussian :
mask Wet :
M
M
Fluid simulation
• Edge darkening
MM )1( pp
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
dry wet
0
0
00
0
0
0
0
0
1
1
1 1
1
1
1
1
1
M
.1
.1
.10
.4
.4
.4
0
0
.6
.6
.6 1
.9
.9
.9
1
1
M’
0
0
00
0
0
0
0
0
.4
.4
.4 0
.1
.1
.1
0
0
(1-M’)M
Fluid simulation
• Main loop
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For e
ach
time
step
Fluid simulation
• Moving Pigments – To move as specified by the velocity field u,v
jig ,
jiji gu ,,5.0 jiji gu ,,5.0
jiji gv ,5.0,
jiji gv ,5.0,
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Moving Pigments – To move as specified by the velocity field u,v
),0max(),0max(
),0max(),0max(
),0max(
),0max(
),0max(
),0max(
,5.0,,5.0,
,,5.0,,5.0,,
,5.0,1,1,
,5.0,1,1,
,,5.0,1,1
,,5.0,1,1
jijijiji
jijijijijiji
jijijiji
jijijiji
jijijiji
jijijiji
gvgv
gugugg
gvgg
gvgg
gugg
gugg
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Main loop
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For e
ach
time
step
Fluid simulation
• Transferring Pigments– Adsorption and desorption
Adsorption ,h
wh /1,1Desorption
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Main loop
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For e
ach
time
step
Fluid simulation
• Backruns – Diffusing water through the capillary layer
• Spreading slowly into a drying region
• Transfer water to its dryer neighbors until they are saturated
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Fluid simulation
• Drybrush effect– By excluding any lower pixel than threshold
Rendering
• Optical properties of pigments– Optical composition – subtractive color mixing
Rendering
• Optical properties of pigments– Kubelka-Munk (KM) Model– To compute Reflectance R and Transmittance T
using K and S
unit length
absorbed
K
backscatteredS
Rendering
• Optical properties of pigments– Kubelka-Munk (KM) Model
bSdbbSda
bT
bSdbbSda
bSdR
coshsinh
coshsinh
sinh
1 and , /)( where 2 abSKSa
Rendering
• Optical properties of pigments– Kubelka-Munk (KM) Model– For multiple layers
21
21
21
22
11
1
1
RR
TTT
RR
RTRR
Rendering
• Optical properties of pigments– Kubelka-Munk (KM) Model
We need S and K values
Make user choose them intuitively
Rendering
• Optical properties of pigments– User selects Rw and Rb
Rendering
• Optical properties of pigments– User selects Rw and Rb
1 and ,1
2
1
)1(
)1(
)1)((coth
1
2
21
abR
RRRawhere
aSK
Rb
aRab
bS
w
wbw
w
w
Applications
• 1. Interactive painting with watercolors
• 2. Automatic image “watercolorization”
• 3. Non-photorealistic rendering of 3D models
Applications
• 1. Interactive painting with watercolors
Applications
• 2. Automatic image “watercolorization”
– Color separation
– Brushstroke Planning
Applications
• 2. Automatic image “watercolorization”– Color separation
• Determine the thickness of each pigment by brute-force search for all color combinations
Applications
• 2. Automatic image “watercolorization”– Brushstroke planning
Applications
• 3. Non-photorealistic rendering of 3D models– Using “photorealistic” scene of 3D model
Results
Results
Results
Results
Conclusion
• Various artistic effects of watercolor– Water and pigment simulation– Pigment Rendering
• Application– Interactive system– Automatic “watercolorization” of 2D and 3D
Further work
• Other effects– Spattering and drybrush
• Automatic rendering– Applying automatic recognition
• Generalization – Integration of Wet-in-wet and backruns
• Animation issues– Reducing temporal artifacts