1. Computer-Generated Watercolor
Cassidy J. Curtis
Sean E. Anderson
Joshua E. Seims
Kurt W. Fleischer
David H. Salesin

2. Outline Introduction Related work Background Overview
Watercolor simulation
Rendering
Applications
Results
Conclusion

3. Introduction
Various artistic effects of watercolor

4. Related work Simulating artists’ traditional media and tools
Watercolor : [David Small 1991]
Sumie : [Guo and Kunii 1991]
Commercial package
Fractal Design Painter

5. Background Properties of watercolor Watercolor paper Pigment Binder
Surfactant

6. Background Watercolor Effects a) dry-brush b) Edge darkening
c) Backruns
d) granulation and separation of pigments
e) Flow patterns
f) color glazing

7. Overview Computer-generated watercolor
1. Fluid (and pigment) simulation for each glaze
2. Rendering
Glaze: physical properties, area

8. Fluid simulation
Three-layer model

9. Fluid simulation Paper Generation
Height field model ( 0 < h < 1 )
Based on pseudo-random process
Fluid capacity c: proportional to h

10. Fluid simulation Main loop Moving Water Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For each time step

11. Fluid simulation Main loop Moving Water Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For each time step

12. Moving water conditions of water 1. To remain within the wet-area mask
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
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

13. Fluid simulation Configuration Staggered grid i,j Moving Water
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Configuration
Staggered grid
i,j

14. Fluid simulation Updating the water velocities
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Updating the water velocities
Governing Equation (2D Navier-Stoke Eqn.)

15. Fluid simulation Derivation of Navier-Stoke Eqn.(1/5) Basic Eqn.:
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Derivation of Navier-Stoke Eqn.(1/5)
Basic Eqn.:
For unit volume:

16. Fluid simulation Derivation of Navier-Stoke Eqn.(2/5)
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Derivation of Navier-Stoke Eqn.(2/5)
Two kind of measurements
fluid
solid
Control volume

17. Fluid simulation Derivation of Navier-Stoke Eqn.(3/5) Eulerian view
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Derivation of Navier-Stoke Eqn.(3/5)
Eulerian view

18. Fluid simulation Derivation of Navier-Stoke Eqn.(4/5) Governing Eq.:
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Derivation of Navier-Stoke Eqn.(4/5)
Governing Eq.:
Forces:
Gravity:
Viscosity:
Pressure:

19. Fluid simulation Derivation of Navier-Stoke Eqn.(5/5)
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Derivation of Navier-Stoke Eqn.(5/5)
Navier-Stoke Eqn.
For 2D case,

20. Fluid simulation Updating the water velocities
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Updating the water velocities
Numerical integration for u

21. Fluid simulation Updating the water velocities
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Updating the water velocities
Applying paper slope effect:
Applying Drag Force:

22. Fluid simulation Mass conservation (1/3) Divergence free condition
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Mass conservation (1/3)
Divergence free condition

23. Fluid simulation Mass conservation (2/3)
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Mass conservation (2/3)
Relaxation (iterative procedure)

24. Fluid simulation Mass conservation (3/3)
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Mass conservation (3/3)
Relaxation (iterative procedure)

25. Fluid simulation Edge darkening To flow outward
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Edge darkening
To flow outward
Remove some water at the boundary

26. Fluid simulation Edge darkening dry wet 1 M .1 .4 .6 1 .9 M’ .4 .1
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Edge darkening
dry
wet 1 M .1 .4 .6 1 .9 M’ .4 .1
(1-M’)M

27. Fluid simulation Main loop Moving Water Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For each time step

28. Fluid simulation Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Moving Pigments
To move as specified by the velocity field u,v

29. Fluid simulation Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Moving Pigments
To move as specified by the velocity field u,v

30. Fluid simulation Main loop Moving Water Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For each time step

31. Fluid simulation Transferring Pigments Adsorption and desorption
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Transferring Pigments
Adsorption and desorption
Adsorption
Desorption

32. Fluid simulation Main loop Moving Water Moving Pigments
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
For each time step

33. Fluid simulation Backruns Diffusing water through the capillary layer
Applying Capillary Flow
Moving Water
Moving Pigments
Transferring Pigments
Backruns
Diffusing water through the capillary layer
Spreading slowly into a drying region
Transfer water to its dryer neighbors until they are saturated

34. Fluid simulation Drybrush effect
By excluding any lower pixel than threshold

35. Rendering Optical properties of pigments
Optical composition – subtractive color mixing

36. Rendering S K Optical properties of pigments Kubelka-Munk (KM) Model
To compute Reflectance R and Transmittance T using K and S
backscattered S
unit length
absorbed K

37. Rendering
Optical properties of pigments
Kubelka-Munk (KM) Model

38. Rendering Optical properties of pigments Kubelka-Munk (KM) Model
For multiple layers

39. Rendering Optical properties of pigments We need S and K values
Kubelka-Munk (KM) Model
We need S and K values
Make user choose them intuitively

40. Rendering
Optical properties of pigments
User selects Rw and Rb

41. Rendering
Optical properties of pigments
User selects Rw and Rb

42. Applications 1. Interactive painting with watercolors
2. Automatic image “watercolorization”
3. Non-photorealistic rendering of 3D models

43. Applications
1. Interactive painting with watercolors

44. Applications 2. Automatic image “watercolorization” Color separation
Brushstroke Planning

45. Applications 2. Automatic image “watercolorization” Color separation
Determine the thickness of each pigment by brute-force search for all color combinations

46. Applications 2. Automatic image “watercolorization”
Brushstroke planning

47. Applications 3. Non-photorealistic rendering of 3D models
Using “photorealistic” scene of 3D model

48. Results

49. Results

50. Results

51. Results

52. Conclusion Various artistic effects of watercolor Application
Water and pigment simulation
Pigment Rendering
Application
Interactive system
Automatic “watercolorization” of 2D and 3D

53. Further work Other effects Automatic rendering Generalization
Spattering and drybrush
Automatic rendering
Applying automatic recognition
Generalization
Integration of Wet-in-wet and backruns
Animation issues
Reducing temporal artifacts