An Efficient Brush Model for Physically-Based 3D Painting

1. An Efficient Brush Model for Physically-Based 3D Painting Nelson S.-H. CHU (cpegnel@ust.hk) Chiew-Lan TAI (taicl@ust.hk) The Hong Kong University of Science and Technology October 9, 2002, Beijing, China

2. Input:Brush movements Simulation of Brush & ink Output:Realistic brushwork Overview • Brush simulation for digital painting • Chinese brush • Physically-based • Interactive

3. 2D dab shapes Motivation • Digital painting • Convenient, easy to experiment • 2D mark-making methods • Works well for ‘hard’ media like pastel • Spotted shape as brush footprint Painting & strokes made using commercial software Corel Painter

4. Execution + Elastic Brush Motivation • Chinese brush • Expressive lining instrument • Soft-yet-resilient quality • 惟笔软则奇怪生焉。–蔡邕(东汉) • Deft manipulation • Spontaneous painting style • Spontaneity • Rhythmic vitality

5. Motivation By Zhao Shao’ang

6. Motivation By Wu Guanzhong 1999

7. Motivation • Extend the expressiveness of Chinese brushes into digital domain • Help promote Chinese cultural heritage • Explore new possibilities for development • 保留传统,只有发展才能保留,不发展就不可能保留。–吴冠中 • Creates new computer graphics tools • High-quality calligraphic Oriental fonts • Non-photorealistic rendering of 3D objects

8. Previous Work • Stroke Appearance • Brush Model + Painting Process

9. Previous Work • Stroke Appearance • B. Pham ’91 (B-spline + offset curves) • S. Hsu et al. ’94 (Picture deformation) • Brush Model + Painting Process

10. Previous Work • Stroke Appearance • Brush Model + Painting Process • Geometric • S. Strassmann ’86 (1D texture) • Painting Software Corel Painter (2D dab shape) • Physically-based • J. Lee ’99 (Homogeneous elastic rods) • S. Saito et al. ’99 (Point mass at tip + Bezier spine) • B. Baxter et al. ’01 (Spring-mass system) • Geometric + Physical behaviors • H. Wong et al. ’00 (Cone) • S. Xu et al. ’02 (Tuft-like objects)

11. Our Brush Model

12. Without lateral spreading No deformation at all (brush penetrates paper) Without tip splitting Model in full gear Our Brush Model

13. Skeleton Surface Brush Modeling • Layered approach • Brush skeleton • Determines dynamics • Brush surface • Determines footprint

14. Brush Modeling • Brush Skeleton • Spine • Connected line segments • Forgeneral bending • Lateral nodes • Slides along the sides of a spine node • Forlateral deformation

15. paper footprint Brush Modeling • Brush Surface • Cross-section  = two half-ellipses • Sweep  along spine • Bristle splitting by alpha map Tuft cross-section

16. Brush Dynamics • Variational approach • Brush skeleton of next frame obtained by energy minimization • Minimum principle for incremental displacements • As a constrained optimization problem • Objective function:Total Energy = deformation energy + frictional energy • Constraints: All nodes above paper • Solve using sequential quadratic programming

17. Angular Springs: between consecutive lateral nodes Displacement Springs: between spine nodes & its lateral nodes Angular Springs: between consecutive spine nodes Brush Dynamics • Skeleton spring system

18. Brush Dynamics • Brush behaviors expected by real-brush users • Brush Plasticity • Wetted brush are plastic • Paper pore resistance • Small pores on paper surface • Fine brush tip gets trapped

19. Brush Dynamics • Brush Plasticity • Shift the spring energy function so that the zero (lowest) energy position is now at  •  = min (’, ), ’ = position from last frame  = max. shift

20. Brush Dynamics • Paper pore Resistance • As a moving blocking-plane constraint • Prevents brush tip from going towards the direction it is pointing • Adjustable lead distance

21. Summary of New Features • Brush flattening and spreading • Brush splitting at bristle level • Brush Plasticity • Paper pore resistance

22. Summary of New Features • Brush flattening and spreading • Lateral nodes • Brush splitting at bristle level • Brush Plasticity • Paper pore resistance

23. Summary of New Features • Brush flattening and spreading • Lateral nodes • Brush splitting at bristle level • Alpha map • Brush Plasticity • Paper pore resistance

24. Summary of New Features • Brush flattening and spreading • Lateral nodes • Brush splitting at bristle level • Alpha map • Brush Plasticity • Zero-shifting • Paper pore resistance

25. Summary of New Features • Brush flattening and spreading • Lateral nodes • Brush splitting at bristle level • Alpha map • Brush Plasticity • Zero-shifting • Paper pore resistance • Blocking-plane constraint

26. Video Demonstration

27. Conclusions • Efficient model for brush deformation • Plausible brush dynamics • Bending, flattening, spreading & splitting • Plasticity • Paper pore resistance • Real-time on consumer-level PC • Oil or watercolor brushes can be modeled with small modifications

28. Future Work • Painting media modeling • Ink diffusion • Paper texture • Tuft hierarchy • Physics simulation • Investigate vectorial dynamics • User interface • Haptic input device • Stereo display

29. Thank you! • Questions?  Contact: cpegnel@ust.hk taicl@ust.hk Slide show of sample output

30. Brush Dynamics • Vectorial approach • F=ma, for a certain F, small m large a • Need to solve stiff differential equations  • Variational approach • Get into next state by minimization energy functional • Minimum principle for incremental displacements • Observations • Little inertia, highly damped forces • Almost always in steady state

31. Spine Bending Energy + Deformation Energy Lateral Deformation Energy = + Total Energy + Internal Energy Frictional Energy Brush Dynamics