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. Pacific Graphics 2002, Beijing, China Overview Brush simulation for digital painting Chinese brush Physically-based Interactive Input: Brush movements Simulation of Brush & ink Output: Realistic brushwork

3. Pacific Graphics 2002, Beijing, China 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 2D dab shapes

4. Pacific Graphics 2002, Beijing, China 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 Execution + Elastic Brush

5. Pacific Graphics 2002, Beijing, China Motivation By Zhao Shao’ang

6. Pacific Graphics 2002, Beijing, China Motivation By Wu Guanzhong 1999

7. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Previous Work Stroke Appearance Brush Model + Painting Process

9. Pacific Graphics 2002, Beijing, China Previous Work Stroke Appearance B. Pham ’91 (B-spline + offset curves) S. Hsu et al. ’94 (Picture deformation) Brush Model + Painting Process

10. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Our Brush Model

12. Pacific Graphics 2002, Beijing, China Our Brush Model Model in full gearWithout tip splitting Without lateral spreading No deformation at all (brush penetrates paper)

13. Pacific Graphics 2002, Beijing, China Brush Modeling Layered approach Brush skeleton Determines dynamics Brush surface Determines footprint Surface Skeleton

14. Pacific Graphics 2002, Beijing, China Brush Modeling Brush Skeleton Spine Connected line segments For general bending Lateral nodes Slides along the sides of a spine node For lateral deformation

15. Pacific Graphics 2002, Beijing, China Brush Modeling Brush Surface Cross-section  = two half-ellipses Sweep  along spine Bristle splitting by alpha map Tuft cross-section paper footprint

16. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Brush Dynamics Skeleton spring system Angular Springs: between consecutive spine nodes Angular Springs: between consecutive lateral nodes Displacement Springs: between spine nodes & its lateral nodes

18. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Summary of New Features Brush flattening and spreading Brush splitting at bristle level Brush Plasticity Paper pore resistance

22. Pacific Graphics 2002, Beijing, China Summary of New Features Brush flattening and spreading Lateral nodes Brush splitting at bristle level Brush Plasticity Paper pore resistance

23. Pacific Graphics 2002, Beijing, China Summary of New Features Brush flattening and spreading Lateral nodes Brush splitting at bristle level Alpha map Brush Plasticity Paper pore resistance

24. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Video Demonstration

27. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Future Work Painting media modeling Ink diffusion Paper texture Tuft hierarchy Physics simulation Investigate vectorial dynamics User interface Haptic input device Stereo display

29. Pacific Graphics 2002, Beijing, China Thank you! Questions? Slide show of sample output  Contact: cpegnel@ust.hk taicl@ust.hk

30. Pacific Graphics 2002, Beijing, China 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. Pacific Graphics 2002, Beijing, China Brush Dynamics Spine Bending Energy Lateral Deformation Energy Internal Energy + + Total Energy Deformation Energy Frictional Energy + =