an efficient brush model for physically-based 3d painting nelson s.-h. chu ([email protected])...
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An Efficient Brush Model for Physically-Based 3D Painting
Nelson S.-H. CHU ([email protected])Chiew-Lan TAI ([email protected])
The Hong Kong University of Science and Technology
October 9, 2002, Beijing, China
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
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
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 BrushExecution + Elastic Brush
Pacific Graphics 2002, Beijing, China
Motivation
By Zhao Shao’ang
Pacific Graphics 2002, Beijing, China
Motivation
By Wu Guanzhong 1999
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
Pacific Graphics 2002, Beijing, China
Previous Work
Stroke Appearance Brush Model + Painting Process
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
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)
Pacific Graphics 2002, Beijing, China
Our Brush Model
Pacific Graphics 2002, Beijing, China
Our Brush Model
Model in full gear Without tip splitting
Without lateral spreading
No deformation at all(brush penetrates
paper)
Pacific Graphics 2002, Beijing, China
Brush Modeling
Layered approach Brush skeleton
Determines dynamics Brush surface
Determines footprint
Surface
Skeleton
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
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
paperfootprint
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
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
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
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
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
Pacific Graphics 2002, Beijing, China
Summary of New Features
Brush flattening and spreading Brush splitting at bristle level Brush Plasticity Paper pore resistance
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
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
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
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
Pacific Graphics 2002, Beijing, China
Video Demonstration
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
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
Pacific Graphics 2002, Beijing, China
Thank you!
Questions?
Slide show of sample output
Contact: [email protected] [email protected]
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
Pacific Graphics 2002, Beijing, China
Brush Dynamics
Spine BendingEnergy
Lateral DeformationEnergy
Internal Energy
+
+Total Energy
DeformationEnergy
FrictionalEnergy
+=