An Efficient Brush Model for Physically-Based 3D Painting

1
An Efficient Brush Model for Physically-Based 3D
Painting

• Nelson S.-H. CHU (cpegnel_at_ust.hk)
• Chiew-Lan TAI (taicl_at_ust.hk)
• The Hong Kong University of Science and
  Technology
• October 9, 2002, Beijing, China

2
Overview

• Brush simulation for digital painting
• Chinese brush
• Physically-based
• Interactive

3
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
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Motivation

• Chinese brush
• Expressive lining instrument
• Soft-yet-resilient quality
• ????????? ??(??)
• Deft manipulation

• Spontaneous painting style
• Spontaneity
• Rhythmic vitality

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Motivation
By Zhao Shaoang
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Motivation
By Wu Guanzhong 1999
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Motivation

• Extend the expressiveness of Chinese brushes into
  digital domain
• Help promote Chinese cultural heritage
• Explore new possibilities for development
• ????,????????,?????????? ???
• Creates new computer graphics tools
• High-quality calligraphic Oriental fonts
• Non-photorealistic rendering of 3D objects

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Previous Work

• Stroke Appearance
• Brush Model Painting Process

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Previous Work

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

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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)

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Our Brush Model
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Our Brush Model
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Brush Modeling

• Layered approach
• Brush skeleton
• Determines dynamics
• Brush surface
• Determines footprint

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Brush Modeling

• Brush Skeleton
• Spine
• Connected line segments
• For general bending
• Lateral nodes
• Slides along the sides of a spine node
• For lateral deformation

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Brush Modeling

• Brush Surface
• Cross-section ? two half-ellipses
• Sweep ? along spine
• Bristle splitting by alpha map

Tuft cross-section
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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

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Brush Dynamics

• Skeleton spring system

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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

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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

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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

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Summary of New Features

• Brush flattening and spreading
• Brush splitting at bristle level
• Brush Plasticity
• Paper pore resistance

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Summary of New Features

• Brush flattening and spreading
• Lateral nodes
• Brush splitting at bristle level
• Brush Plasticity
• Paper pore resistance

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Summary of New Features

• Brush flattening and spreading
• Lateral nodes
• Brush splitting at bristle level
• Alpha map
• Brush Plasticity
• Paper pore resistance

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Summary of New Features

• Brush flattening and spreading
• Lateral nodes
• Brush splitting at bristle level
• Alpha map
• Brush Plasticity
• Zero-shifting
• Paper pore resistance

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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

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Video Demonstration
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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

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Future Work

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

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Thank you!

• Questions?

? Contact cpegnel_at_ust.hk taicl_at_ust.hk
Slide show of sample output
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Brush Dynamics

• Observations
• Little inertia, highly damped forces
• Almost always in steady state

• Vectorial approach
• Fma, 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

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Brush Dynamics