An Efficient Brush Model for PhysicallyBased 3D Painting

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

• Nelson S.-H. Chu
• Chiew-Lan Tai

2
Benefits Over Existing Models

• Brush flattening
• Bristle spreading
• Plasticity of wetted brushes
• Resistance of paper surface

3
Block Diagram

• Artists use a brush connected to several sensors
  to paint
• The movements of the brush are interpreted by the
  brush, ink, and paper models
• The brush and strokes are the rendered on the
  screen

4
User Interface

• Sensors attached to real brush to provide input
• Ultrasound receivers and buzzer provide 6 degrees
  of freedom
• Gyroscopes provide brush orientation information

5
Actual Brush

• Made of animal hairs
• Kernel is hard, outer layers are soft
• Good brushes are elastic
• Tip is less stiff than the root

6
Brush Skeleton

• Brush is modeled by line segments
• Spine nodes are made up of consecutively shorter
  line segments
• This makes the brush more flexible at the tip
• Lateral nodes are attached to each spine node
• Connection points are modeled by bend springs
• Lateral line segments are modeled by stretch
  springs
• Columns of spine nodes and lateral nodes
  represent groups of bristles

7
Tuft Cross Section

• Spine nodes are represented at cylindrical groups
  of bristles
• Lateral nodes are elliptical groups of bristles
• Entire tuft is modeled with ellipses at each
  spinal node

8
Brush Surface

• Lateral nodes allow the simulation of bristle
  spreading
• An alpha map is used for fine bristle splitting
  effects
• Currently a static alpha map is used

9
Brush Dynamics

• Exact Newtonian physics is not practical
• Instead, energy minimization is used
• An energy function is set up for the system and
  its steady state is determined by finding a local
  energy minimum numerically.
• The state of the system at the previous time step
  is used as the new initial value
• This is a static contained minimization problem
• Sequential Quadratic Programming (SQP) is used to
  solve the energy minimization problem

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Energy Minimization

• Initialize (? f , f f ) (? i , f i )
• Determine if any nodes penetrate the paper
• Set minimization constraints for those nodes
• Solve energy minimization problem for the state
  of the system and update accordingly

11
Energy Functions

• E Edeform Efrict
• Edeform has a spine and lateral component, each
  of which have bend and stretch components
• BendEnergy(?)kbend?3
• Estretch(d,?)kstretchd-(rs(?))3
• ddistance from node, rradius of node
• S is a function of the bend angle
• Efrict u Sum(F(kfXpar(1-kf)Xperp))
• Fnormal force, kfweighting value
• Xpar/perpdistance moved parallel and
  perpendicular

12
Plasticity

• Brushes have different plasticities
• Type of brush
• Wetness of brush
• Plasticity is the amount by which the brush
  returns to its original shape
• BendEnergy(?)k?-p3 where pmin(?, alpha)
• Alpha changes according to wetness of brush,
  larger alpha corresponds to more plasticity

13
Ink Depositing

• Ink and moisture information is stored at each
  node
• The brush footprint is the orthogonal projection
  of the penetrating portion of the brush onto the
  paper
• Ink is either subtracted from the tuft upon
  depositing, or maintained to allow continuous
  painting
• If the ink is subtracted the tuft alpha map is
  modified too reflect this

14
Specs

• System written in Object Pascal using Borland
  Delphi 6
• Runs real-time at 25 frames per second on a 1GHz
  Pentium-III with a GeForce2 Pro graphics card
• Most time frames require less then 10 SQP
  iterations

15
Results
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