Sculpted Data Driven and Physically Based Character Deformation

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Sculpted Data Driven and Physically Based
Character Deformation

• Patrick Coleman
• CSC 2529 Character Animation
• February 12, 2003

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Papers

• Pose Space Deformation A Unified Approach to
  Shape and Interpolation and Skeleton-Driven
  Deformation J.P. Lewis, Matt Cordner, Nickson
  Fong
• DyRT Dynamic Response Textures for Real Time
  Deformation Simulation with Graphics
  Hardware Doug L. James and Dinesh K. Pai
• Interactive Skeleton-Driven Dynamic
  Deformations Capell, Green, Curless, Duchamp,
  Popovic

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Pose Space Deformation

• Common Approaches to Character Deformation
• Skeletal driven deformation for articulated body
  motion
• Shape interpolation among a set of poses for
  facial animation
• Pose Space Deformation
• Combine these approaches and address their
  shortcomings

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Skeletal Subspace Deformation

• Surface Points are tied to joints, linearly
  weighted
• User often tweaks weights to achieve desired
  response
• Restrictive subspace not capable of achieving all
  desired poses
• Leads to unnatural deformations to certain poses
• Maya smooth skinning

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SSD Problems
Elbow twist
Collapsing Elbow
Maya Example
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Shape Interpolation

• Linearly combine a number of key poses using
  slider values

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Shape Interpolation

• Linearly combine a number of key poses using
  slider values
• Allows user to explicitly sculpt poses
• Positional interpolation is only C0 continuous
• Poses can add up or cancel out unexpectedly
• Maya Blend Shape

Maya Example
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PSD

• Skeletal-driven deformation among a set of key
  poses
• User sculpts set of poses
• Scattered data interpolation to determine
  configuration driven deformation
• Facial animation among a set of key poses
• Scattered data interpolation driven by relative
  key pose weights

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Scattered Data Interpolation

• Locally weight nearby configurations using
  precomputed radial basis functions
• Allows smooth interpolation among configurations
  if desired
• Precomputation to achieve real-time deformation
• User must avoid very similar poses

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Suggested Facial Space

• Adapted from psychological research

Aroused
alarmed
delighted
frustrated
Pleasure
Displeasure
serene
tired
Sleepy
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PSD Summary

• Data driven approach to dynamic deformation
• Data supplied by user sculpting important poses
• Scattered data interpolation among key poses to
  determine intermediate poses using radial basis
  functions
• Can be skeleton driven
• Can be blendShaped (sliders to distribute
  weight among poses)

no, blendShaped is not a real word.
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Dynamic Response Textures

• Geometrically complex, interactive,
  physically-based, volumetric, deformation models,
  with negligible main CPU costs.
• Modal Analysis to determine how modal deformation
  of surface points
• Hardware vertex program to drive deformations
  based on rigid body motion

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Modal Analysis

• Reduce vibration to a set of frequency modes
• Overall Deformation is a superposition of
  deformation due to each mode
• u displacementM mass matrixD dampening
  coefficient matrix (sM) K stiffness
  coefficient matrix

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Modal Analysis

• Determine a set of vibration modes
• Natural frequency of vibration
• Modal dampening

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Low Frequency Modes for Torso
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Applying Modal Vibration

• Assume system is a rest at time t0
• Integrate solution to modal ODE to time
  t Solution is dependent on force matrix, modal
  vibration frequency, and modal dampening factor
• Throw away high frequency modes Not very
  noticeable Can cause temporal aliasing

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Rigid Motion Excitement

• Allows use of skeletal motion to drive local
  modal deformation
• Consider both linear and angular velocity
• Euler discretization of acceleration
• Digital filter for efficient integration
• Assumes modal vibration is not dependent on
  skeletal deformation
• This allows pre-computation of all deformation
  parameters
• Interpolate deformation with base pose across
  affected region

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Hardware Acceleration

• NVIDIA GeForce3 vertex program

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DyRT Video
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DyRT Summary

• Fast application of tissue response to dynamic
  movement
• Modal analysis to reduce deformation to discrete
  modes
• Precomputation of response functions
• Part of the rendering pipeline (hardware program)
• Models wearing tight red shorts with SIGGRAPH
  logos embedded in a Texan theme are kind of scary

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Interactive Skeleton Driven Dynamic Deformations

• Simulation of secondary motion of deformable
  objects in real time
• Framework
• Embed object in volumetric grid with bone
  constraints
• Constrain grid to lie along bones for efficient
  computation
• Superpose locally linear simulations driven by
  single bone
• Hierarchical basis on grid to adapt to level of
  detail

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Problem Formulation

• Rest state of object
• Deformation
• Overall system state

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Hierarchical grid basis

• Subdivide grid over detail of object
• Trilinear basis functions
• falls off from one to zero along lines of
  control mesh

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Equations of Motion

• Euler-Lagrange equations
• First three terms reduce to numerical integration
• Integration Subdivide control mesh to desired
  level Compute basis function values at each
  vertex Tetrahedralize domain (allows piecewise
  linear approximation of functions) Integrate
  over each tetrahedron using linear
  approximations of basis functions

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System setup

• Manual definition of skeleton, control mesh,
  regions of local linearization

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Solving the System

• Linearize equations at each time step
  (Baraff/Witkin 98)
• Conjugate Gradient solver applied to sparse
  linear system of second equation, direct solution
  of first equation follows

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Bone Constraints

• Some velocities are known
• Second equation reduces to
• Same form, lower complexity

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Position Constraints

• Allow for interaction with other objects, user
• Velocity enforced in CG solver by projecting
  constraint onto simulation space velocity
  components (Barraff/Witkin 98)
• Introduction of new detail coefficients in
  basis

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Local Linearization

• Locally linearize influence of nearby bones
• Use manually assigned vertex weights to blend
  among regions
• Independently solve each region
• Composite regional solutions

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Other details

• Twisting motion is penalized with stiffness
  dependent on potential gradient along deformation
• Adaptive addition and removal of basis functions
  in hierarchy

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ISDDD Video
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ISDDD Summary

• Real-time dynamic response for elastically
  deformable models
• Objects are embedded in a hierarchical control
  mesh to which the finite element method is
  applied
• Alignment of control grid to skeleton simplifies
  solution
• Locally linearized regions of influence to reduce
  complexity
• Point constraints allow interaction

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Useful References(if you really want to
understand whats going on)

• Dynamic Response Textures
• Good Vibrations Modal Dynamics for Graphics and
  Animation Pentland and Williams, SIGGRAPH 1989
• A User-Programmable Vertex Engine Lindholm,
  Kilgard, Moreton, SIGGRAPH 2001
• Interactive Skeleton Driven Dynamic Deformations
• Large Steps in Cloth Simulation Baraff
  Witkin, SIGGRAPH 1998
• Physically Based Modeling Baraff Witkin,
  SIGGRAPH 2001 Course notes, available from
  Pixars web site
• An Introduction to the Conjugate Gradient Method
  Without the Agonizing Pain Shewchuk, 1994. See
  citation in Baraff/Witkin 1998