1. Sculpted Data Driven and Physically Based Character Deformation
Patrick Coleman
CSC 2529 Character Animation
February 12, 2003

2. 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

3. 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

4. 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
Wk: point weight
L, k, delta: skeletal movement motion
L, k,0: world transform of skeleton
L,p,0: world transform of surface

5. SSD Problems
Elbow twist
Collapsing Elbow
…Maya Example…

6. Shape Interpolation
Linearly combine a number of key poses using slider values

7. …Maya Example… 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…

8. 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

9. 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
Linear combination of nonlinear functions
Phi is gaussian—user controlled locality of configuration
Sk: key shapes
S: intermediate position in n dimensional space (same as linearly interpolated shape)

10. Suggested Facial Space
Adapted from psychological research
Aroused
alarmed
delighted
frustrated
Displeasure
Pleasure
serene
tired
Sleepy

11. 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 blendShape’d* (sliders to distribute weight among poses)
*no, “blendShape’d” is not a real word.

12. 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

13. Modal Analysis Reduce vibration to a set of frequency modes
Overall Deformation is a superposition of deformation due to each mode
u: displacement M: mass matrix D: dampening coefficient matrix (=sM) K: stiffness coefficient matrix

14. Modal Analysis Determine a set of vibration modes:
Natural frequency of vibration:
Modal dampening:

15. Low Frequency Modes for Torso

16. 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

17. 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

18. Hardware Acceleration
NVIDIA GeForce3 vertex program

19. DyRT Video

20. 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…

21. 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

22. Problem Formulation Rest state of object: Deformation:
Overall system state:
Each phi is a finite basis, there are a of them

23. Hierarchical grid basis
Subdivide grid over detail of object
Trilinear basis functions:
falls off from one to zero along lines of control mesh
S is bone, this talks about a on s

24. 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

25. System setup
Manual definition of skeleton, control mesh, regions of local linearization

26. 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

27. Bone Constraints Some velocities are known Second equation reduces to:
Same form, lower complexity

28. 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

29. Local Linearization Locally linearize influence of nearby bones
Use manually assigned vertex weights to blend among regions
Independently solve each region
Composite regional solutions:

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

31. ISDDD Video

32. 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

33. Useful References(if you really want to understand what’s 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
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 Pixar’s web site
“An Introduction to the Conjugate Gradient Method Without the Agonizing Pain” Shewchuk, See citation in Baraff/Witkin 1998