Transcript Overview Class #8 (Tues, Feb 10) • • • • • Deformation in Graphics Assignments due today. “5 late days” rule. Hand-in procedures... AFS disk space: – /afs/cs.cmu.edu/academic/class/15863-s03 – alla/ cdtwigg/ dmowatt/ ids/ kayvonf/

Overview
Class #8 (Tues, Feb 10)
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Deformation in Graphics
Assignments due today.
“5 late days” rule.
Hand-in procedures...
AFS disk space:
– /afs/cs.cmu.edu/academic/class/15863-s03
– alla/ cdtwigg/ dmowatt/ ids/
kayvonf/ mig/
mmt/
rmelamud/ sriramv/ barbic/ djames/ gbr/
jongchul/
mbz/
mmandel/ mwh/ rywang/
Deformation in Graphics
• Long history in graphics
• Two classes of deformation
– Purely geometric deformation
– Physically based deformation
• Both are extremely important in practice
• Why?
– Goals, realism, animator control, ...
• Deformation basis, u=Uq
– Local vs global bases related to sparsity of U and
(often) formulation stiffness of time-stepping
Geometric Deformation
Alan H. Barr, Global and Local Deformations of Solid
Primitives, Computer Graphics (Proceedings of
SIGGRAPH 84). 18(3), pp. 21-30, 1984.
• Introduced hierarchical
transformation of surfaces
• Local/tangent transformation
matrices (Jacobians)
• Locally specified deformation
• Blending of fundamental
deformations: twisting, bending,
tapering, ...
• Now mainstream
Thomas W. Sederberg, Scott R. Parry, Free-Form
Deformation of Solid Geometric Models, Computer
Graphics (Proceedings of SIGGRAPH 86). 20(4), pp.
151-160, 1986.
Sabine Coquillart, Extended Free-Form Deformation: A
Sculpturing Tool for 3D Geometric Modeling,Computer
Graphics (Proceedings of SIGGRAPH 90). 24(4), pp.
187-196, 1990.
Sabine Coquillart, Extended Free-Form Deformation: A
Sculpturing Tool for 3D Geometric Modeling,Computer
Graphics (Proceedings of SIGGRAPH 90). 24(4), pp.
187-196, 1990.
William M. Hsu, John F. Hughes, Henry Kaufman, Direct
manipulation of free-form deformations, Computer
Graphics (Proceedings of SIGGRAPH 92). 26(2), pp.
177-184, 1992.
• Working with control points can be
awkward
• Apply (displacement) constraints
directly to surface
William M. Hsu, John F. Hughes, Henry Kaufman, Direct
manipulation of free-form deformations, Computer
Graphics (Proceedings of SIGGRAPH 92). 26(2), pp.
177-184, 1992.
If not all control points can move...
Karan Singh, Eugene L. Fiume, Wires: A Geometric
Deformation Technique, Proceedings of SIGGRAPH 98.
pp. 405-414, 1998.
Physically Based Deformation
Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K.
Elastically Deformable Models, ACM SIGGRAPH 87,
205-214, 1987.
• Major contribution to physically based
deformable models in graphics (read!)
• Lagrangian derivation of eqns of motion
(similar to our equations yesterday)
Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K.
Elastically Deformable Models, ACM SIGGRAPH 87,
205-214, 1987.
• Finite difference discretization on grids
• Semi-implicit integration...
Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K.
Elastically Deformable Models, ACM SIGGRAPH 87,
205-214, 1987.
Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K.
Elastically Deformable Models, ACM SIGGRAPH 87,
205-214, 1987.
Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K.
Elastically Deformable Models, ACM SIGGRAPH 87,
205-214, 1987.
John C. Platt, Alan H. Barr
Constraint methods for flexible models, ACM
SIGGRAPH Computer Graphics, June 1988.
• Look at deformation as a
minimization process:
– locally minimize f(x)
• Consider two types of constraints:
– Reaction constraints
– Augmented Lagrangian constraints
• Nice description of Lagrangian
constraints for deformable models;
saddle point problem
• Constrained optimization problem:
John C. Platt, Alan H. Barr
Constraint methods for flexible models, ACM
SIGGRAPH Computer Graphics, June 1988.
John C. Platt, Alan H. Barr
Constraint methods for flexible models, ACM
SIGGRAPH Computer Graphics, June 1988.
John C. Platt, Alan H. Barr
Constraint methods for flexible models, ACM
SIGGRAPH Computer Graphics, June 1988.
Alex Pentland, John Williams, Good Vibrations: Modal
Dynamics for Graphics and Animation, Computer
Graphics (Proceedings of SIGGRAPH 89). 23(3), pp.
215-222, 1989.
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Modal analysis for linear elastodynamics
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Modal transformation converts coupled ODEs
into a decoupled system of ODEs
No time-stepping stiffness
More later with DyRT02 and sound
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Alex Pentland, John Williams, Good Vibrations: Modal
Dynamics for Graphics and Animation, Computer
Graphics (Proceedings of SIGGRAPH 89). 23(3), pp.
215-222, 1989.
Alex Pentland, John Williams, Good Vibrations: Modal
Dynamics for Graphics and Animation, Computer
Graphics (Proceedings of SIGGRAPH 89). 23(3), pp.
215-222, 1989.
• “Approximate modes”
• Volumetric collision handling
Dimitri Metaxas, Demetri Terzopoulos, Dynamic
deformation of solid primitives with constraints, ACM
SIGGRAPH Computer Graphics, 26(2), p.309-312, July
1992.
• Use global deformation basis with, e.g.,
FEM models
• Unstabilized system
• Baumgarte stabilization used
• Use a specialized local constraint solver
Dimitri Metaxas, Demetri Terzopoulos, Dynamic
deformation of solid primitives with constraints, ACM
SIGGRAPH Computer Graphics, 26(2), p.309-312, July
1992.
Dimitri Metaxas, Demetri Terzopoulos, Dynamic
deformation of solid primitives with constraints, ACM
SIGGRAPH Computer Graphics, 26(2), p.309-312, July
1992.
David Baraff, Andrew Witkin, Dynamic simulation of
non-penetrating flexible bodies, Computer Graphics
(Proceedings of SIGGRAPH 92). 26(2), pp. 303-308,
1992.
• Addresses defo numerical stiffness
• Use global deformation basis, similar to
Pentland and Williams, but don’t
assume linear elastodynamics
• Related to “subspace projection”
• Use derivation from Witkin-Welch-1990.
Marie-Paule Gascuel, An implicit formulation for
precise contact modeling between flexible solids, ACM
SIGGRAPH 93, p.313-320, September 1993.
• Implicit handling of contact between
quasistatic deformable models.
• Two components:
– A rigid component which obeys the rigid
body equations of motion. Its mass
distribution corresponds to the object’s
rest shape.
– A deformable layer at rest relative to the
rigid layer.
• Stiffness modeled using field functions
Marie-Paule Gascuel, An implicit formulation for
precise contact modeling between flexible solids, ACM
SIGGRAPH 93, p.313-320, September 1993.
• Contact zone definition: fi(P) = fj(P)
Marie-Paule Gascuel, An implicit formulation for
precise contact modeling between flexible solids, ACM
SIGGRAPH 93, p.313-320, September 1993.
Marie-Paule Gascuel, An implicit formulation for
precise contact modeling between flexible solids, ACM
SIGGRAPH 93, p.313-320, September 1993.
Also work by Desbrun + Cani. Will discuss implicit methods more later.
Demetri Terzopoulos , Hong Qin, Dynamic NURBS with
geometric constraints for interactive sculpting, ACM
Transactions on Graphics (TOG), v.13 n.2, p.103-136,
April 1994.
• Use NURBS as shape functions
• Adds support for forces and
other constraints to geometric
modeling
• Lagrangian mechanics
Demetri Terzopoulos , Hong Qin, Dynamic NURBS with
geometric constraints for interactive sculpting, ACM
Transactions on Graphics (TOG), v.13 n.2, p.103-136,
April 1994.
• Final Baumgarte stabilized (a,b) system:
Dynamic Free-Form Deformations for Animation Synthesis
Petros Faloutsos, Michiel van de Panne, Demetri Terzopoulos.
IEEE Transactions on Visualization and Computer Graphics. 3(3), pp. 201214, 1997.
• Use FFDs as shape functions
Sarah F. F. Gibson, 3D Chainmail: a Fast Algorithm for
Deforming Volumetric Objects, 1997 Symposium on
Interactive 3D Graphics. pp. 149-154, 1997.
• Simple energy minimizing relaxation
scheme
• Quasistatic deformation in the limit
• Simple but works for huge systems
– Complex volume models