SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Good vibrations: modal dynamics for graphics and animation
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Interactive spacetime control for animation
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Motion editing with spacetime constraints
Proceedings of the 1997 symposium on Interactive 3D graphics
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Faking Dynamics of Ropes and Springs
IEEE Computer Graphics and Applications
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Efficient synthesis of physically valid human motion
ACM SIGGRAPH 2003 Papers
Keyframe control of smoke simulations
ACM SIGGRAPH 2003 Papers
Motion sketching for control of rigid-body simulations
ACM Transactions on Graphics (TOG)
Fluid control using the adjoint method
ACM SIGGRAPH 2004 Papers
Synthesizing physically realistic human motion in low-dimensional, behavior-specific spaces
ACM SIGGRAPH 2004 Papers
Adaptation of performed ballistic motion
ACM Transactions on Graphics (TOG)
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
Model reduction for real-time fluids
ACM SIGGRAPH 2006 Papers
Subspace gradient domain mesh deformation
ACM SIGGRAPH 2006 Papers
Keyframe control of complex particle systems using the adjoint method
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Constraint-based motion optimization using a statistical dynamic model
ACM SIGGRAPH 2007 papers
TRACKS: toward directable thin shells
ACM SIGGRAPH 2007 papers
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Efficient symbolic differentiation for graphics applications
ACM SIGGRAPH 2007 papers
Animating oscillatory motion with overlap: wiggly splines
ACM SIGGRAPH 2008 papers
Modular bases for fluid dynamics
ACM SIGGRAPH 2009 papers
Deformable object animation using reduced optimal control
ACM SIGGRAPH 2009 papers
Geodesics in Shape Space via Variational Time Discretization
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Skipping steps in deformable simulation with online model reduction
ACM SIGGRAPH Asia 2009 papers
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Interactive surface modeling using modal analysis
ACM Transactions on Graphics (TOG)
Modal shape analysis beyond Laplacian
Computer Aided Geometric Design
An efficient construction of reduced deformable objects
ACM Transactions on Graphics (TOG)
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Creating motions of objects or characters that are physically plausible and follow an animator's intent is a key task in computer animation. The spacetime constraints paradigm is a valuable approach to this problem, but it suffers from high computational costs. Based on spacetime constraints, we propose a framework for controlling the motion of deformable objects that offers interactive response times. This is achieved by a model reduction of the underlying variational problem, which combines dimension reduction, multipoint linearization, and decoupling of ODEs. After a preprocess, the cost for creating or editing a motion is reduced to solving a number of one-dimensional spacetime problems, whose solutions are the wiggly splines introduced by Kass and Anderson [2008]. We achieve interactive response times through a new fast and robust numerical scheme for solving the one-dimensional problems that is based on a closed-form representation of the wiggly splines.