Space-time editing of elastic motion through material optimization and reduction

Li, Siwang; Huang, Jin; Goes, Fernando de; Jin, Xiaogang; Bao, Hujun; Desbrun, Mathieu

doi:10.1145/2601097.2601217

Cited by 57 publications

(36 citation statements)

References 38 publications

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“…We demonstrate how to apply model reduction to the material distribution, and present an interactive design process where we are able to rapidly iterate many design options and display the resulting shapes and forces using a haptic multimodal interface. Material optimization for space-time motion editing has also recently been explored by Li et al [2014]. They optimized materials to minimize control forces under spacetime position constraints, whereas in our method, forces are prescribed as inputs.…”

Section: Related Workmentioning

confidence: 99%

Interactive Material Design Using Model Reduction

Chen

et al. 2015

ACM Trans. Graph.

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We demonstrate an interactive method to create heterogeneous continuous deformable materials on complex three-dimensional meshes. The user specifies displacements and internal elastic forces at a chosen set of mesh vertices. Our system then rapidly solves an optimization problem to compute a corresponding heterogeneous spatial distribution of material properties using the Finite Element Method (FEM) analysis. We apply our method to linear and nonlinear isotropic deformable materials. We demonstrate that solving the problem interactively in the full-dimensional space of individual tetrahedron material values is not practical. Instead, we propose a new model reduction method that projects the material space to a low-dimensional space of material modes. Our model reduction accelerates optimization by two orders of magnitude and makes the convergence much more robust, making it possible to interactively design material distributions on complex meshes. We apply our method to precise control of contact forces and control of pressure over large contact areas between rigid and deformable objects for ergonomics. Our tetrahedron-based dithering method can efficiently convert continuous material distributions into discrete ones and we demonstrate its precision via FEM simulation. We physically display our distributions using haptics, as well as demonstrate how haptics can aid in the material design. The produced heterogeneous material distributions can also be used in computer animation applications.

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Section: Related Workmentioning

confidence: 99%

Interactive Material Design Using Model Reduction

Chen

et al. 2015

ACM Trans. Graph.

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“…Recent works find optimal material properties for deformation behavior under external forces for 3D fabrication [Bickel et al 2009] and animation control [Lee and Lin 2012;Li et al 2014;Xu et al 2015]. Contact sounds are also affected by object material properties, where pleasing and repeatable sound requires stiffness for vibration.…”

Section: Contact Sound Simulationmentioning

confidence: 99%

Computational design of metallophone contact sounds

Bharaj¹,

Levin

Tompkin³

et al. 2015

ACM Trans. Graph.

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Metallophones such as glockenspiels produce sounds in response to contact. Building these instruments is a complicated process, limiting their shapes to well-understood designs such as bars. We automatically optimize the shape of arbitrary 2D and 3D objects through deformation and perforation to produce sounds when struck which match user-supplied frequency and amplitude spectra. This optimization requires navigating a complex energy landscape, for which we develop Latin Complement Sampling to both speed up finding minima and provide probabilistic bounds on landscape exploration. Our method produces instruments which perform similarly to those that have been professionallymanufactured, while also expanding the scope of shape and sound that can be realized, e.g., single object chords. Furthermore, we can optimize sound spectra to create overtones and to dampen specific frequencies. Thus our technique allows even novices to design metallophones with unique sound and appearance.

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“…Motions are computed by solving nonlinear constrained space-time optimization problems, and model reduction techniques are used to accelerate the computations (see Barbič et al [2009] and Hildebrandt et al [2012]). Recently, space-time optimization of the dynamics of elastic objects has been used for interactive editing of simulations and animations [Barbič et al 2012;Li et al 2014] and for creating motions that interpolate a set of partial keyframes [Schulz et al 2014]. …”

Section: Related Workmentioning

confidence: 99%

Real-Time Nonlinear Shape Interpolation

et al. 2015

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We introduce a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. To achieve this, we restrict the optimization to a low-dimensional subspace that is specifically designed for the shape interpolation problem. The construction of the subspace is based on two components: a formula for the calculation of derivatives of the interpolated shapes and a Krylov-type sequence that combines the derivatives and the Hessian of the objective functional. To make the computational cost for solving the reduced optimization problem independent of the resolution of the example shapes, we combine the dimensional reduction with schemes for the efficient approximation of the reduced nonlinear objective functional and its gradient. In our experiments, we obtain rates of 20-100 interpolated shapes per second, even for the largest examples which have 500k vertices per example shape.

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Space-time editing of elastic motion through material optimization and reduction

Cited by 57 publications

References 38 publications

Interactive Material Design Using Model Reduction

Interactive Material Design Using Model Reduction

Computational design of metallophone contact sounds

Real-Time Nonlinear Shape Interpolation

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