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11
An Efficient Construction of Reduced Deformable Objects
"... Figure 1: Nonlinear simulation of a deformable object with 92 k tets computed at over 120 Hz after about 4 mins of preprocessing. Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forc ..."
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Cited by 7 (4 self)
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Figure 1: Nonlinear simulation of a deformable object with 92 k tets computed at over 120 Hz after about 4 mins of preprocessing. Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for realtime simulation of deformable objects and interactive deformationbased editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches.
An Asymptotic Numerical Method for Inverse Elastic Shape Design
"... Inverse shape design for elastic objects greatly eases the design efforts by letting users focus on desired target shapes without thinking about elastic deformations. Solving this problem using classic iterative methods (e.g., NewtonRaphson methods), however, often suffers from slow convergence t ..."
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Cited by 4 (0 self)
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Inverse shape design for elastic objects greatly eases the design efforts by letting users focus on desired target shapes without thinking about elastic deformations. Solving this problem using classic iterative methods (e.g., NewtonRaphson methods), however, often suffers from slow convergence toward a desired solution. In this paper, we propose an asymptotic numerical method that exploits the underlying mathematical structure of specific nonlinear material models, and thus runs orders of magnitude faster than traditional Newtontype methods. We apply this method to compute rest shapes for elastic fabrication, where the rest shape of an elastic object is computed such that after physical fabrication the real object deforms into a desired shape. We illustrate the performance and robustness of our method through a series of elastic fabrication experiments.
Animating deformable objects using sparse spacetime constraints
 ACM TRANSACTIONS ON GRAPHICS
"... We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and within a few seconds generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and veloc ..."
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Cited by 3 (2 self)
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We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and within a few seconds generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to lowdimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion.
ABSTRACT The PseudoRigidBody Model for Fast, Accurate, NonLinear Elasticity
, 2013
"... This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu. ..."
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This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu.
Geometry processing
"... The field of geometry processing concerns the representation, analysis, manipulation, and optimization of geometric data. It has made rapid progress motivated by, enabling, and improving the technological possibilities for the creation of digital models from realworld objects. For example, laser ..."
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The field of geometry processing concerns the representation, analysis, manipulation, and optimization of geometric data. It has made rapid progress motivated by, enabling, and improving the technological possibilities for the creation of digital models from realworld objects. For example, laser scanners sample millions of points from the surface of physical objects with high accuracy and software tools produce complex digital shapes from the sampled data. This development has a strong impact on the structure of shape processing in industry. As a consequence, software systems must be adjusted to follow this trend. For example, CAD systems, which traditionally use spline representation of surfaces, need to be able to process and optimize highly resolved polygonal meshes. This creates a demand for differential geometric concepts for polygonal meshes and stable numerical, geometric, and topological algorithms.
Interactive elastic motion editing . . .
"... We present an intuitive and interactive approach for motion editing through spacetime constraints on positions. Given an input motion of an elastic body, our approach enables the user to interactively edit node positions in order to alter and finetune the motion. We formulate our motion editing as ..."
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We present an intuitive and interactive approach for motion editing through spacetime constraints on positions. Given an input motion of an elastic body, our approach enables the user to interactively edit node positions in order to alter and finetune the motion. We formulate our motion editing as an optimization problem with dynamics constraints to enforce a physicallyplausible result. Through linearization of the editing around the input trajectory, we simplify this constrained optimal control problem into an unconstrained quadratic optimization. The optimal motion thus becomes the solution of a dense linear system, which we solve efficiently by applying the adjoint method in each iteration of a conjugate gradient solver. We demonstrate the efficiency and quality of our motion editing technique on a series of examples.
Deformation Capture and Modeling of Soft Objects
"... Figure 1: Our system can capture and model deformation behavior of generic soft objects from kinematic data alone. We can then synthesize new motions that satisfy userspecified constraints and respond to dynamic perturbations. Top: left a dinosaur walking; middle a pot holder jumping; right a co ..."
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Figure 1: Our system can capture and model deformation behavior of generic soft objects from kinematic data alone. We can then synthesize new motions that satisfy userspecified constraints and respond to dynamic perturbations. Top: left a dinosaur walking; middle a pot holder jumping; right a coat hanger skipping. Bottom: lotus leaves moving in an artificial wind field. We present a datadriven method for deformation capture and modeling of general soft objects. We adopt an iterative framework that consists of one component for physicsbased deformation tracking and another for spacetime optimization of deformation parameters. Low cost depth sensors are used for the deformation capture, and we do not require any forcedisplacement measurements, thus making the data capture a cheap and convenient process. We augment a stateoftheart probabilistic tracking method to robustly handle noise, occlusions, fast movements and large deformations. The spacetime optimization aims to match the simulated trajectories with the tracked ones. The optimized deformation model is then used to boost the accuracy of the tracking results, which can in turn improve the deformation parameter estimation itself in later iterations. Numerical experiments demonstrate that the tracking and parameter optimization components complement each other nicely. Our spacetime optimization of the deformation model includes not only the material elasticity parameters and dynamic damping coefficients, but also the reference shape which can differ significantly from the static shape for soft objects. The resulting optimization problem is highly nonlinear in high dimensions, and challenging to solve with previous methods. We propose a novel splitting algorithm that alternates between reference shape optimization and deformation parameter estimation, and thus enables tailoring the optimization of each subproblem more efficiently and robustly.
RealTime Nonlinear Shape Interpolation
"... We introduce a scheme for realtime 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 lowdimensional object in a highdimensional shape space. The interpola ..."
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We introduce a scheme for realtime 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 lowdimensional object in a highdimensional 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 lowdimensional 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 Krylovtype 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 20100 interpolated shapes per second even for the largest examples which have 500k vertices per example shape.
Interactive Material Design Using Model Reduction
"... We demonstrate an interactive method to edit the material properties of threedimensional deformable objects. The user specifies displacements and forces at a set of mesh vertices, and our system interactively computes a spatial distribution of material properties, given those constraints. We apply ..."
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We demonstrate an interactive method to edit the material properties of threedimensional deformable objects. The user specifies displacements and forces at a set of mesh vertices, and our system interactively computes a spatial distribution of material properties, given those constraints. We apply our method to linear isotropic materials, simulated using the Finite Element Method (FEM). We demonstrate that solving the problem in the fulldimensional space of individual tetrahedron material values is not practical. Instead, we propose a new model reduction method that projects the material space to a lowdimensional 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 edit 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. We physically display our distributions using haptics, as well as demonstrate how haptics can also aid in the material design. The produced inhomogeneous material distributions can also be used in computer animation applications.