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73
Laplacian Surface Editing
, 2004
"... Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We p ..."
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Cited by 242 (28 self)
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Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive freeform deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.
Realtime subspace integration for St. VenantKirchhoff deformable models
 ACM Transactions on Graphics
, 2005
"... In this paper, we present an approach for fast subspace integration of reducedcoordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reducedcoordinate deformable models for ob ..."
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Cited by 123 (12 self)
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In this paper, we present an approach for fast subspace integration of reducedcoordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reducedcoordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation models with linear materials (as commonly used in graphics) result in internal force models that are simply cubic polynomials in reduced coordinates. Coefficients of these polynomials can be precomputed, for efficient runtime evaluation. This allows simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating lowdimensional subspace bases: modal derivatives and an interactive sketching technique. Massscaled principal component analysis (massPCA) is suggested for dimensionality reduction. Finally, several examples are given from computer animation to illustrate high performance, including forcefeedback haptic rendering of a complicated object undergoing large deformations.
Interactive SkeletonDriven Dynamic Deformations
 ACM Transactions on Graphics
, 2002
"... This paper presents a framework for the skeletondriven animation of elastically deformable characters. A character is embedded in a coarse volumetric control lattice, which provides the structure needed to apply the finite element method. To incorporate skeletal controls, we introduce line constrai ..."
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Cited by 96 (1 self)
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This paper presents a framework for the skeletondriven animation of elastically deformable characters. A character is embedded in a coarse volumetric control lattice, which provides the structure needed to apply the finite element method. To incorporate skeletal controls, we introduce line constraints along the bones of simple skeletons. The bones are made to coincide with edges of the control lattice, which enables us to apply the constraints efficiently using algebraic methods. To accelerate computation, we associate regions of the volumetric mesh with particular bones and perform locally linearized simulations, which are blended at each time step. We define a hierarchical basis on the control lattice, so for detailed interactions the simulation can adapt the level of detail. We demonstrate the ability to animate complex models using simple skeletons and coarse volumetric meshes in a manner that simulates secondary motions at interactive rates.
Precomputing interactive dynamic deformable scenes
 ACM Trans. Graph
, 2003
"... dynamics by driving the scene with parameterized interactions representative of runtime usage. (b) Model reduction on observed dynamic deformations yields a lowrank approximation to the system’s parameterized impulse response functions. (c) Deformed state geometries are then sampled and used to pre ..."
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Cited by 89 (8 self)
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dynamics by driving the scene with parameterized interactions representative of runtime usage. (b) Model reduction on observed dynamic deformations yields a lowrank approximation to the system’s parameterized impulse response functions. (c) Deformed state geometries are then sampled and used to precompute and coparameterize a radiance transfer model for deformable objects. (d) The final simulation responds plausibly to interactions similar to those precomputed, includes complex collision and global illumination effects, and runs in real time. We present an approach for precomputing datadriven models of interactive physically based deformable scenes. The method permits realtime hardware synthesis of nonlinear deformation dynamics, including selfcontact and global illumination effects, and supports realtime user interaction. We use datadriven tabulation of the system’s deterministic state space dynamics, and model reduction to build efficient lowrank parameterizations of the deformed shapes. To support runtime interaction, we also tabulate impulse response functions for a palette of external excitations. Although our approach simulates particular systems under very particular interaction conditions, it has several advantages. First, parameterizing all possible scene deformations enables us to precompute novel reduced coparameterizations of global scene illumination for lowfrequency lighting conditions. Second, because the deformation dynamics are precomputed and parameterized as a whole, collisions are resolved within the scene during precomputation so that runtime selfcollision handling is implicit. Optionally, the datadriven models can be synthesized on programmable graphics hardware, leaving only the lowdimensional state space dynamics and appearance data models to be computed by the main CPU.
A Virtual Node Algorithm for Changing Mesh Topology during Simulation
 ACM Trans. Graph. (SIGGRAPH Proc
, 2004
"... We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This resu ..."
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Cited by 82 (6 self)
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We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This results in elements that contain both real material and empty regions. The missing material is contained in another copy (or copies) of this element. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material in a fashion consistent with the embedded geometry. This approach enables efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small CFL time step restrictions since they are embedded in well shaped larger elements. To enable robust simulation of embedded geometry, we propose new algorithms for handling rigid body and self collisions. In addition, we present several mechanisms for influencing and controlling fracture with grain boundaries, prescoring, etc. We illustrate our method for both volumetric and thinshell simulations.
Optimizing cubature for efficient integration of subspace deformations
 ACM Transactions on Graphics (SIGGRAPH Asia
, 2008
"... We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integr ..."
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Cited by 34 (5 self)
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We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multidimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an rdimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.VenantKirchhoff, MooneyRivlin, ArrudaBoyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration.
Skipping Steps in Deformable Simulation with Online Model Reduction
"... Finite element simulations of nonlinear deformable models are computationally costly, routinely taking hours or days to compute the motion of detailed meshes. Dimensional model reduction can make simulations orders of magnitude faster, but is unsuitable for general deformable body simulations beca ..."
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Cited by 34 (4 self)
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Finite element simulations of nonlinear deformable models are computationally costly, routinely taking hours or days to compute the motion of detailed meshes. Dimensional model reduction can make simulations orders of magnitude faster, but is unsuitable for general deformable body simulations because it requires expensive precomputations, and it can suppress motion that lies outside the span of a prespecified lowrank basis. We present an online model reduction method that does not have these limitations. In lieu of precomputation, we analyze the motion of the full model as the simulation progresses, incrementally building a reducedorder nonlinear model, and detecting when our reduced model is capable of performing the next timestep. For these subspace steps, fullmodel computation is “skipped ” and replaced with a very fast (on the order of milliseconds) reduced order step. We present algorithms for both dynamic and quasistatic simulations, and a “throttle ” parameter that allows a user to trade off between faster, approximate previews and slower, more conservative results. For detailed meshes undergoing lowrank motion, we have observed speedups of over an order of magnitude with our method.
A Multigrid Framework for RealTime Simulation of Deformable Volumes
 WORKSHOP ON VIRTUAL REALITY INTERACTION AND PHYSICAL SIMULATION (2005) F. GANOVELLI AND C. MENDOZA (EDITORS)
, 2005
"... In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and nonlinear Green strain into this framework. Based on a 3D finite eleme ..."
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Cited by 33 (11 self)
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In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and nonlinear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus with a dynamic range of several orders of magnitude. Using the linearized strain measure, we can simulate 50 thousand tetrahedral elements with 20 fps on a single processor CPU. By using corotational linearized and nonlinear Green strain, we can still simulate five thousand and two thousand elements, respectively, at the same rates.
A New Paradigm for Recognizing 3D Object Shapes from Range Data
 In Proc. of the Int. Conf. on Computer Vision (ICCV
, 2003
"... Most of the work on 3D object recognition from range data has used an alignmentverification approach in which a specific 3D object is matched to an exact instance of the same object in a scene. This approach has been successfully used in industrial machine vision, but it is not capable of dealing ..."
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Cited by 32 (2 self)
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Most of the work on 3D object recognition from range data has used an alignmentverification approach in which a specific 3D object is matched to an exact instance of the same object in a scene. This approach has been successfully used in industrial machine vision, but it is not capable of dealing with the complexities of recognizing classes of similar objects. This paper undertakes this task by proposing and testing a componentbased methodology encompassing three main ingredients: 1) a new way of learning and extracting shapeclass components from surface shape information; 2) a new shape representation called a symbolic surface signature that summarizes the geometric relationships among components; and 3) an abstract representation of shape classes formed by a hierarchy of classifiers that learn objectclass parts and their spatial relationships from examples.
Realtime Control of Physically Based Simulations using Gentle Forces
"... Figure 1: Realtime control ensures fixed simulation outcome regardless of runtime user forces: First: the rest configuration of the “T”shape structure and the two target balls. Second: reference motion from an external simulator; the two ends of the “T ” impact the two balls. Third: userperturbed ..."
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Cited by 31 (4 self)
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Figure 1: Realtime control ensures fixed simulation outcome regardless of runtime user forces: First: the rest configuration of the “T”shape structure and the two target balls. Second: reference motion from an external simulator; the two ends of the “T ” impact the two balls. Third: userperturbed realtime simulation, without control. The two ends miss the target. Fourth: controlled userperturbed realtime simulation, with gentle control forces, tracks the reference motion and successfully impacts the target. The perturbation force load (green arrow; applied 1/5 through the simulation, only in the third and fourth motion) pushes the “T ” in the opposite direction of motion. Recent advances have brought realtime physically based simulation within reach, but simulations are still difficult to control in real time. We present interactive simulations of passive systems such as deformable solids or fluids that are not only fast, but also directable: they follow given input trajectories while simultaneously reacting to user input and other unexpected disturbances. We achieve such directability using a realtime controller that runs in tandem with a realtime physically based simulation. To avoid stiff and overcontrolled systems where the natural dynamics are overpowered, the injection of control forces has to be minimized. This search for gentle forces can be made tractable in realtime by linearizing the system dynamics around the input trajectory, and then using a timevarying linear quadratic regulator to build the controller. We show examples of controlled complex deformable solids and fluids, demonstrating that our approach generates a requested fixed outcome for reasonable user inputs, while simultaneously providing runtime motion variety.