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338
Discrete mechanics and variational integrators
 Acta Numer
, 2001
"... This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the disc ..."
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Cited by 225 (31 self)
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This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic
Physically Based Deformable Models in Computer Graphics
 EUROGRAPHICS 2005 STAR – STATE OF THE ART REPORT
, 2005
"... Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich [GM97] have been addressed, thereby making these models interesting and useful for both offline and realtime applications, such as motio ..."
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Cited by 158 (3 self)
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Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich [GM97] have been addressed, thereby making these models interesting and useful for both offline and realtime applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, massspring systems, meshfree methods, coupled particle systems and reduced deformable models based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.
STRANDS: Interactive Simulation of Thin Solids using Cosserat Models
 EUROGRAPHICS 2002
, 2002
"... STRANDS are thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, a ..."
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Cited by 89 (4 self)
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STRANDS are thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, and vegetation in animation. Physical models based on spring meshes or 3D finite elements for such thin solids are either inaccurate or inefficient for interactive simulation. In this paper we show that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects. The physical model reduces to a system of spatial ordinary differential equations that can be solved efficiently for typical boundary conditions. The model handles the important geometric nonlinearity due to large changes in shape. We introduce Cosserattype physical models, describe efficient numerical methods for interactive simulation of these models, and implementation results.
Hierarchical Modeling and Analysis of Embedded Systems
, 2003
"... This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is ..."
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Cited by 76 (25 self)
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This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination
Adjoint sensitivity analysis for differentialalgebraic equations: algorithms and software
, 2002
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Notes on triangular sets and triangulationdecomposition algorithms II: Differential Systems
 SYMBOLIC AND NUMERICAL SCIENTIFIC COMPUTING
, 2003
"... This is the second in a series of two tutorial articles devoted to triangulationdecomposition algorithms. The value of these notes resides in the uniform presentation of triangulationdecomposition of polynomial and differential radical ideals with detailed proofs of all the presented results.We em ..."
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Cited by 59 (8 self)
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This is the second in a series of two tutorial articles devoted to triangulationdecomposition algorithms. The value of these notes resides in the uniform presentation of triangulationdecomposition of polynomial and differential radical ideals with detailed proofs of all the presented results.We emphasize the study of the mathematical objects manipulated by the algorithms and show their properties independently of those. We also detail a selection of algorithms, one for each task. The present article deals with differential systems. It uses results presented in the first article on polynomial systems but can be read independently.
Multiresolution green’s function methods for interactive simulation of largescale elastostatic objects
 ACM Trans. Graph
, 2003
"... This thesis presents a framework for lowlatency interactive simulation of linear elastostatic models and other systems associated with linear elliptic partial differention equations. This approach makes it feasible to interactively simulate largescale physical models. Linearity is exploited by for ..."
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Cited by 48 (11 self)
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This thesis presents a framework for lowlatency interactive simulation of linear elastostatic models and other systems associated with linear elliptic partial differention equations. This approach makes it feasible to interactively simulate largescale physical models. Linearity is exploited by formulating the boundary value problem (BVP) solution in terms of Green’s functions (GFs) which may be precomputed to provide speed and cheap lookup operations. Runtime BVPs are solved using a collection of Capacitance Matrix Algorithms (CMAs) based on the ShermanMorrisonWoodbury formula. Temporal coherence is exploited by caching and reusing, as well as sequentially updating, previous capacitance matrix inverses. Multiresolution enhancements make it practical to simulate and store very large models. Efficient compressed representations of precomputed GFs are obtained using secondgeneration wavelets defined on surfaces. Fast inverse wavelet transforms allow fast summation methods to be used to accelerate runtime BVP solution. Wavelet GF compression factors are directly related to interactive simulation speedup, and examples are provided with
Consolidation of Unorganized Point Clouds for Surface Reconstruction
"... We consolidate an unorganized point cloud with noise, outliers, nonuniformities, and in particular interference between closeby surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optim ..."
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Cited by 45 (10 self)
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We consolidate an unorganized point cloud with noise, outliers, nonuniformities, and in particular interference between closeby surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlierfree and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a prioritydriven normal propagation scheme based on a new priority measure and an orientationaware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the closeby surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data. 1
Semiimplicit spectral deferred correction methods for ordinary differential equations
 Commun. Math. Sci
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