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312
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 167 (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.
Point Based Animation of Elastic, Plastic and Melting Objects
, 2004
"... We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original sha ..."
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Cited by 119 (12 self)
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We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio. In each step
R.: Interpolating and approximating implicit surfaces from polygon soup
 In Proceedings of ACM SIGGRAPH
, 2004
"... This paper describes a method for building interpolating or approximating implicit surfaces from polygonal data. The user can choose to generate a surface that exactly interpolates the polygons, or a surface that approximates the input by smoothing away features smaller than some userspecified size ..."
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Cited by 118 (2 self)
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This paper describes a method for building interpolating or approximating implicit surfaces from polygonal data. The user can choose to generate a surface that exactly interpolates the polygons, or a surface that approximates the input by smoothing away features smaller than some userspecified size. The implicit functions are represented using a moving leastsquares formulation with constraints integrated over the polygons. The paper also presents an improved method for enforcing normal constraints and an iterative procedure for ensuring that the implicit surface tightly encloses the input vertices.
Moving Least Square Reproducing Kernel Method (III): Wavelet Packet Its Applications
, 1997
"... This work is a natural extension of the work done in Part II of this series. A new partition of unity  the synchronized reproducing kernel (SRK) interpolantis proposed within the framework of moving least square reproducing kernel representation. It is a further development and generalization ..."
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Cited by 64 (13 self)
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This work is a natural extension of the work done in Part II of this series. A new partition of unity  the synchronized reproducing kernel (SRK) interpolantis proposed within the framework of moving least square reproducing kernel representation. It is a further development and generalization of the reproducing kernel particle method (RKPM), which demonstrates some superior computational capability in multiple scale numerical simulations. To form such an interpolant, a class of new wavelet functions are introduced in an unconventional way, and they form an independent sequence that is referred to as the wavelet packet. By choosing different combinations in the wavelet series expansion, the desirable synchronized convergence effect in interpolation can be achieved. Based upon the builtin consistency conditions, the differential consistency conditions for the wavelet functions are derived. It serves as an indispensable instrument in establishing the interpolation error estimate, w...
The Natural Element Method In Solid Mechanics
, 1998
"... The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal descripti ..."
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Cited by 61 (14 self)
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The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal description of the boundary @ In the Natural Element Method, the trial and test functions are constructed using natural neighbor interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N . The interpolants are smooth (C NEM is identical to linear finite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and nonconvex bodies (cracks) using NEM is also described.
The extended/generalized finite element method: An overview of the method and its applications
 International Journal for Numerical Methods in Engineering
, 2010
"... Abstract. The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evo ..."
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Cited by 59 (3 self)
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Abstract. The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.
Animating Gases with Hybrid Meshes
, 2005
"... This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with re ..."
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Cited by 57 (2 self)
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This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with regular hexahedral cells in a single mesh. This hybrid mesh offers both accuracy near obstacles and efficiency in open regions.
Generalized finite element methods for three dimensional structural mechanics problems
 Computers and Structures
"... The present paper summarizes the generalized nite element method formulation and demonstrates some of its advantages over traditional nite element methods to solve complex, threedimensional structural mechanics problems. ..."
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Cited by 50 (8 self)
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The present paper summarizes the generalized nite element method formulation and demonstrates some of its advantages over traditional nite element methods to solve complex, threedimensional structural mechanics problems.
Local maximumentropy approximation schemes: a seamless bridge between finite elements and meshfree methods
 Int. J. Numer. Methods Engrg
, 2005
"... We present a oneparameter family of approximation schemes, which we refer to as local maximumentropy approximation schemes, that bridges continuously two important limits: Delaunay triangulation and maximumentropy (maxent) statistical inference. Local maxent approximation schemes represent a com ..."
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Cited by 45 (3 self)
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We present a oneparameter family of approximation schemes, which we refer to as local maximumentropy approximation schemes, that bridges continuously two important limits: Delaunay triangulation and maximumentropy (maxent) statistical inference. Local maxent approximation schemes represent a compromise—in the sense of Pareto optimality—between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width. Local maxent approximation schemes are entirely defined by the node set and the domain of analysis, and the shape functions are positive, interpolate affine functions exactly, and have a weak Kroneckerdelta property at the boundary. Local maxent approximation may be regarded as a regularization, or thermalization, of Delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation. Local maxent approximation schemes can be taken as a convenient basis for the numerical solution of PDEs in the style of meshfree Galerkin methods. In test cases characterized by smooth solutions we find that the accuracy of local maxent approximation schemes is vastly superior to that of finite elements. Copyright � 2005 John
Conforming polygonal finite elements
 International Journal for Numerical Methods in Engineering
, 2004
"... In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are bettersuited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, rece ..."
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Cited by 44 (11 self)
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In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are bettersuited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to construct different trial and test approximations on polygonal elements. A particular and notable contribution is the use of meshfree (naturalneighbour, nn) basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons. This numerical formulation enables the construction of conforming approximation on ngons (n � 3), and hence extends the potential applications of finite elements to convex polygons of arbitrary order. Numerical experiments on secondorder elliptic boundaryvalue problems are presented to demonstrate the accuracy and convergence of the proposed method. Copyright � 2004 John Wiley & Sons, Ltd. KEY WORDS: meshfree methods; natural neighbour interpolants; natural element method; Laplace interpolant; Wachspress basis functions; mean value coordinates