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235
Asrigidaspossible shape manipulation
 ACM Trans. Graph
, 2005
"... We present an interactive system that lets a user move and deform a twodimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The ..."
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Cited by 189 (18 self)
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We present an interactive system that lets a user move and deform a twodimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The system then computes the positions of the remaining free vertices by minimizing the distortion of each triangle. While physically based simulation or iterative refinement can also be used for this purpose, they tend to be slow. We present a twostep closedform algorithm that achieves realtime interaction. The first step finds an appropriate rotation for each triangle and the second step adjusts its scale. The key idea is to use quadratic error metrics so that each minimization problem becomes a system of linear equations. After solving the simultaneous equations at the beginning of interaction, we can quickly find the positions of free vertices during interactive manipulation. Our approach successfully conveys a sense of rigidity of the shape, which is difficult in spacewarp approaches. With a multiplepoint input device, even beginners can easily move, rotate, and deform shapes at will.
Mesh Editing with PoissonBased Gradient Field Manipulation
 ACM TRANS. GRAPH
, 2004
"... In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pl ..."
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Cited by 175 (17 self)
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In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.
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 164 (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.
AsRigidAsPossible Surface Modeling
 TO APPEAR AT THE EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING
, 2007
"... Modeling tasks, such as surface deformation and editing, can be analyzed by observing the local behavior of the surface. We argue that defining a modeling operation by asking for rigidity of the local transformations is useful in various settings. Such formulation leads to a nonlinear, yet conceptu ..."
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Cited by 119 (7 self)
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Modeling tasks, such as surface deformation and editing, can be analyzed by observing the local behavior of the surface. We argue that defining a modeling operation by asking for rigidity of the local transformations is useful in various settings. Such formulation leads to a nonlinear, yet conceptually simple energy formulation, which is to be minimized by the deformed surface under particular modeling constraints. We devise a simple iterative mesh editing scheme based on this principle, that leads to detailpreserving and intuitive deformations. Our algorithm is effective and notably easy to implement, making it attractive for practical modeling applications.
Meshbased inverse kinematics
 ACM Trans. Graph
, 2005
"... The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid m ..."
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Cited by 98 (8 self)
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The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid mesh configurations, and a selection mechanism for choosing among them. Drawing an analogy to the traditional use of skeletonbased inverse kinematics for posing skeletons, we define meshbased inverse kinematics as the problem of finding meaningful mesh deformations that meet specified vertex constraints. Our solution relies on example meshes to indicate the class of meaningful deformations. Each example is represented with a feature vector of deformation gradients that capture the affine transformations which individual triangles undergo relative to a reference pose. To pose a mesh, our algorithm efficiently searches among all meshes with specified vertex positions to find the one that is closest to some pose in a nonlinear span of the example feature vectors. Since the search is not restricted to the span of example shapes, this produces compelling deformations even when the constraints require poses that are different from those observed in the examples. Furthermore, because the span is formed by a nonlinear blend of the example feature vectors, the blending component of our system may also be used independently to pose meshes by specifying blending weights or to compute multiway morph sequences.
Subspace Gradient Domain Mesh Deformation
 In SIGGRAPH ’06
, 2006
"... In this paper we present a general framework for performing constrained mesh deformation tasks with gradient domain techniques. We present a gradient domain technique that works well with a wide variety of linear and nonlinear constraints. The constraints we introduce include the nonlinear volume co ..."
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Cited by 95 (14 self)
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In this paper we present a general framework for performing constrained mesh deformation tasks with gradient domain techniques. We present a gradient domain technique that works well with a wide variety of linear and nonlinear constraints. The constraints we introduce include the nonlinear volume constraint for volume preservation, the nonlinear skeleton constraint for maintaining the rigidity of limb segments of articulated figures, and the projection constraint for easy manipulation of the mesh without having to frequently switch between multiple viewpoints. To handle nonlinear constraints, we cast mesh deformation as a nonlinear energy minimization problem and solve the problem using an iterative algorithm. The main challenges in solving this nonlinear problem are the slow convergence and numerical instability of the iterative solver. To address these issues, we develop a subspace technique that builds a coarse control mesh around the original mesh and projects the deformation energy and constraints onto the control mesh vertices using the mean value interpolation. The energy minimization is then carried out in the subspace formed by the control mesh vertices. Running in this subspace, our energy minimization solver is both fast and stable and it provides interactive responses. We demonstrate our deformation constraints and subspace deformation technique with a variety of constrained deformation examples.
A sketchbased interface for detailpreserving mesh editing
 ACM Trans. Graph
, 2005
"... In this paper we present a method for the intuitive editing of surface meshes by means of viewdependent sketching. In most existing shape deformation work, editing is carried out by selecting and moving a handle, usually a set of vertices. Our system lets the user easily determine the handle, eit ..."
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Cited by 91 (6 self)
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In this paper we present a method for the intuitive editing of surface meshes by means of viewdependent sketching. In most existing shape deformation work, editing is carried out by selecting and moving a handle, usually a set of vertices. Our system lets the user easily determine the handle, either by silhouette selection and cropping, or by sketching directly onto the surface. Subsequently, an edit is carried out by sketching a new, viewdependent handle position or by indirectly influencing differential properties along the sketch. Combined, these editing and handle metaphors greatly simplify otherwise complex shape modeling tasks.
iWIRES: An analyzeandedit approach to shape manipulation
 ACM SIGGRAPH Trans. Graph
, 2009
"... Figure 1: A complex model (left) consisting of 108 components is analyzed and 250 intelligent wires (in green) are extracted. Editing a few wires induces a new wire configuration (in blue) and leads to the result on the right. Manmade objects are largely dominated by a few typical features that car ..."
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Cited by 88 (25 self)
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Figure 1: A complex model (left) consisting of 108 components is analyzed and 250 intelligent wires (in green) are extracted. Editing a few wires induces a new wire configuration (in blue) and leads to the result on the right. Manmade objects are largely dominated by a few typical features that carry special characteristics and engineered meanings. Stateoftheart deformation tools fall short at preserving such characteristic features and global structure. We introduce iWIRES, a novel approach based on the argument that manmade models can be distilled using a few special 1D wires and their mutual relations. We hypothesize that maintaining the properties of such a small number of wires allows preserving the defining characteristics of the entire object. We introduce an analyzeandedit approach, where prior to editing, we perform a lightweight analysis of the input shape to extract a descriptive set of wires. Analyzing the individual and mutual properties of the wires, and augmenting them with geometric attributes makes them intelligent and ready to be manipulated. Editing the object by modifying the intelligent wires leads to a powerful editing framework that retains the original design intent and object characteristics. We show numerous results of manipulation of manmade shapes using our editing technique.
Geometric modeling in shape space
 In Proc. SIGGRAPH
, 2007
"... Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an asisometricaspossible fashion (shown in green), and the resulting path is geodesically continued (shown in purple) to naturally extend the sequence. No semantic information, ..."
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Cited by 74 (8 self)
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Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an asisometricaspossible fashion (shown in green), and the resulting path is geodesically continued (shown in purple) to naturally extend the sequence. No semantic information, segmentation, or knowledge of articulated components is used. We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes – triangular meshes or more generally straight line graphs in Euclidean space – are treated as points in a shape space. We introduce useful Riemannian metrics in this space to aid the user in design and modeling tasks, especially to explore the space of (approximately) isometric deformations of a given shape. Much of the work relies on an efficient algorithm to compute geodesics in shape spaces; to this end, we present a multiresolution framework to solve the interpolation problem – which amounts to solving a boundary value problem – as well as the extrapolation problem – an initial value problem – in shape space. Based on these two operations, several classical concepts like parallel transport and the exponential map can be used in shape space to solve various geometric modeling and geometry processing tasks. Applications include shape morphing, shape deformation, deformation transfer, and intuitive shape exploration.
Mesh parameterization methods and their applications
 FOUNDATIONS AND TRENDSÂŐ IN COMPUTER GRAPHICS AND VISION
, 2006
"... We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, intersurface mapping, and parameterization with co ..."
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Cited by 69 (2 self)
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We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, intersurface mapping, and parameterization with constraints. We start by describing the wide range of applications where parameterization tools have been used in recent years. We then briefly review the pertinent mathematical background and terminology, before proceeding to survey the existing parameterization techniques. Our survey summarizes the main ideas of each technique and discusses its main properties, comparing it to other methods available. Thus it aims to provide guidance to researchers and developers when assessing the suitability of different methods for various applications. This survey focuses on the practical aspects of the methods available, such as time complexity and robustness and shows multiple examples of parameterizations generated using different methods, allowing the reader to visually evaluate and compare the results.