Understanding how an animal can deform and articulate is essential for a realistic modification of its 3D model. In this paper, we show that such information can be learned from user-clicked 2D images and a template 3D model of the target animal. We present a volumetric deformation framework that produces a set of new 3D models by deforming a template 3D model according to a set of user-clicked images. Our framework is based on a novel locally-bounded deformation energy, where every local region has its own stiffness value that bounds how much distortion is allowed at that location. We jointly learn the local stiffness bounds as we deform the template 3D mesh to match each user-clicked image. We show that this seemingly complex task can be solved as a sequence of convex optimization problems. We demonstrate the effectiveness of our approach on cats and horses, which are highly deformable and articulated animals. Our framework produces new 3D models of animals that are significantly more plausible than methods without learned stiffness.
Most real world objects consist of non-uniform materials; as a result, during deformation the bending and shearing are distributed non-uniformly and depend on the local stiffness of the material. In the virtual environment there are three prevalent approaches to model deformation: purely geometric, physically driven, and skeleton based. This paper proposes a new approach to model deformation that incorporates non-uniform materials into the geometric deformation framework. Our approach provides a simple and intuitive method to control the distribution of the bending and shearing throughout the model according to the local material stiffness. Thus, we are able to generate realistic looking, material-aware deformations at interactive rates. Our method works on all types of models, including models with continuous stiffness gradation and non-articulated models such as cloth. The material stiffness across the surface can be specified by the user with an intuitive paint-like interface or it can be learned from a sequence of sample deformations.  One of the main challenges in editing a mesh is to retain the visual appearance of the surface after applying various modifications. In this paper we advocate the use of linear differential coordinates as means to preserve the high-frequency detail of the surface. The differential coordinates represent the details and are defined by a linear transformation of the mesh vertices. This allows the reconstruction of the edited surface by solving a linear system that satisfies the reconstruction of the local details in least squares sense. Since the differential coordinates are defined in a global coordinate system they are not rotation-invariant. To compensate for that, we rotate them to agree with the rotation of an approximated local frame. We show that the linear least squares system can be solved fast enough to guarantee interactive response time thanks to a precomputed factorization of the coefficient matrix. We demonstrate that our approach enables to edit complex detailed meshes while keeping the shape of the details in their natural orientation. This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed high-resolution meshes like those produced by scanning real-world objects. The challenge of manipulating such complex surfaces is threefold: The deformation technique has to be sufficiently fast, robust, intuitive, and easy to control to be useful for interactive applications. An intuitive and, thus, predictable deformation tool should provide physically plausible and aesthetically pleasing surface deformations, which, in particular, requires its geometric details to be preserved. The methods that we survey generally formulate surface deformation as a global variational optimization problem that addresses the differential properties of the edited surface. Efficiency and robustness are achieved by linearizing the underlying objective functional such that the global optimization amounts to solving a sparse linear system of equations. We review the different deformation energies and detail preservation techniques that were proposed in recent years, together with the various techniques to rectify the linearization artifacts. Our goal is to provide the reader with a systematic classification and comparative description of the different techniques, revealing the strengths and weaknesses of each approach in common editing scenarios. Deformation transfer applies the deformation exhibited by a source triangle mesh onto a different target triangle mesh. Our approach is general and does not require the source and target to share the same number of vertices or triangles, or to have identical connectivity. The user builds a correspondence map between the triangles of the source and those of the target by specifying a small set of vertex markers. Deformation transfer computes the set of transformations induced by the deformation of the source mesh, maps the transformations through the correspondence from the source to the target, and solves an optimization problem to consistently apply the transformations to the target shape. The resulting system of linear equations can be factored once, after which transferring a new deformation to the target mesh requires only a backsubstitution step. Global properties such as foot placement can be achieved by constraining vertex positions. We demonstrate our method by retargeting full body key poses, applying scanned facial deformations onto a digital character, and remapping rigid and non-rigid animation sequences from one mesh onto another. We present a novel technique for large deformations on 3D meshes using the volumetric graph Laplacian. We first construct a graph representing the volume inside the input mesh. The graph need not form a solid meshing of the input mesh's interior; its edges simply connect nearby points in the volume. This graph's Laplacian encodes volumetric details as the difference between each point in the graph and the average of its neighbors. Preserving these volumetric details during deformation imposes a volumetric constraint that prevents unnatural changes in volume. We also include in the graph points a short distance outside the mesh to avoid local self-intersections. Volumetric detail preservation is represented by a quadric energy function. Minimizing it preserves details in a least-squares sense, distributing error uniformly over the whole deformed mesh. It can also be combined with conventional constraints involving surface positions, details or smoothness, and efficiently minimized by solving a sparse linear system.We apply this technique in a 2D curve-based deformation system allowing novice users to create pleasing deformations with little effort. A novel application of this system is to apply nonrigid and exaggerated deformations of 2D cartoon characters to 3D meshes. We demonstrate our system's potential with several examples. We present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh is embedded in a layer of volumetric prisms, which are coupled through non-linear, elastic forces. To deform the mesh, prisms are rigidly transformed to satisfy user constraints while minimizing the elastic energy. The rigidity of the prisms prevents degenerations even under extreme deformations, making the method numerically stable. For the underlying geometric optimization we employ both local and global shape matching techniques. Our modeling framework allows for the specification of various geometrically intuitive parameters that provide control over the physical surface behavior. While computationally more involved than previous methods, our approach significantly improves robustness and simplifies user interaction for large, complex deformations. The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible met als. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.  We present an algorithm that generates natural and intuitive deformations via direct manipulation for a wide range of shape representations and editing scenarios. Our method builds a space deformation represented by a collection of affine transformations organized in a graph structure. One transformation is associated with each graph node and applies a deformation to the nearby space. Positional constraints are specified on the points of an embedded object. As the user manipulates the constraints, a nonlinear minimization problem is solved to find optimal values for the affine transformations. Feature preservation is encoded directly in the objective function by measuring the deviation of each transformation from a true rotation. This algorithm addresses the problem of "embedded deformation" since it deforms space through direct manipulation of objects embedded within it, while preserving the embedded objects' features. We demonstrate our method by editing meshes, polygon soups, mesh animations, and animated particle systems. 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 skeleton-based inverse kinematics for posing skeletons. we define mesh-based 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 multi-way morph sequences. 