Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an as-isometricas-possible 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.

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. Man-made objects are largely dominated by a few typical features that carry special characteristics and engineered meanings. Stateof-the-art deformation tools fall short at preserving such characteristic features and global structure. We introduce iWIRES, a novel approach based on the argument that man-made 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 analyze-and-edit approach, where prior to editing, we perform a light-weight 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 man-made shapes using our editing technique.

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 non-linear, 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 detail-preserving and intuitive deformations. Our algorithm is effective and notably easy to implement, making it attractive for practical modeling applications.

In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent real-time range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondences, holes due to occlusion are filled in from other frames. Our reconstruction technique is based on a statistical framework: The reconstruction should both match the measured data points and maximize prior probability densities that prefer smoothness, rigid deformation and smooth movements over time. The optimization procedure consists of an inner loop that optimizes the 4D shape using continuous numerical optimization and an outer loop that infers the discrete 4D topology of the data set using an iterative model assembly algorithm. We apply the technique to a variety of data sets, demonstrating that the new approach is capable of robustly retrieving animated models with correspondences from data sets suffering from significant noise, outliers and acquisition holes.

We present a novel algorithm to jointly capture the motion and the dynamic shape of humans from multiple video streams without using optical markers. Instead of relying on kinematic skeletons, as traditional motion capture methods, our approach uses a deformable high-quality mesh of a human as scene representation. It jointly uses an imagebased 3D correspondence estimation algorithm and a fast Laplacian mesh deformation scheme to capture both motion and surface deformation of the actor from the input video footage. As opposed to many related methods, our algorithm can track people wearing wide apparel, it can straightforwardly be applied to any type of subject, e.g. animals, and it preserves the connectivity of the mesh over time. We demonstrate the performance of our approach using synthetic and captured real-world video sequences and validate its accuracy by comparison to the ground truth. 1.

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.

This paper introduces a method for mesh editing, aimed at preserving shape and volume. We present two new developments: the first is a minimization of a functional expressing a geometric distance measure between two isometric surfaces. The second is a local volume analysis linking the volume of an object to its surface curvature. Our method is based upon the moving frames representation of meshes. Applying a rotation field to the moving frames defines an isometry. Given rotational constraints, the mesh is deformed by an optimal isometry defined by minimizing the distance measure between the original and the deformed meshes. The resulting isometry nicely preserves the surface details, but, when large rotations are applied, the volumetric behavior of the model may be unsatisfactory. Using the local volume analysis, we define a scalar field by which we scale the moving frames. The scaled and rotated moving frames restore the volumetric properties of the original mesh, while properly maintaining the surface details. Our results show that even extreme deformations can be applied to meshes, with only minimal distortion of surface details and object volume.

Figure 1: Two representative models that users can interactively manipulate within our deformation system. (a) (column 1:) A desk lamp connected by revolute joints, and its color-coded components. The lampshade is manipulated with the same handle trajectory for three cases: (column 2:) joint-unaware deformation has difficulty facing the lampshade backward because of immovable joints, and links are bent unnaturally(131 cells). (column 3:) joint-aware deformation with fully rigid links(6 cells). (column 4:) joint-aware deformation with two deformable links in the middle(76 cells). (b) An Aibo-like robot dog with a soft tail, a soft body, and two soft ears interactively posed to walk and stand up. (b) Complex mesh models of man-made objects often consist of multiple components connected by various types of joints. We propose a joint-aware deformation framework that supports the direct manipulation of an arbitrary mix of rigid and deformable components. First we apply slippable motion analysis to automatically detect multiple types of joint constraints that are implicit in model geometry. For single-component geometry or models with disconnected components, we support user-defined virtual joints. Then we integrate manipulation handle constraints, multiple components, joint constraints, joint limits, and deformation energies into a single volumetric-cell-based space deformation problem. An iterative, parallelized Gauss-Newton solver is used to solve the resulting nonlinear optimization. Interactive deformable manipulation is demonstrated on a variety of geometric models while automatically respecting their multi-component nature and the natural behavior of their joints.

We present mesh puppetry, a variational framework for detailpreserving mesh manipulation through a set of high-level, intuitive, and interactive design tools. Our approach builds upon traditional rigging by optimizing skeleton position and vertex weights in an integrated manner. New poses and animations are created by specifying a few desired constraints on vertex positions, balance of the character, length and rigidity preservation, joint limits, and/or selfcollision avoidance. Our algorithm then adjusts the skeleton and solves for the deformed mesh simultaneously through a novel cascading optimization procedure, allowing realtime manipulation of meshes with 50K+ vertices for fast design of pleasing and realistic poses. We demonstrate the potential of our framework through an interactive deformation platform and various applications such as deformation transfer and motion retargeting.

We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object’s volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes.