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.

Abstract—Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles. Index Terms—Interaction techniques, surface representations, geometric algorithms. æ 1

We present Easy Mesh Cutting, an intuitive and easy-to-use mesh cutout tool. Users can cut meaningful components from meshes by simply drawing freehand sketches on the mesh. Our system provides instant visual feedback to obtain the cutting results based on an improved region growing algorithm using a feature sensitive metric. The cutting boundary can be automatically optimized or easily edited by users. Extensive experimentation shows that our approach produces good cutting results while requiring little skill or effort from the user and provides a good user experience. Based on the easy mesh cutting framework, we introduce two applications including sketch-based mesh editing and mesh merging for geometry processing. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Geometric algorithms, languages, and systems 1.

We present a method for modifying the topology of a 3D model with user control. The heart of our method is a guided topology editing algorithm. Given a source model and a user-provided target shape, the algorithm modifies the source so that the resulting model is topologically consistent with the target. Our algorithm permits removing or adding various topological features (e.g., handles, cavities and islands) in a common framework and ensures that each topological change is made by minimal modification to the source model. To create the target shape, we have also designed a convenient 2D sketching interface for drawing 3D line skeletons. As demonstrated in a suite of examples, the use of sketching allows more accurate removal of topological artifacts than previous methods, and enables creative designs with specific topological goals. CR Categories: I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid, and object representations— Geometric algorithms, languages, and systems

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.

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

This article presents an intuitive and easy-to-use system for interactively posing 3D facial expressions. The user can model and edit facial expressions by drawing freeform strokes, by specifying distances between facial points, by incrementally editing curves on the face, or by directly dragging facial points in 2D screen space. Designing such an interface for 3D facial modeling and editing is challenging because many unnatural facial expressions might be consistent with the user’s input. We formulate the problem in a maximum a posteriori framework by combining the user’s input with priors embedded in a large set of facial expression data. Maximizing the posteriori allows us to generate an optimal and natural facial expression that achieves the goal specified by the user. We evaluate the performance of our system by conducting a thorough comparison of our method with alternative facial modeling techniques. To demonstrate the usability of our system, we also perform a user study of our system and compare with state-of-the-art facial expression modeling software (Poser 7).

the line drawings are not projections of the 3D model, but rather the input that generates the model. We present a new sketch-based modeling approach in which models are interactively designed by drawing their 2D silhouettes from different views. The core idea of our paper is to limit the input to 2D silhouettes, removing the need to explicitly create or position 3D elements. Arbitrarily complex models can be constructed by assembling them out of parts defined by their silhouettes, which can be combined using CSG operations. We introduce a new simplified algorithm to compute CSG solids that leverages special properties of silhouette cylinders to convert the 3D CSG problem into one that can be handled entirely with 2D operations, making implementation simpler and more robust. We evaluate our approach by modeling a random sampling of man-made objects taken from the words in WordNet, and show that all of the tested man-made objects can be modeled quickly and easily using our approach.

Assembly-based modeling is a promising approach to broadening the accessibility of 3D modeling. In assembly-based modeling, new models are assembled from shape components extracted from a database. A key challenge in assembly-based modeling is the identification of relevant components to be presented to the user. In this paper, we introduce a probabilistic reasoning approach to this problem. Given a repository of shapes, our approach learns a probabilistic graphical model that encodes semantic and geometric relationships among shape components. The probabilistic model is used to present components that are semantically and stylistically compatible with the 3D model that is being assembled. Our experiments indicate that the probabilistic model increases the relevance of presented components.

This thesis presents a modeling system that constructs 3D models of particular object classes, such as cups, airplanes, and fish, from 2D sketches. The core of the system is a sketch recognition algorithm that seeks to match the points and curves of a set of given 2D templates to the sketch. The matching process employs an optimization metric that is based on curve feature vectors. The search space of possible correspondences is restricted by encoding knowledge about relative part locations into the 2D template. Once a best-fit template is found, a 3D object is constructed using a series of measurements that are extracted from the labelled 2D sketch. The sketch-recognition and modeling algorithms are applied to sketches of cups and mugs, airplanes, and fish. The system allows non-experts to use drawings to quickly create 3D models of specific object classes.