Real-time Deformation with Coupled Cages and Skeletons

Real-time character deformation is an essential topic in Computer Animation. Deformations can be achieved by using several techniques, but the skeleton-based ones are the most popular. Skeletons allow artists to deform articulated parts of the digital characters by moving their bones. Other techniques, like cage-based ones, are gaining popularity but struggle to be included in animation workflows because they require to change the animation pipeline substantially. This thesis formalizes a technique that allows animators to embed cage-based deformations in standard skeleton-based pipelines. The described skeleton/cage hybrid allows artists to enrich the expressive powers of the skeletons with the degrees of freedom offered by cages. Furthermore, this thesis describes two Graphical User Interfaces dedicated to deformations and animations. The first one, CageLab, allows artists to define cage-based deformations and perform cage editing. The second one, SuperCages GUI, allows artists to author animations and deformations by using the skeleton/cage hybrid described earlier

Topological Rigid String Theory and Two Dimensional QCD

We present a string theory that reproduces the large-$N$ expansion of two dimensional Yang-Mills gauge theory on arbitrary surfaces. First, a new class of topological sigma models is introduced, with path integrals localized to the moduli space of harmonic maps. The Lagrangian of these harmonic topological sigma models is of fourth order in worldsheet derivatives. Then we gauge worldsheet diffeomorphisms by introducing the induced worldsheet metric. This leads to a topological string theory, whose Lagrangian coincides in the bose sector with the rigid string Lagrangian discussed some time ago by Polyakov and others as a candidate for QCD string theory. The path integral of this topological rigid string theory is localized to the moduli spaces of minimal-area maps, and calculates their Euler numbers. The dependence of the large-$N$ QCD partition functions on the target area emerges from measuring the volume of the moduli spaces, and can be reproduced by adding a Nambu-Goto term (improved by fermionic terms) to the Lagrangian of the topological rigid string.Comment: 55 pages, phyzzx, no figures. (One subsection added, on "Comparison to Previous Results"; final version to appear in Nucl. Phys. B.

A Revisit of Shape Editing Techniques: from the Geometric to the Neural Viewpoint

3D shape editing is widely used in a range of applications such as movie production, computer games and computer aided design. It is also a popular research topic in computer graphics and computer vision. In past decades, researchers have developed a series of editing methods to make the editing process faster, more robust, and more reliable. Traditionally, the deformed shape is determined by the optimal transformation and weights for an energy term. With increasing availability of 3D shapes on the Internet, data-driven methods were proposed to improve the editing results. More recently as the deep neural networks became popular, many deep learning based editing methods have been developed in this field, which is naturally data-driven. We mainly survey recent research works from the geometric viewpoint to those emerging neural deformation techniques and categorize them into organic shape editing methods and man-made model editing methods. Both traditional methods and recent neural network based methods are reviewed

OptCtrlPoints: Finding the Optimal Control Points for Biharmonic 3D Shape Deformation

We propose OptCtrlPoints, a data-driven framework designed to identify the optimal sparse set of control points for reproducing target shapes using biharmonic 3D shape deformation. Control-point-based 3D deformation methods are widely utilized for interactive shape editing, and their usability is enhanced when the control points are sparse yet strategically distributed across the shape. With this objective in mind, we introduce a data-driven approach that can determine the most suitable set of control points, assuming that we have a given set of possible shape variations. The challenges associated with this task primarily stem from the computationally demanding nature of the problem. Two main factors contribute to this complexity: solving a large linear system for the biharmonic weight computation and addressing the combinatorial problem of finding the optimal subset of mesh vertices. To overcome these challenges, we propose a reformulation of the biharmonic computation that reduces the matrix size, making it dependent on the number of control points rather than the number of vertices. Additionally, we present an efficient search algorithm that significantly reduces the time complexity while still delivering a nearly optimal solution. Experiments on SMPL, SMAL, and DeformingThings4D datasets demonstrate the efficacy of our method. Our control points achieve better template-to-target fit than FPS, random search, and neural-network-based prediction. We also highlight the significant reduction in computation time from days to approximately 3 minutes.Comment: Pacific Graphics 2023 (Full Paper

Boneless Pose Editing and Animation

Abstract. In this paper, we propose a pose editing and animation method for triangulated surfaces based on a user controlled partitioning of the model into deformable parts and rigid parts which are denoted handles. In our pose editing system, the user can sculpt a set of poses simply by transforming the handles for each pose. Using Laplacian editing, the deformable parts are deformed to match the handles. In our animation system the user can constrain one or several handles in order to define a new pose. New poses are interpolated from the examples poses, by solving a small non-linear optimization problem in order to obtain the interpolation weights. While the system can be used simply for building poses, it is also an animation system. The user can specify a path for a given constraint and the model is animated correspondingly.

Data-driven weight optimization for real-time mesh deformation

3D model deformation has been an active research topic in geometric processing. Due to its efficiency, linear blend skinning (LBS) and its follow-up methods are widely used in practical applications as an efficient method for deforming vector images, geometric models and animated characters. LBS needs to determine the control handles and specify their influence weights, which requires expertise and is time-consuming. Further studies have proposed a method for efficiently calculating bounded biharmonic weights of given control handles which reduces user effort and produces smooth deformation results. The algorithm defines a high-order shape-aware smoothness function which tends to produce smooth deformation results, but fails to generate locally rigid deformations. To address this, we propose a novel data-driven approach to producing improved weights for handles that makes full use of available 3D model data by optimizing an energy consisting of data-driven, rigidity and sparsity terms, while maintaining its advantage of allowing handles of various forms. We further devise an efficient iterative optimization scheme. Through contrast experiments, it clearly shows that linear blend skinning based on our optimized weights better reflects the deformation characteristics of the model, leading to more accurate deformation results, outperforming existing methods. The method also retains real-time performance even with a large number of deformation examples. Our ablation experiments also show that each energy term is essential