As-Rigid-As-Possible Surface Morphing

This paper presents a new morphing method based on the “as-rigid-as-possible” approach. Unlike the original as-rigid-as-possible method, we avoid the need to construct a consistent tetrahedral mesh, but instead require a consistent triangle surface mesh and from it create a tetrahedron for each surface triangle. Our new approach has several significant advantages. It is much easier to create a consistent triangle mesh than to create a consistent tetrahedral mesh. Secondly, the equations arising from our approach can be solved much more efficiently than the corresponding equations for a tetrahedral mesh. Finally, by incorporating the translation vector in the energy functional controlling interpolation, our new method does not need the user to arbitrarily fix any vertex to obtain a solution, allowing artists automatic control of interpolated mesh positions

Variational Autoencoders for Deforming 3D Mesh Models

3D geometric contents are becoming increasingly popular. In this paper, we study the problem of analyzing deforming 3D meshes using deep neural networks. Deforming 3D meshes are flexible to represent 3D animation sequences as well as collections of objects of the same category, allowing diverse shapes with large-scale non-linear deformations. We propose a novel framework which we call mesh variational autoencoders (mesh VAE), to explore the probabilistic latent space of 3D surfaces. The framework is easy to train, and requires very few training examples. We also propose an extended model which allows flexibly adjusting the significance of different latent variables by altering the prior distribution. Extensive experiments demonstrate that our general framework is able to learn a reasonable representation for a collection of deformable shapes, and produce competitive results for a variety of applications, including shape generation, shape interpolation, shape space embedding and shape exploration, outperforming state-of-the-art methods.Comment: CVPR 201

Rigidity controllable as-rigid-as-possible shape deformations

Shape deformation is one of the fundamental techniques in geometric processing. One principle of deformation is to preserve the geometric details while distributing the necessary distortions uniformly. To achieve this, state-of-the-art techniques deform shapes in a locally as-rigid-as-possible (ARAP) manner. Existing ARAP deformation methods optimize rigid transformations in the 1-ring neighborhoods and maintain the consistency between adjacent pairs of rigid transformations by single overlapping edges. In this paper, we make one step further and propose to use larger local neighborhoods to enhance the consistency of adjacent rigid transformations. This is helpful to keep the geometric details better and distribute the distortions more uniformly. Moreover, the size of the expanded local neighborhoods provides an intuitive parameter to adjust physical stiffness. The larger the neighborhood is, the more rigid the material is. Based on these, we propose a novel rigidity controllable mesh deformation method where shape rigidity can be flexibly adjusted. The size of the local neighborhoods can be learned from datasets of deforming objects automatically or specified by the user, and may vary over the surface to simulate shapes composed of mixed materials. Various examples are provided to demonstrate the effectiveness of our method

Biharmonic deformation transfer with automatic key point selection

Deformation transfer is an important research problem in geometry processing and computer animation.A fundamental problem for existing deformation transfer methods is to build reliable correspondences. This is challenging, especially when the source and target shapes differ significantly and manual labeling is typically used. We propose a novel deformation transfer method that aims at minimizing user effort. We adapt a biharmonic weight deformation framework which is able to produce plausible deformation even with only a few key points. We then develop an automatic algorithm to identify a minimum set of key points on the source model that characterizes the deformation well. While minimal user effort is still needed to specify corresponding points on the target model for the selected key points, our approach avoids the difficult problem of choosing key points. Experimental results demonstrate that our method, despite requiring little user effort, produces better deformation results than alternative solutions. Keywords: shape deformation; biharmonic weights; key point selection; deformation transfe

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

Spatio-temporal information system for the geosciences: concepts, data models, software, and applications

The development of spatio–temporal geoscience information systems (TGSIS) as the next generation of geographic information systems (GIS) and geoscience information systems (GSIS) was investigated with respect to the following four aspects: concepts, data models, software, and applications. These systems are capable of capturing, storing, managing, and querying data of geo–objects subject to dynamic processes, thereby causing the evolution of their geometry, topology and geoscience properties. In this study, five data models were proposed. The first data model represents static geo–objects whose geometries are in the 3–dimensional space. The second and third data models represent geological surfaces evolving in a discrete and continuous manner, respectively. The fourth data model is a general model that represents geo–objects whose geometries are n–dimensional embedding in the m–dimensional space R^m, m >= 3. The topology and the properties of these geo–objects are also represented in the data model. In this model, time is represented as one dimension (valid time). Moreover, the valid time is an independent variable, whereas geometry, topology, and the properties are dependent (on time) variables. The fifth data model represents multiple indexed geoscience data in which time and other non–spatial dimensions are interpreted as larger spatial dimensions. To capture data in space and time, morphological interpolation methods were reviewed, and a new morphological interpolation method was proposed to model geological surfaces evolving continuously in a time interval. This algorithm is based on parameterisation techniques to locate the cross–reference and then compute the trajectories complying with geometrical constraints. In addition, the long transaction feature was studied, and the data schema, functions, triggers, and views were proposed to implement the long transaction feature and the database versioning in PostgreSQL. To implement database versioning tailored to geoscience applications, an algorithm comparing two triangulated meshes was also proposed. Therefore, TGSIS enable geologists to manage different versions of geoscience data for different geological paradigms, data, and authors. Finally, a prototype software system was built. This system uses the client/server architecture in which the server side uses the PostgreSQL database management system and the client side uses the gOcad geomodeling system. The system was also applied to certain sample applications