In computer-aided design(CAD) and computer-aided manufacturing(CAM), developable surface approximation is important yet existing methods are limited to single rectangular surfaces. We propose a novel piecewise method for Boundary Representation (B-Rep) models with complex boundaries: greedy region-growing segments surfaces by local geometry, grouping adjacent regions across surfaces into common patches; each patch is fitted to a plane, cylinder, cone, or tangent surface; adaptive subdivision controls global error; and trimming preserves original boundaries. Empirical results demonstrate that our method generates fewer or higher-quality developable patches under identical tolerance constraints compared to existing approaches, validating the effectiveness and superiority of our method, demonstrating broad applicability to multiple parametric surfaces with complex boundaries.
Volume electron microscopy (EM) now enables nanometric-scale 3D reconstructions of neural tissue, opening the door to quantitative, morphology-driven neuroscience beyond connectivity alone. While previous studies relied on handcrafted descriptors and classical machine learning for morphology analysis, recent progress in deep learning for 3D shape understanding offers new opportunities to learn robust, task-specific representations directly from geometric data. In this paper we present NeMoCo, a geometry learning framework that targets the key practical bottleneck in connectomics and ultrastructural analysis: the scarcity and cost of dense expert annotations for the long tail of neurite and organelle phenotypes. NeMoCo formulates representation learning for EM-derived neurite meshes in a self-supervised Momentum Contrast (MoCo) style. We use DiffusionNet (Sharp et al., 2022) as a mesh encoder with intrinsic spectral descriptors (HKS) and train with a momentum-updated teacher encoder and a large memory bank of negatives. To learn invariances that are essential in practice, we generate paired geometric views via controlled affine transformations and resolution changes (including mesh decimation), encouraging embeddings to be stable under nuisance variability while remaining discriminative. We provide an extensive study of augmentation strength and temperature, and evaluate learned representations through frozen retrieval and non-parametric classification (frozen kNN), as well as downstream supervised fine-tuning under limited labels. NeMoCo demonstrates that MoCo-style self-supervision yields robust neurite morphology embeddings on EM meshes, improving label-efficiency and offering a scalable foundation for retrieval, clustering, and phenotype discovery in ultrastructural neuroscience. All the data and the code used for NeMoCo are available at https://github.com/Uzshah/NeMoCo.
Combining physically-based simulation with stylized visual effects not only requires changing the appearance of surfaces, but their shapes as well. We describe a new expressive rendering method for liquid animations, which can be used on top of any preexisting particle-based simulation. Our solution builds on visual particles that carry both water and air distributions, both evolving through particle history based on kinematic information from the simulation. These density fields are combined at each frame to create the implicit iso-surface of interest, rendered in an adapted style. By defining a series of visual particle states, we parametrize this model to capture the typical stylized geometry of water bodies used to highlight dynamic motion in paintings and cartoons, such as elongating droplets, concavities carved at the crest of breaking waves, and stylized air–water mixtures such as bubbles and foam , which we further enhance in 3D scenes using a dedicated stylized surface-color pattern. Regardless of the 2D or 3D nature of the input simulation, our solution maintains temporal coherence and ensures that water bodies keep an approximately constant surface in 2D, resp. volume in 3D, over time. Finally, we conducted a user study to show the effectiveness of our method against state-of-the-art AI-based tools and a hands-on evaluation with a professional artist, in a variety of animation scenarios where stylized shapes are needed. This is an extension of our previous work presented at STAG 2025. It introduces new material, including a refined blending operator, a stylized surface-color pattern, performance metrics, and artist evaluations.
Abstract This chapter provides the basic statistical theory for Gaussian graphical models, primarily for undirected graphs, but also for directed acyclic graphs, also known as Gaussian Bayesian networks. The analysis includes issues of faithfulness, causal interpretation, path decomposition of covariances, and causal effects in linear structural equation models. Algorithms for maximum likelihood estimates are described and studied in some detail, as is conjugate Bayesian analysis, using inverse Markov Wishart laws.
Abstract This chapter provides some basic results about matrix calculus and the linear algebra of interaction subspaces, as well as the formal theory of means and covariances for random elements of vector spaces.
Abstract This chapter provides the basic theory of conditional independence, for sigma-algebras and for general probabilistic independence, and the abstract theory of graphoids and semi-graphoids, as well as conditional independence based on separation properties in graphs. Undirected graphs, directed acyclic graphs, and chain graphs are discussed in some detail, including issues of separation and Markov equivalence and representation of equivalence classes of graphs.
Abstract This chapter is concerned with Markov theory, or, in other words, with the relation between probabilistic independence models and graph separation. It covers Markov theory for undirected graphs, directed acyclic graphs, and chain graphs and the relation to factorization of densities and of Markov kernels. A large fraction of the chapter is concerned with hyper Markov properties, i.e. with Markov properties of families of distributions (meta Markov models) and Markov properties of random distributions, as for example used in Bayesian analysis and as descriptions of sampling distributions of maximum likelihood estimators.
Abstract This describes the classical theory of log-linear models as used in contingency table analysis. It is shown that these constitute regular exponential families, and results about maximum likelihood estimation and conjugate Bayesian analysis are established. Some emphasis is placed on the exploitation of graph decompositions for simplification of the analysis, including computation of maximum likelihood estimates and distributions of exact conditional tests. Basic asymptotic results are established, in particular asymptotic conditional independence relations for estimators. The analysis is extended to Bayesian networks and chain graph models.
Integrating Virtual Reality (VR) and Human–Computer Interaction (HCI) has transformed user engagement with virtual environments, enhancing immersion and usability. Technologies like Cave Automatic Virtual Environment (CAVE) and Head-Mounted Displays (HMDs) have shown significant promise in visualizing data, especially for examining and comprehending intricate 3D datasets, such as graph visualizations. To explore the effectiveness of these technologies in data visualization, we conducted a user study comparing user experience and performance across these two systems when interacting with a large 3D graph. The virtual environment and interaction modalities were adapted to each platform: the HMD setup utilized dual 6-DOF controllers, while the CAVE configuration employed a Flystick2 controller and a trackball. Preliminary data on participants’ demographics, motion sickness sensitivity, and prior experience with graph theory were collected to provide context for the findings. Results show that users in the HMD condition reported significantly higher levels of perceived presence and involvement, as well as improved task performance in navigation and interaction tasks. While both systems were rated similarly for perceived usefulness and ease of use, the HMD environment offered a more immersive and emotionally positive experience overall. These findings contribute to immersive analytics research by demonstrating the comparative strengths of HMD-based systems for individual 3D graph exploration, while highlighting the potential advantages of CAVE for low-discomfort settings. The study underscores the importance of aligning system design with user profiles and task demands to optimize data exploration in virtual environments.
In practical engineering applications, the application of coatings designed from Computer-Aided Design (CAD) models (e.g., stealth coatings for aircraft) onto three-dimensional components must take into account the material’s ductility limits. Conventional mesh-based conformal parameterization, which directly maps surface meshes to planar domains, often results in uncontrolled distortion, and the quality of the mapping is heavily influenced by mesh density and quality. In contrast, we propose a novel Polynomial splines over Hierarchical T-meshes (PHT-splines) based conformal parameterization that achieves globally C1-continuous mappings with controlled distortion through adaptive refinement. This adaptive mechanism incorporates dedicated conformal metrics to suppress excessive mapping distortion observed in numerical tests and enables direct texture coordinate localization. Experimental results demonstrate the superior performance of our approach in industrial CAD applications such as texture mapping and remeshing, successfully bridging the gap between theoretical conformal geometry and practical engineering requirements.
Abstract This chapter provides the basic theory of graphs with multiple types of edge and associated algorithms as they are used in the remainder of the book. It introduces terminology and discusses separation and connectivity, colouring issues, and identification of chordal graphs. In addition, it describes hypergraphs and associated junction forests, as used for both computational and conceptual purposes.
Abstract This chapter is concerned with the analysis of graphical models for mixed data, i.e. data where some variables are discrete and some continuous. Graphs that keep track of the type of variables are marked graphs, and the relevant theory is described first in the chapter. Models are based on conditional Gaussian distributions so that the distributions of the continuous variables conditionally on the discrete are multivariate Gaussian, and the theory of such distributions is also given here. An important concept is the weak marginal of such a distribution, since standard marginals will take the distributions out of its class. The maximum likelihood theory and the conjugate Bayesian theory are developed in detail.
Abstract This chapter is concerned with estimation of the graphical structure from data. It first describes general principles for the methods and then develops methods first for undirected graphs and then for directed acyclic graphs and chain graphs. Maximum likelihood, penalized maximum likelihood, and Bayesian methods are developed in detail for estimating trees, and special properties for estimating decomposable graphs are studied. An important method is known as the graphical lasso, and this is also described. For directed acyclic graphs, both methods based on scoring functions and constraint bases algorithms are described, the latter also extended to chain graph models.
Abstract This chapter provides basic results about the multivariate Gaussian distribution and derived distributions, such as the Wishart distribution and inverse Wishart distribution. Densities, moments, means, and covariances, and decomposition and transformation results are described.
Abstract This chapter gives an overview of various mathematical prerequisites, including basic measure theory, the theory of Markov kernels, convex optimization, information theoretic concepts, specific algorithms, and concepts related to sufficiency.
Airborne point clouds provide a rich but unstructured description of urban environments, making their direct use in visualization, simulation, and geospatial applications difficult in non-trivial use-cases. This paper presents CityLODer, a automatic and scalable pipeline for converting raw data into usable 3D city representations with a unified procedure. Building on the earlier LiD2LOD system, CityLODer broadens the reconstruction process to a more comprehensive urban representation that includes both buildings and roads. The tool produces semantic CityGML Level of Detail 1 models, together with lightweight triangular meshes. Particular attention is given to robustness, ease of use, and automation, allowing the pipeline to process large airborne datasets with limited manual intervention. We demonstrate the system on historical urban scenarios characterized by irregular layouts and complex morphology, showing that CityLODer can generate compact, semantically structured, and visually effective city models from raw point-cloud data.
This paper presents an automatic hexahedral mesh generation method for B-rep axisymmetric models, with core innovations of distance-energy-based block structure optimization and geometric hard-edge aware low-distortion approximately isometric mapping, eliminating manual intervention and improving mesh quality. Axisymmetric models are classified into six categories via feature recognition and matched with blocking templates. Singular points are optimized using CVT distance energy, redundant soft-edge constraints are removed, and high-quality meshes are generated via 3D TFI. Algorithm contributions include the distance-energy optimization and hard-edge mapping; engineering implementation integrates the method into the CAE software SuperMesh with GUI-driven automation. Experiments show that the method generates tens of millions of elements within minutes, with minimum Jacobian ratio above 0.81, maximum aspect ratio below 4.89, and geometric error less than 0.08%, meeting high-precision simulation requirements. The approach is strictly limited to B-rep axisymmetric models without generalization guarantees for arbitrary topologies.
The paper focuses on the design of an energy-minimizing spline that approximates a curve, fits a set of points, and adapts its shape to nearby obstacles. This issue, significant in many fields, has been addressed numerous times, but the mathematical solutions are often complicated. The proposed spline offers less complicated and straightforward computation and, what is more, introduces additional features, such as replicating the shape of both the approximated curve and obstacles, forming an approximated offset curve and preserving C0 to C2 continuity at a junction point. Its behavior is controlled by user-defined scalar parameters. The model, which combines internal and external energies, can be easily modified and upgraded, is generalizable to higher dimensions, and solved using linear least squares. This spline has many potential applications, particularly in computer graphics, geoinformatics, and cartography. Its properties are demonstrated using both synthetic and real cartographic data.
Speech-driven 3D motion generation has garnered increasing research attention. However, it faces significant challenges in achieving style controllability, primarily due to the scarcity of motion style annotations. To address this, we propose a novel diffusion-based framework for co-speech holistic motion generation that enables example-based style control from videos. Our approach integrates hierarchical speech encoding with rhythm-aware denoising to produce natural and synchronized gestures and expressions. For effective style guidance, we introduce a contrastive style encoder that captures discriminative style representations from reference clips without explicit labeling, enabling generalization to motion styles unseen during training. Furthermore, we design a neural mapper that aligns 2D and 3D gesture features in a shared embedding space, facilitating direct style extraction from in-the-wild videos and seamless transfer to 3D motion. Extensive experiments and user studies show that our proposed approach achieves state-of-the-art performance in both qualitative and quantitative evaluations, offering a flexible solution for controllable motion generation.
