Monte Carlo PDE solvers have become increasingly popular for solving heat-related partial differential equations in geometry processing and computer graphics due to their robustness in handling complex geometries. While existing methods can handle Dirichlet, Neumann, and linear Robin boundary conditions, nonlinear boundary conditions arising from thermal radiation remain largely unexplored. In this paper, we introduce a Picard-style fixed-point iteration framework that enables Monte Carlo PDE solvers to handle nonlinear radiative boundary conditions. While strict theoretical convergence is not generally guaranteed, our method remains stable and empirically convergent with a properly chosen relaxation coefficient. Even with imprecise initial boundary estimates, it progressively approaches the correct solution. Compared to standard linearization strategies, the proposed approach achieves significantly higher accuracy. To further address the high variance inherent in Monte Carlo estimators, we propose a heteroscedastic regression-based denoising technique specifically designed for on-boundary solution estimates, filling a gap left by prior variance reduction methods that focus solely on interior points. We validate our approach through extensive evaluations on synthetic benchmarks and demonstrate its effectiveness on practical heat radiation simulations with complex geometries.

Surface offsetting is a fundamental geometric operation in computer-aided design, manufacturing, robotics, and computational physics. Despite its conceptual simplicity, generating offset surfaces robustly and efficiently for complex and irregular geometries remains a persistent challenge, hindered by self-intersections, topological inconsistencies, and feature degradation. This paper reviews recent advances in the field of surface offsetting, offering a structured overview of the evolution of techniques from classical constructive methods to contemporary neural implicit representations. Our survey addresses a gap in the literature, as prior foundational reviews over the past two decades in this field focused primarily on parametric methods. We introduce a taxonomy that organizes existing algorithms into five principal classes: Constructive, Spatial Discretization, Optimization-based, Field-based, and Learning-based approaches. An analysis of 46 representative algorithms reveals trade-offs in algorithm design: achieving both geometric accuracy and topological correctness proves difficult, and representation choices introduce inherent complexity constraints. We identify open problems including offset generation for surfaces with open boundaries, preservation of thin features, and resolution of self-intersections in concave regions. These challenges point toward promising research directions, including extending classical offset theory to non-manifold and open-boundary domains, developing scalable geometric predicates, and designing hybrid neural representations that disentangle distance-field smoothness from geometric sharpness.

Stochastic PDE solvers have emerged as a powerful alternative to traditional discretization-based methods for solving partial differential equations (PDEs), especially in geometry processing and graphics. While off-centered estimators enhance sample reuse in WoS-type Monte Carlo solvers, they introduce correlation artifacts and bias when Green’s functions are approximated. In this paper, we propose a statistically weighted off-centered WoS-type estimator that leverages local similarity filtering to selectively combine samples across neighboring evaluation points. Our method balances bias and variance through a principled weighting strategy that suppresses unreliable estimators. We demonstrate our approach’s effectiveness on various PDEs—including screened Poisson equations—and boundary conditions, achieving consistent improvements over existing solvers such as vanilla Walk on Spheres, mean value caching, and boundary value caching. Our method also naturally extends to gradient field estimation and mixed boundary problems.

Node-link diagrams are widely used to visualize graphs. Most graph layout algorithms only use graph topology for aesthetic goals (e.g., minimize node occlusions and edge crossings) or use node attributes for exploration goals (e.g., preserve visible communities). Existing hybrid methods that bind the two perspectives still suffer from various generation restrictions (e.g., limited input types and required manual adjustments and prior knowledge of graphs) and the imbalance between aesthetic and exploration goals. In this article, we propose a flexible embedding-based graph exploration pipeline to enjoy the best of both graph topology and node attributes. First, we leverage embedding algorithms for attributed graphs to encode the two perspectives into latent space. Then, we present an embedding-driven graph layout algorithm, GEGraph, which can achieve aesthetic layouts with better community preservation to support an easy interpretation of the graph structure. Next, graph explorations are extended based on the generated graph layout and insights extracted from the embedding vectors. Illustrated with examples, we build a layout-preserving aggregation method with Focus+Context interaction and a related nodes searching approach with multiple proximity strategies. Finally, we conduct quantitative and qualitative evaluations, a user study, and two case studies to validate our approach.

Utilizing Visualization-oriented Natural Language Interfaces (V-NLI) as a complementary input modality to direct manipulation for visual analytics can provide an engaging user experience. It enables users to focus on their tasks rather than having to worry about how to operate visualization tools on the interface. In the past two decades, leveraging advanced natural language processing technologies, numerous V-NLI systems have been developed in academic research and commercial software, especially in recent years. In this article, we conduct a comprehensive review of the existing V-NLIs. In order to classify each article, we develop categorical dimensions based on a classic information visualization pipeline with the extension of a V-NLI layer. The following seven stages are used: query interpretation, data transformation, visual mapping, view transformation, human interaction, dialogue management, and presentation. Finally, we also shed light on several promising directions for future work in the V-NLI community.

Declarative programmatic approaches are an essential modality for data visualization construction. Despite the powerful customization ability, declarative programming requires users to create charts from scratch, thus building a well-designed visualization is an effort-consuming process. In this paper, we propose leveraging examples to alleviate the problem. The use of examples plays a vital role in visualization design. Users can be allowed to browse through designs for inspiration and adapt them for their own visualizations. In this demo, we directly leverage the entire Vega/Vega-Lite example galleries as chart templates and introduce an authoring pipeline to conveniently instantiate templates with the user's data for extensible programmatic modifications. Finally, we build GALVIS, an example-powered declarative programming tool for visualization construction, enabling efficient declarative programming and retaining the full spectrum of Vega/Vega-Lite characteristics.

General visualization recommendation systems typically make design decisions for the dataset automatically. However, most of them can only prune meaningless visualizations but fail to recommend targeted results. This paper contributes TaskVis, a task-oriented visualization recommendation system that allows users to select their tasks precisely on the interface. We first summarize a task base with 18 classical analytic tasks by a survey both in academia and industry. On this basis, we maintain a rule base, which extends empirical wisdom with our targeted modeling of the analytic tasks. Then, our rule-based approach enumerates all the candidate visualizations through answer set programming. After that, the generated charts can be ranked by four ranking schemes. Furthermore, we introduce a task-based combination recommendation strategy, leveraging a set of visualizations to give a brief view of the dataset collaboratively. Finally, we evaluate TaskVis through a series of use cases and a user study.

In this paper, we present a novel feature extraction approach called FLDA for unsteady flow fields based on Latent Dirichlet allocation (LDA) model. Analogous to topic modeling in text analysis, in our approach, pathlines and features in a given flow field are defined as documents and words respectively. Flow topics are then extracted based on Latent Dirichlet allocation. Different from other feature extraction methods, our approach clusters pathlines with probabilistic assignment, and aggregates features to meaningful topics at the same time. We build a prototype system to support exploration of unsteady flow field with our proposed LDA-based method. Interactive techniques are also developed to explore the extracted topics and to gain insight from the data. We conduct case studies to demonstrate the effectiveness of our proposed approach.