We introduce a new offset meshing method that handles clean 3D surface meshes of arbitrary geometry and topology—where “clean” refers to meshes that are watertight, manifold, and free of self-intersections. Our approach also extends to imperfect, or “dirty,” meshes that violate these conditions, although the problem becomes significantly more difficult in such scenarios, and faithful feature preservation near defective areas cannot always be assured. In contrast to prior techniques, which have largely focused on constant-radius offsets, our method is, to our knowledge, the first to support mitered offsets while effectively preserving sharp features. Our method is designed based on several core principles: (1) explicitly generating the offset vertices and triangles with feature-capturing energy and constraints; (2) prioritizing the generation of the offset geometry before establishing its connectivity, (3) employing exact algorithms in critical pipeline steps for robustness, balancing the use of floating-point computations for efficiency, (4) applying various conservative speed up strategies including early reject non-contributing computations to the final output. Our approach further uniquely supports variable offset distances on input surface elements, offering a wider range of practical applications compared to conventional methods. For benchmarking purposes, we performed an extensive comparison against state-of-the-art offset methods using a curated subset of the Thingi10K dataset. Our results demonstrate the superiority of our approach over current state-of-the-art methods in terms of element count, feature preservation, and non-uniform offset distances of the resulting offset mesh surfaces, marking a significant advancement in the field.

Occlusion culling is a cornerstone of real-time rendering, particularly in mobile games where limited GPU bandwidth demands highly efficient scene management. At the heart of occlusion culling lies the use of simplified proxy geometry-called occluders-that approximate scene geometry for rapid visibility testing. However, producing high-quality occluders that are low in polygon count, conservative in coverage, and tightly aligned with the original geometry remains a manual and labor-intensive process. In this paper, we present a fast and fully automated two-stage approach for robust occluder generation tailored to real-world game assets. Our method begins with a novel strategy for inward offset mesh computation, followed by a conservative simplification step leveraging a new variant of Quadric Error Metrics (QEM). This approach effectively handles noisy and topologically complex inputs, generating production-ready occluders in seconds. Extensive experiments on a wide range of asset types demonstrate that our technique achieves aggressive triangle reduction while preserving critical occlusion fidelity. By offering a practical and scalable solution, our method bridges the gap between academic research and demanding needs for game development.

This article proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets (FSs) can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 FSs, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 FSs, there are both type-1 FSs and interval type-2 FSs in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty of the interval type-2 (IT2) FS is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of FSs is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and FS updating algorithm is employed to initialize the reference rule base and the type of FS, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.

In this article, a novel design of a hierarchicalfuzzy system (HFS) based on a self-organized fuzzy partition and fuzzy autoencoder is proposed. The initial rule set of the system is empty, and all the fuzzy sets and fuzzy rules are generated by a self-organized fuzzy partition algorithm. By adopting an improved box plot data standardization method, the processed data can more accurately represent the distribution characteristics of the input data, which improve the accuracy and the rationality. A fuzzy autoencoder is used to train the HFS layer by layer, which can not only ensure the effectiveness of the fuzzy system's hidden layer variables but also provide interpretability. Compared with the traditional fuzzy logic system, the HFS reduces the total number of rules and the complexity. The proposed HFS is tested on three different regression datasets. The experimental results illustrate that the hierarchical self-organized fuzzy system still performs better in terms of regression accuracy indicators than the self-organized fuzzy system.