Search for: All records

This paper introduces a method to synthesize a 3D tensor field within a constrained geometric domain represented as a tetrahedral mesh. Whereas previous techniques optimize forisotropicfields, we focus onanisotropictensor fields that are smooth and aligned with the domain boundary or user guidance. The key ingredient of our method is a novel computational design framework, built on top of thesymmetric orthogonally decomposable(odeco) tensor representation, to optimize the stretching ratios and orientations for each tensor in the domain. In contrast to past techniques designed only forisotropictensors, we demonstrate the efficacy of our approach in generating smooth volumetric tensor fields with highanisotropyand shape conformity, especially for the domain with complex shapes. We apply these anisotropic tensor fields to various applications, such as anisotropic meshing, structural mechanics, and fabrication. 

We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic shapes. The volumetric RPD discretizes the input 3D volume into sub-regions given a set of medial spheres. With this intermediate structure, we convert the homotopy equivalency between the generated medial mesh and the input 3D shape into a localized contractibility checking for each restricted element (power cell, power face, power edge), by checking their connected components and Euler characteristics. We further propose a fractional Euler characteristic algorithm for efficient GPU-based computation of Euler characteristic for each restricted element on the fly while computing the volumetric RPD. Compared with existing voxel-based or point-cloud-based methods, our approach is the first to adaptively and directly revise the medial mesh without globally modifying the dependent structure, such as voxel size or sampling density, while preserving its topology and medial features. In comparison with the feature preservation method MATFP [Wang et al. 2022], our method provides geometrically comparable results with fewer spheres and more robustly captures the topology of the input 3D shape. 

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach [Garland and Heckbert 1997] prioritizes accuracy and can preserve strong feature lines/points as well, but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) [Du et al. 1999] energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset [Koch et al. 2019], along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding. Please refer to the teaser figure for illustration. 

Harnessing commonsense knowledge poses a significant challenge for machine comprehension systems. This paper primarily focuses on incorporating a specific subset of commonsense knowledge, namely, script knowledge. Script knowledge is about sequences of actions that are typically performed by individuals in everyday life. Our experiments were centered around the MCScript dataset, which was the basis of the SemEval-2018 Task 11: Machine Comprehension using Commonsense Knowledge. As a baseline, we utilized our Three-Way Attentive Networks (TriANs) framework to model the interactions among passages, questions, and answers. Building upon the TriAN, we proposed to: (1) integrate a pre-trained language model to capture script knowledge; (2) introduce multi-layer attention to facilitate multi-hop reasoning; and (3) incorporate positional embeddings to enhance the model’s capacity for event-ordering reasoning. In this paper, we present our proposed methods and prove their efficacy in improving script knowledge integration and reasoning.