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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. 

Despite achieving impressive improvement in accuracy, most existing monocular 3D human mesh reconstruction methods require large-scale 2D/3D ground-truths for supervision, which limits their applications on unlabeled in-the-wild data that is ubiquitous. To alleviate the reliance on 2D/3D ground-truths, we present a self-supervised 3D human pose and shape reconstruction framework that relies only on self-consistency between intermediate representations of images and projected 2D predictions. Specifically, we extract 2D joints and depth maps from monocular images as proxy inputs, which provides complementary clues to infer accurate 3D human meshes. Furthermore, to reduce the impacts from noisy and ambiguous inputs while better concentrate on the high-quality information, we design an uncertainty-aware module to automatically learn the reliability of the inputs at body-joint level based on the consistency between 2D joints and depth map. Experiments on benchmark datasets show that our approach outperforms other state-of-the-art methods at similar supervision levels. 

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.