Many modeling tasks from disparate domains can be framed in the same way, computing spherical signals from geometric inputs, for example, computing the radar response of different objects or navigating through an environment. This paper introduces G2Sphere, a general method for mapping object geometries to spherical signals. G2Sphere operates entirely in Fourier space, encoding geometric structure into latent Fourier features using equivariant neural networks and outputting the Fourier coefficients of the continuous target signal, which can be evaluated at any resolution. By utilizing a hybrid GNN-spherical CNN architecture, our method achieves a much higher frequency output signal than comparable equivariant GNNs and avoids hand-engineered geometry features used previously by purely spherical methods. We perform experiments on various challenging domains, including radar response modeling, aerodynamic drag prediction, and policy learning for manipulation and navigation. We find that G2Sphere outperforms competitive baselines in terms of accuracy and inference time, and we demonstrate that equivariance and Fourier features lead to improved sample efficiency and generalization.

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.

Recent advances in radiance fields and novel view synthesis enable creation of realistic digital twins from photographs. However, current methods struggle with flat, texture-less surfaces, creating uneven and semi-transparent reconstructions, due to an ill-conditioned photometric reconstruction objective. Surface reconstruction methods solve this issue but sacrifice visual quality. We propose a novel hybrid 2D/3D representation that jointly optimizes constrained planar (2D) Gaussians for modeling flat surfaces and freeform (3D) Gaussians for the rest of the scene.

Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner - particularly under spatial constraints - remains an open challenge, as existing approaches struggle to balance surface quality, robustness, and efficiency. We address this by introducing a novel method for handle-guided neural field deformation, which leverages discrete local surface representations to optimize the As-Rigid-As-Possible deformation energy. To this end, we propose the local patch mesh representation, which discretizes level sets of a neural signed distance field by projecting and deforming flat mesh patches guided solely by the SDF and its gradient. We conduct a comprehensive evaluation showing that our method consistently outperforms baselines in deformation quality, robustness, and computational efficiency. We also present experiments that motivate our choice of discretization over marching cubes. By bridging classical geometry processing and neural representations through local patch meshing, our work enables scalable, high-quality deformation of neural fields and paves the way for extending other geometric tasks to neural domains.

Unsigned distance fields (UDFs) are widely used in 3D deep learning due to their ability to represent shapes with arbitrary topology. While prior work has largely focused on learning UDFs from point clouds or multi-view images, extracting meshes from UDFs remains challenging, as the learned fields rarely attain exact zero distances. A common workaround is to reconstruct signed distance fields (SDFs) locally from UDFs to enable surface extraction via Marching Cubes. However, this often introduces topological artifacts such as holes or spurious components. Moreover, local SDFs are inherently incapable of representing non-manifold geometry, leading to complete failure in such cases.

High-fidelity 3D object synthesis remains significantly more challenging than 2D image generation due to the unstructured nature of mesh data and the cubic complexity of dense volumetric grids. Existing two-stage pipelines--compressing meshes with a VAE (using either 2D or 3D supervision), followed by latent diffusion sampling--often suffer from severe detail loss caused by inefficient representations and modality mismatches introduced in VAE.

Articulated objects, as prevalent entities in human life, their 3D representations play crucial roles across various applications. However, achieving both high-fidelity textured surface reconstruction and dynamic generation for articulated objects remains challenging for existing methods. In this paper, we present REArtGS, a novel framework that introduces additional geometric and motion constraints to 3DGaussian primitives, enabling realistic surface reconstruction and generation for articulated objects. Specifically, given multi-view RGB images of arbitrary two states of articulated objects, we first introduce an unbiased Signed Distance Field (SDF) guidance to regularize Gaussian opacity fields, enhancing geometry constraints and improving surface reconstruction quality. Then we establish deformable fields for 3DGaussians constrained by the kinematic structures of articulated objects, achieving unsupervised generation of surface meshes in unseen states. Extensive experiments on both synthetic and real datasets demonstrate our approach achieves high-quality textured surface reconstruction for given states, and enables high-fidelity surface generation for unseen states.

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However, existing methods often yield unstructured meshes and exhibit poor interactivity, making them impractical for artistic workflows. To address these limitations, we represent 3D assets as shape programs and introduce ShapeCraft, a novel multi-agent framework for text-to-3D generation. At its core, we propose a Graph-based Procedural Shape (GPS) representation that decomposes complex natural language into a structured graph of sub-tasks, thereby facilitating accurate LLM comprehension and interpretation of spatial relationships and semantic shape details. Specifically, LLM agents hierarchically parse user input to initialize GPS, then iteratively refine procedural modeling and painting to produce structured, textured, and interactive 3D assets. Qualitative and quantitative experiments demonstrate ShapeCraft's superior performance in generating geometrically accurate and semantically rich 3D assets compared to existing LLM-based agents. We further show the versatility of ShapeCraft through examples of animated and user-customized editing, highlighting its potential for broader interactive applications.

Transferring appearance to 3D assets using different representations of the appearance object-such as images or text-has garnered interest due to its wide range of applications in industries like gaming, augmented reality, and digital content creation. However, state-of-the-art methods still fail when the geometry between the input and appearance objects is significantly different. A straightforward approach is to directly apply a 3D generative model, but we show that this ultimately fails to produce appealing results. Instead, we propose a principled approach inspired by universal guidance. Given a pretrained rectified flow model conditioned on image or text, our training-free method interacts with the sampling process by periodically adding guidance.