signed distance functions

This work addresses the lack of physical plausibility in multi-object signed distance field (SDF) modeling, which often suffers from geometric interpenetration. The authors propose S2MDF—a lightweight, plug-and-play hard-constraint module that enforces non-overlapping conditions on vector-valued SDFs without modifying the underlying network architecture. To the best of our knowledge, this is the first approach to completely eliminate geometric intersections among multiple SDFs through hard constraints, avoiding the need for intricate loss function tuning. S2MDF can be flexibly applied during either training or post-processing and, when combined with a Marching Cubes–compatible linear interpolation-based meshing strategy, reduces object overlap to numerical precision across several state-of-the-art methods while preserving high-fidelity geometry reconstruction—significantly outperforming existing soft-constraint alternatives.

To address the low boundary accuracy, high storage overhead, and poor dynamic adaptability of 3D obstacle reconstruction in dense urban autonomous driving, this paper proposes a static Signed Distance Function (SDF) mapping method leveraging LiDAR point clouds and Implicit Neural Representations (INRs). It is the first work to systematically integrate differentiable SDF representations with an end-to-end learnable reconstruction framework in autonomous driving, overcoming geometric detail limitations inherent in conventional polygonal modeling. The resulting SDF map enables high-fidelity implicit surface reconstruction, compact memory footprint, and continuous geometric reasoning. Experiments demonstrate that, compared to voxel-based approaches, the proposed method achieves a threefold improvement in effective spatial resolution, reduces storage requirements by 60%, and significantly enhances collision detection accuracy and robustness under congested, dynamic traffic conditions.

This work proposes the first open-world, feedforward model for convex decomposition of 3D shapes—a long-standing challenge in geometry processing. By learning a continuous feature field and integrating self-supervised geometric optimization objectives, the method decomposes arbitrary 3D shapes—represented as meshes, CAD models, or Gaussian splats—into unions of convex parts without requiring manual annotations or assumptions about closed-category objects. The core innovations lie in geometric constraints derived directly from the definition of convexity, a feature-field clustering mechanism, and strong generalization across diverse shape representations. Experiments demonstrate that the approach consistently produces high-quality convex decompositions across multiple 3D representations and exhibits exceptional generalization capability on open-world objects.

To address the challenge of learning signed distance functions (SDFs) from sparse point clouds—where insufficient geometric detail impairs surface reconstruction—this paper proposes an end-to-end dynamic deformation framework. The method jointly optimizes an explicit parametric surface and an implicit SDF field through three core components: (1) a bijective surface parameterization (BSP) that establishes invertible mappings between local surface patches and the global shape; (2) a grid-based deformation optimization (GDO) strategy that co-refines both the parameterized surface and the implicit field; and (3) a synergistic learning mechanism integrating bijective neural mappings, local patch embeddings, and differentiable rendering. Evaluated on both synthetic and real-world scanned datasets, the approach achieves significant improvements in SDF reconstruction accuracy and topological consistency over state-of-the-art methods.

Controllable geometric generation remains challenging in scenarios lacking large-scale 3D shape datasets. Method: This paper proposes a data-free neural implicit field generation framework that encodes user-specified design objectives—such as smoothness, genus (number of holes), and connectivity—as partial differential equation (PDE) constraints, geometric differential operator regularizers, and a multi-objective Lagrangian optimization objective, all directly embedded into neural field training. Contribution/Results: It establishes the first data-free paradigm for implicit shape generation; introduces explicit diversity constraints to mitigate mode collapse; and enables joint yet disentangled control over geometric and topological attributes. Experiments on multiple benchmarks and real-world engineering design tasks demonstrate precise, stable control over surface smoothness, connectivity, and genus, while consistently producing high-quality, diverse, and feasible shape ensembles.

This work addresses the inefficiency of existing differentiable simulation frameworks in generating contact manifolds due to conventional collision-handling logic, which hinders both differentiability and parallel computation. The authors propose a novel contact manifold generation method that balances efficiency and differentiability by bridging convex primitives and distance-barrier approaches. Specifically, they introduce smooth, analytically defined signed distance primitives for vertex–face collisions and, for the first time, present a differentiable edge–edge collision routine that simultaneously outputs signed distances and contact normals. Implemented within a JAX-based, massively vectorized framework, the method demonstrates significantly faster collision detection than Mujoco XLA on benchmark tasks, thereby validating its dual advantages in computational efficiency and end-to-end differentiability.

This work addresses the challenge of unified collision handling for high-dimensional robotic arms in unstructured environments, where differentiable and scene-agnostic distance queries are lacking. To this end, we propose CSSDF-Net, which, for the first time, directly learns a neural implicit signed distance field in configuration space, offering a unified geometric representation for safety. By integrating a spatial hashing–based data generation pipeline that encodes robot geometric priors, our method achieves zero-shot generalization to arbitrary obstacle point clouds. Experiments demonstrate that CSSDF-Net exhibits gradient stability, efficient collision avoidance, and low-latency inference on both planar and 7-DoF manipulators, enabling trajectory optimization and model predictive control under safety constraints, and facilitating deployment in previously unseen complex environments.

Natural image generation typically relies on Euclidean assumptions, overlooking the intrinsic nonlinear geometric structure of the data. This work observes that image semantics are primarily governed by directional components, while the magnitude can be approximated by a global mean, enabling images to be modeled on a hyperspherical manifold. Building on this insight, the paper introduces two novel approaches: Spherical Optimal Transport Conditional Flow Matching (SOT-CFM), which leverages angular distances, and Spherical Flow Matching (SFM), which directly constrains the dynamics to the manifold. To the best of our knowledge, this is the first successful formulation of natural image generation on a hypersphere via flow matching. Experiments demonstrate that the proposed methods significantly outperform Euclidean baselines across multiple benchmarks, confirming the advantages of geometry-aware modeling in generative tasks.

Existing methods for outdoor 3D scene generation often suffer from insufficient geometric coverage and unstable synthesis due to the absence of an effective automatic viewpoint scheduling mechanism. This work proposes a novel framework tailored for outdoor scenes that automatically schedules viewpoints by constructing a directed generation graph to determine anchor views and interpolation trajectories. By incorporating object identity images and geometry-aware fitting parameters, the approach enables fine-grained control over both appearance and structure. Integrating multi-view image synthesis, 3D reconstruction, and object-level conditional guidance within explicit geometric constraints, the method significantly enhances generation quality and controllability, achieving state-of-the-art performance.

This work addresses the problem of signed distance function (SDF) reconstruction from unoriented point clouds by proposing a high-order variational method that achieves geometrically consistent, high-fidelity reconstructions both locally and globally. The key innovation lies in explicitly incorporating the medial axis of the underlying surface—defined as the jump set of the SDF gradient—into the learning process. This is accomplished through an Ambrosio–Tortorelli-type phase-field approximation to model gradient discontinuities, combined with the Eikonal equation and a zero-level-set constraint. The method jointly optimizes a neural representation of the SDF alongside the phase-field function. Experimental results demonstrate that the proposed approach significantly outperforms existing techniques in both quantitative metrics and qualitative visual quality.