collision mesh generation

The two-dimensional irregular cutting and packing (C&P) problem suffers from tight coupling between geometric feasibility checking and optimization, hindering algorithmic innovation and reproducibility. Method: This paper introduces a geometry–optimization decoupling paradigm and presents *jagua-rs*, the first open-source, domain-specific collision detection engine for irregular C&P. Built in Rust, it leverages exact polygonal modeling and computational geometry theory to deliver high performance and robustness, supporting arbitrary rotations, translations, and complex boundary interactions. Geometric feasibility verification is fully abstracted into standardized, language-agnostic APIs. Contribution/Results: jagua-rs decouples geometric reasoning from optimization logic, enabling researchers to focus exclusively on algorithm design without implementing low-level geometric primitives. It significantly lowers the barrier to entry for irregular C&P research and provides a unified, reliable geometric foundation for heuristic, metaheuristic, and learning-based approaches.

This work addresses the inefficiency and labor-intensive nature of manually creating collision geometries for 3D models by proposing a bottom-up mesh decomposition approach that automatically generates efficient, editable, and rigid-body-simulation-ready convex primitive-based collision shapes. The key innovation lies in introducing, for the first time, a quadric-surface-inspired simplification strategy into convex primitive fitting, which preserves convexity and surface coverage while enabling user-guided refinement. Evaluated on over 60 Sketchfab models using a mesh-simplification-driven fitting algorithm, Hausdorff and Chamfer distance metrics, and physical simulation benchmarks, the method consistently outperforms V-HACD and CoACD by producing more accurate collision geometries with significantly smaller volumes—occupying less than one-third the storage—and achieves notably faster simulation speeds across 24 test cases.

Manually editing heterogeneous collision meshes in bulk is time-consuming and poorly scalable, while existing automatic methods often fail to accurately capture user intent. This work introduces neural symbolic program synthesis to 3D collision mesh editing for the first time, formulating the task as a programming-by-example problem: users provide only a few edited examples, and the system automatically synthesizes a reusable program that generalizes to similar meshes. Evaluated on 24 tasks involving 600 meshes, the approach successfully completes 23 tasks, requiring an average of just 2.2 examples per task and synthesizing programs in approximately 3.5 seconds, thereby significantly improving both editing efficiency and scalability.

This paper addresses topological ambiguities and numerical robustness issues in Constructive Solid Geometry (CSG) Boolean operations and mesh repair—arising from non-manifold intersections, multi-operand expressions, and degenerate geometries (e.g., coplanar or collinear features). We present the first algorithm to construct an exact Weiler spatial decomposition model. Our method integrates exact geometric predicates (via multi-precision arithmetic), co-refinement, radial sorting, constrained Delaunay triangulation, and symbolic perturbation to achieve precise intersection localization, unambiguous face classification, and consistent regional subdivision. Key contributions include: (1) the first complete, exact implementation of the Weiler model; and (2) a unified geometric kernel architecture that systematically handles all degenerate cases, eliminating duplicate faces and topological inconsistencies. Evaluated on the Thingi10K and ThingiCSG benchmarks, our approach demonstrates significantly higher robustness than state-of-the-art methods.

To address the low efficiency of collision detection in robot scenarios with high geometric complexity, this work pioneers the direct utilization of GPU hardware ray tracing (RT Core) for discrete collision detection between voxelized meshes, and extends it to continuous collision detection along piecewise linear and quadratic B-spline trajectories. The method integrates bounding volume hierarchy (BVH) acceleration, volumetric coverage error analysis, and CUDA-specific optimizations to balance accuracy and scalability. Experiments on a representative scenario comprising 24k robot triangles and 190k obstacle triangles demonstrate a 2.8× speedup for batched discrete collision detection and up to a 7× speedup for continuous collision detection. Furthermore, the trade-off between accuracy and performance is systematically quantified. This work establishes a new paradigm for real-time, high-fidelity robotic collision detection.

Plane-based Geometric Algebra (PGA) suffers from low representational efficiency and limited expressiveness for modeling discrete geometric entities—specifically, k-simplices (e.g., vertices, edges, faces) and k-complexes (e.g., point clouds, line complexes, triangle meshes)—in computational geometry. Method: We propose a unified, compact PGA-based representation framework. Our approach introduces Euclidean and ideal norms to derive a dimension-agnostic, closed-form k-metric formula—unifying length, area, volume, and higher-dimensional measures—and enables coordinate-free computation of geometric quantities such as centroids and inertia tensors. By integrating the join operator, simplex decomposition, and linear combinations, the framework supports algebraic construction and manipulation of both k-simplices and k-complexes. Results: Experiments demonstrate significant efficiency and practicality in mesh processing tasks. The method establishes a scalable, coordinate-free geometric computing paradigm for high-dimensional discrete geometry modeling.

Existing point-to-mesh distance query methods suffer from high precomputation costs and quadratic growth in candidate counts when handling rotationally symmetric structures, leading to inefficiency. This work proposes an efficient query framework that adaptively introduces auxiliary sites to localize complex interference, transforming interference detection into sphere–triangle collision tests based on Voronoi cell corners. Instead of conventional kd-tree searches, the method employs recursive dynamic programming. Combined with BVH acceleration and optimized spatial partitioning, the approach achieves 3–10× speedup in preprocessing and 1.5× faster query times, with particularly notable gains on rotationally symmetric geometries such as spheres and cones.

Existing robot self-collision matrix tools suffer from static visualization, lack of proximity query support, reliance on a single geometric primitive assumption, and cumbersome optimization workflows—limiting flexibility and reusability. This paper proposes an interactive, dynamic matrix generation framework implemented in Rust using the Bevy engine, featuring multi-level collision geometry abstraction, real-time rendering, and interactive fine-tuning. It introduces the first dynamic matrix construction and visualization method supporting proximity queries. Departing from conventional single-primitive constraints, the framework natively supports diverse geometric representations—including spheres, capsules, and convex hulls. The generated matrices are exported in reusable JSON/YAML formats. Evaluation across multiple robotic platforms demonstrates significant improvements: average speedup of 2.3× in both self-collision and self-proximity queries, and a 41% reduction in false-positive rates.

Existing tools struggle to visualize higher-order Voronoi diagrams and Delaunay tessellations under polygonal metrics, particularly Hilbert geometry. This work proposes the first efficient, dynamically interactive visualization system that unifies the generation and display of arbitrary-order Voronoi diagrams, Delaunay tessellations, and their associated clustering, overlapping, and exterior structures under Hilbert, Funk, and Thompson polygonal metrics, leveraging computational geometry algorithms. The core contributions include an integrated framework for generating and interactively exploring higher-order Voronoi diagrams, the discovery that k-th order Voronoi cells need not be star-shaped, and the establishment of theoretical complexity bounds for the underlying algorithms.

This study addresses the limitation that 3D meshes generated from images are predominantly non-convex, necessitating complex post-processing for physical simulation and motion planning. To overcome this, we propose an end-to-end framework that directly predicts convex decomposition geometry from a single RGB image. Specifically, our method freezes a pretrained Hunyuan3D-2 diffusion transformer and trains only a lightweight cross-attention head to generate “convex slot” tokens. Combined with a shape decoder and a half-space parameterization, it outputs compact collision primitives that can be directly loaded into physics engines without any post-processing. Experimental results demonstrate that our approach achieves superior volumetric IoU compared to eight baselines while accelerating inference by 6–37×. Furthermore, the method exhibits compatibility across multiple physics engines, substantially reducing deployment preparation time in real-world robotic scenarios.