Collision between rigid three-dimensional objects is a very common modelling problem in a wide spectrum of scientific disciplines, including Computer Science and Physics. It spans from realistic animation of polyhedral shapes for computer vision to the description of thermodynamic and dynamic properties in simple and complex fluids. For instance, colloidal particles of especially exotic shapes are commonly modelled as hard-core objects, whose collision test is key to correctly determine their phase and aggregation behaviour. In this work, we propose the OpenMP Cuboid Sphere Intersection (OCSI) algorithm to detect collisions between prolate or oblate cuboids and spheres. We investigate OCSI's performance by bench-marking it against a number of algorithms commonly employed in computer graphics and colloidal science: Quick Rejection First (QRI), Quick Rejection Intertwined (QRF) and SIMD Streaming Extensions (SSE). We observed that QRI and QRF significantly depend on the specific cuboid anisotropy and sphere radius, while SSE and OCSI maintain their speed independently of the objects' geometry. While OCSI and SSE, both based on SIMD parallelization, show excellent and very similar performance, the former provides a more accessible coding and user-friendly implementation as it exploits OpenMP directives for automatic vectorization.

中文翻译：

---

硬核胶体长方体和球体之间的快速重叠检测。OCSI算法

刚性三维物体之间的碰撞是包括计算机科学和物理学在内的广泛科学学科中非常常见的建模问题。它涵盖了从用于计算机视觉的多面体形状的逼真动画到简单和复杂流体中的热力学和动态特性的描述。例如，形状特别奇特的胶体粒子通常被建模为硬核物体，其碰撞测试是正确确定其相和聚集行为的关键。在这项工作中，我们提出了 OpenMP Cuboid Sphere Intersection (OCSI) 算法来检测长方体或扁方体与球体之间的碰撞。我们通过对计算机图形学和胶体科学中常用的许多算法进行基准测试来研究 OCSI 的性能：Quick Rejection First (QRI)，快速拒绝交织 (QRF) 和 SIMD 流扩展 (SSE)。我们观察到 QRI 和 QRF 显着依赖于特定的长方体各向异性和球体半径，而 SSE 和 OCSI 保持其速度独立于物体的几何形状。虽然 OCSI 和 SSE 都基于 SIMD 并行化，表现出出色且非常相似的性能，但前者提供了更易于访问的编码和用户友好的实现，因为它利用 OpenMP 指令进行自动矢量化。