Fast Overlap Detection between Hard-Core Colloidal Cuboids and Spheres. The OCSI Algorithm

Abstract

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 Oriented 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 a vectorized version of the OBB-sphere collision detection algorithm that explicitly uses SIMD Streaming Extension (SSE) intrinsics, here referred to as SSE-intr. We observed that QRI and QRF significantly depend on the specific cuboid anisotropy and sphere radius, while SSE-intr and OCSI maintain their speed independently of the objects’ geometry. While OCSI and SSE-intr, 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.