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

Luca Tonti,Alessandro Patti

doi:10.3390/a14030072

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.

Highlights

Employing computer programs and algorithms to generate 2D or 3D images is referred to as rendering
Due to the large number of benchmarks performed, we intended to report here the behaviour of the run-time efficiency of the algorithms with respect to the shape of the cuboid and the sphere only for the programs compiled using Intel® C and Intel® Fortran Compiler, enabling the use of Advanced Vector Extensions (AVX) instruction set for SIMD parallelization
Our analysis focused on a specific acceptance ratio, which is within the usual range applied to efficiently sample the configuration space of hard-core systems in Monte Carlo simulations [52]

Summary

Introduction

Employing computer programs and algorithms to generate 2D or 3D images is referred to as rendering. Understanding the fundamentals of such a complex correlation, which develops over orders of magnitude in length and time scales, dramatically depends on the existence of reliable force fields mimicking the interactions between particles This is not always the case for most exotic particle shapes, whose force field is assumed to be described by mere excluded volume effects and only incorporates a hard-core interaction potential. Incorporating guest spherical particles in these phases is relevant to understand phenomena of diffusion in crowded environments that display a significant degree of ordering In light of these considerations, which highlight the harmonious inter-disciplinary convergence of computer graphics and colloid science, here we report on the specific case of cuboid-sphere collision detection.

Algorithms

Computational Details

Results and Discussion

Conclusions