A New Robust Algorithm for Computation of a Triangle Circumscribed Sphere in E3 and a Hypersphere Simplex

TL;DR

This paper introduces a fast, robust algorithm for computing the circumscribed sphere of a triangle in 3D and higher dimensions, useful for collision detection and ray tracing, optimized for modern hardware like GPUs and CPUs.

Contribution

It presents a novel algorithm for circumscribed sphere computation in E3 and higher dimensions, optimized for hardware acceleration.

Findings

Algorithm is faster than existing methods.

Method is robust against numerical instability.

Suitable for GPU and CPU vector instructions.

Abstract

There are many applications in which a bounding sphere containing the given triangle E3 is needed, e.g. fast collision detection, ray-triangle intersecting in raytracing etc. This is a typical geometrical problem in E3 and it has also applications in computational problems in general. In this paper a new fast and robust algorithm of circumscribed sphere computation in the -dimensional space is presented and specification for the E3 space is given, too. The presented method is convenient for use on GPU or with SSE or Intel AVX instructions on a standard CPU