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

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