Hyperwedge

Abstract

The direct construction of geometric elements in an N dimensional geometric algebra by taking the outer product between \(N-1\) primitive points is one of the cornerstone tools. It is used to construct a variety of objects, from spheres in CGA [], up to quadric [] and even cubic surfaces [] in much higher dimensional algebras. Initial implementations of the latter however revealed that this is not without numerical issues. Naively taking the outer product between \(N-1\) vectors in these high dimensional algebras is not practically possible within the limits of IEEE 64 bit floating point. In this paper we show how established techniques from linear algebra can be used to solve this problem and compute a fast hyperwedge. We demonstrate superior precision and speed, even for low dimensional algebras like 3D CGA.