Robust Barycentric Coordinates Computation of the Closest Point to a Hyperplane in En

Abstract

Barycentric coordinates are well known and used in many applications. They are used for a position computation inside of an (n+1)-sided simplex in an n-dimensional space, i.e. in a triangle in E2 or in a tetrahedron in E3. There are some cases when the given point is theoretically on the hyperplane, i.e. on a plane in E3, but due to numerical imprecision is actually not. Also in some cases we need to compute barycentric coordinates of an n-sided simplex in an n-dimensional space, like barycentric coordinates of a point inside or outside of a triangle in a general position in E3. In those cases different approaches are taken, mostly unreliable and not robust in general. In this paper reliable and robust computation of barycentric coordinates for n-sided simplex in En is described.