In a flat n dimensional Euclidean space we have a body bounded by simplexes; its boundary B is an n−1 dimensional complex. The boundary is given topologically and the coordinates of the vertices are given. We want to divide the interior into well shaped n-simplexes which would thus comprise an oriented n-complex whose boundary is B.

At each vertex there is a Gaussian curvature in this sense. We need to compute this curvature (angle) at each vertex.

Thus begins a long digression.