Orthogonal Projections Based on Hyperbolic and Spherical n-Simplex
  In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection. It is also given the perpendicular foots from a point to k-plane of hyperbolic and spherical n-space. 
Baki Karliga, Murat Savas and Atakan T. Yakut
math.MG