Manifold Learning with Orthogonal Geodesic Grids

In Reverse Engineering, it is capital to find a parametric trimmed surface which approximates a triangular mesh (2-manifold with border) M in R3 -- This article proposes and implements a quasi isometry f: M -> R2 which allows a parameterization of M -- We consider quasi - developable 2- manifolds M in R3 -- f(p) = (u,w) with (u,w) being the coordinates of p in M under a grid of geodesic curves Ci(u) and Cj(w) on M -- We seek that the geodesic curves Ci(u) and Cj(w) be orthogonal to each other on M -- This means, that the Ci(u) should not cross each other, and each Ci(u) should intersect each Cj(w) in perpendicular manne