I was wondering if it is possible to compute the distance between two points which lay on a curved analytical surface. The surface is defined with differential geometry formulae (position vector of each surface point). In particular I have the Lamé parameters of the curve and the radii of curvature. Since the curves generating the surface are parametrized by angles I can't find a direct approach to evaluate the distance (integral along the surface line) without actually performing that integral.
Is that make sense? Is it possible?