Although the length of a curve is given by an explicit formula, it is generally impossible to write out the distance function by any explicit means. In fact, if is compact, there always exist points where is non-differentiable, and it can be remarkably difficult to even determine the location or nature of these points, even in seemingly simple cases such as when is an ellipsoid.
Although the length of a curve is given by an explicit formula, it is generally impossible to wri,te out the distance function by any explicit means. In fact if is compact, there always exist points where is non-differentiable and it can be remarkably difficult to even determine the location or nature of these points, even in seemingly simple cases such as when is an ellips,oid.