Conversions between intrinsic/extrinsic coordinates

I noticed that in wiki there is the follows conversion:















that is the conversion beetwen the cartesian coordinates and the intrinsic (arc length, curvature) "coordinate". In this case, the system is 2D.





There is the 3D case too:











However, is missing the (x, y, z) coordinates in terms of (s, κ, τ). Where I can find this conversion?