I have data points of a catenary curve in 3D space (x,y,z co-ordinates). I am able to fit this data in 2D space properly with normal catenary equation y = a*cosh(x/a). However, on 3D space the catenary is not matching as the 3rd axis is not exactly on a plane and it is kind of rotated.
Can anyone suggest me how to rotate a 2D catenary in 3D space (P.S - I have already tried elementary rotation along all the planes)