co-ordinate system transformation

2018-06-19 23:58:02

I am trying to define a radial deformation (same deformation radially) in terms of Cartesian co-ordinates. The problem is that the cylinder is curved i.e. the center of the cylinder doesn't follow the axis i.e:

I know how to do the co-ordinate transformation for the straight section, just not sure how to do it for the curved section. The center of the pipe in this region can be defined as:

$$y = \sqrt{(0.03)^2 - (x-0.03)^2} + 0.15, y > 0.15$$