Mapping of cylinder to 2D plane I have a cylinder that has rectangular box regions to mark leakage problems. The location of a rectangular box is determined by its initial position in the longitudinal axis and its initial position in the circumferential axis in degree. The length  and width (in degrees, from 0° to 360°) of the boxes are also available.

How can I convert this cylinder to a plane surface so that I can find the location of the rectangular boxes in the 2D plane?
Here I have  three rectangles on the surface.
You already have a 2D parametrisation, don't you? One of the dimensions is the longitudal axis (in mm?) and the other is the circumferential axis (in degrees). The only problem I see is when you have rectangles wrapping around the 0/360-degree boundary. One workaround for that would be to duplicate each rectangle (or just the ones on the boundary) so that you get one copy on each side of the boundary. Does that help? And if you need to have a distance, and not an angle, for the circular dimension, that is readily available as $l = r a \pi/180$, where $r$ is the radius and $a$ is the angle in degrees.