Find a longitudinal axis of the cylinder (a least-squares linear fit to all your points will yield this).
Construct a plane passing through this axis. Any orientation should be fine, but let's say it is perpendicular to a normal passing from the axis to $C$.
Reorientate so the axis is vertical and the plane is divided into "left" and "right" halves by the ...
OK, after thinking about it for a while, I came up with an answer.
Find the caps of the cylinder, in other words two closed disjoint paths along the graph's borders.
Find a path along the face graph from one cap to the other.
Create a new sub-graph by removing all edges which lie along the path found in step 2. Keep track of the ...
The geodesics are the curves on a surface that connect two points A and B with shortest path. The geodesics of cylinder are parallel lines to the axis of the cylinder and circles orthogonal to them:
So if you have any point on the cylinder such as $C$, the shortest path to $C$ starts from itself is one of those circles. But you are saying it's not a perfect ...