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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 ...

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OK, after thinking about it for a while, I came up with an answer. Step 1: Find the caps of the cylinder, in other words two closed disjoint paths along the graph's borders. Step 2: Find a path along the face graph from one cap to the other. Step 3: Create a new sub-graph by removing all edges which lie along the path found in step 2. Keep track of the ...

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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 ...

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