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My problem is the following: I have a cylinder, and a couple of geodesic segments on its surface. The segments are defined by the coordinates of their start and end points. I have to obtain the coordinates of intersections of these segments. Unwrapping the cylinder to a plane would let me easily compute the intersections as the segments would be lines, however there is a problem with periodicity, i.e. by cutting the cylinder I might loose intersections. My question is whether there is any general formula for this situation which would somehow implicitly take into account periodicity.

Thank you!

Bb

botond
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  • Hmm, given two points on the cylinder, there will be infinitely many geodesics connecting them. – fuglede Jun 03 '14 at 14:20
  • Thanks for your answer! I don't see how though... As far as I know, geodesics are the shortest distance between two points, measured on the surface. – botond Jun 03 '14 at 14:48
  • Not quite: in the cylinder case, the geodesics are exactly the helices. So, suppose for instance that the two points lie on a vertical line. Then one geodesic would be simply that vertical line, but you can also imagine a helix connecting the two points (in fact, infinitely many helices will do so). Now of course, you could simply restrict attention to the shortest among all geodesics and ask your question for those. Maybe that's what you want? – fuglede Jun 03 '14 at 14:52
  • One reason for confusion here: Geodesics are locally the shortest path between points, but not necessarily globally so. – Harald Hanche-Olsen Jun 03 '14 at 14:57
  • Sorry for the confusion. What I need is definitely the shortest path that connects the two points. – botond Jun 03 '14 at 15:05

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