I am building an application in which given a surface and a pair of points on it, an analytic expression of some geodesic arc (preferably the one with the shortest length), between them is needed. Furthermore, this parametrized curve, needs to have minimal geodesic curvature.

I have been struggling to find a tool/ algorithm that does this. In this forum, I found this question, however I was not able to extract the information I need from it.

Is there a suggested tool that specializes in minimizing the geodesic curvature of the generated approximation?

I am looking for geodesic curvature less than 10^-8, ideally on any given NURBS representation of a smooth surface.

What I have tried so far:

  • The “geodesic” element in Grasshopper. This produces a geodesic curve with around roughly 10^-1 geodesic curvature. (reference surface is a cone)
  • The “shortpath” algorithm implemented in Grasshopper. This produces a geodesic curve with geodesic curvature roughly of the order 10^-3 to 10^-5. (reference surface is a cone)


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