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algorithmic modeling for Rhino

giancarlo tonoli
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giancarlo tonoli's Discussions

geodesic! I have a doubt...
10 Replies

Hi,If the mathematical definition of a geodesic curve is: the shortest path between two points on a surface, why the geodesic component returns a curve like this? that's a longer curve compared with…Continue

Started this discussion. Last reply by giancarlo tonoli Oct 20, 2011.

 

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giancarlo tonoli is now a member of Grasshopper
May 9, 2013
Chris Tietjen replied to giancarlo tonoli's discussion geodesic! I have a doubt...
"Here's a link that might help. http://www.rdrop.com/~half/Creations/Puzzles/cone.geodesics/index.html The circle on the cone in your definition is not a geodesic as a circle will not unroll into a straight line but rather an arc or on a cone of…"
Oct 19, 2011
Danny Boyes replied to giancarlo tonoli's discussion geodesic! I have a doubt...
"Create a mesh for your surface and try Giulio's Shortest Walk routine."
Oct 19, 2011
Chris Tietjen replied to giancarlo tonoli's discussion geodesic! I have a doubt...
""Although defining a geodesic as the shortest arc between two points on a surface gives the main idea of a geodesic, there is a problem with it as a definition. Not every geodesic is a shortest path in the large, as can be seen by noting that…"
Oct 13, 2011
Daniel Piker replied to giancarlo tonoli's discussion geodesic! I have a doubt...
"Hi Chris, The distinction between locally shortest and globally shortest paths is not limited to closed surfaces. As an example : Here the red path is clearly shorter, but the blue path is the geodesic - because if you unrolled the surface it would…"
Oct 13, 2011
Chris Tietjen replied to giancarlo tonoli's discussion geodesic! I have a doubt...
"Hi Daniel, I think that your response is addressing the issue of a geodesic on a closed surface.  Giancarlo's example is an open surface so it won't have a closed curve for a geodesic at any time.  I wonder if his surface has…"
Oct 13, 2011
Daniel Piker replied to giancarlo tonoli's discussion geodesic! I have a doubt...
"A geodesic is not actually defined as the shortest path between two points on a surface - it is only locally the shortest. So for any 2 points close together on the path it is the shortest route between them, but the whole path may not be the…"
Oct 13, 2011

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