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Author Topic: Knotting Ropes by Geodesic Control  (Read 3139 times)

struktor

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Knotting Ropes by Geodesic Control
« on: June 10, 2012, 09:09:32 AM »
A geodesic or geodetic line is usually the shortest line between two points on the surface.

Hyperboloid Geodesics:
http://demonstrations.wolfram.com/HyperboloidGeodesics/
Cone Geodesics:
http://demonstrations.wolfram.com/ConeGeodesics/

Knotting Ropes by Geodesic Control
http://homepages.inf.ed.ac.uk/tkomura/eg2012He.pdf
http://homepages.inf.ed.ac.uk/tkomura/eg2012.html

Struktor
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squarerigger

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Re: Knotting Ropes by Geodesic Control
« Reply #1 on: June 10, 2012, 07:27:51 PM »
Very interesting demos Struktor - thanks for posting.  I wonder where that could lead us?

SR
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struktor

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Re: Knotting Ropes by Geodesic Control
« Reply #2 on: June 12, 2012, 03:50:13 PM »
The line,wrapped around the block and stretched, lays along the geodesic line.
Knowing this fact can help to determine a line of strand rope.

Ray of light in the vicinity of large masses behaves like a fiber on a reel :)
http://www.math.harvard.edu/archive/118r_spring_05/handouts/geodesics.pdf
In both cases, you can use the same program :)
http://phys23p.sl.psu.edu/phys_anim/papers/geodesic_pov/povray_geodesics.pdf
http://www.sciencetronics.com/geocities/povray/geodesic.html

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