Thank you soooooo much. I'm a sculptor trained as an architect and newish to grasshopper. One of the reasons I am learning grasshopper is to explore knots parametrically- my son did his thesis on knot theory with Colin Adams at Williams college and I had wanted to model his thesis. This tutorial is exactly what I was trying to do, although I have since been told that his thesis isn't possible to materialize because it has more than 3 dimensions. If anyone can help me understand if there is anything in this paper that I can model parametrically, I would be super appreciative. Abstract. We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic. arxiv.org/pdf/1904.06385.pdf
Always a pleasure to see your videos, this is fantastic, thank you!!
Thank you soooooo much. I'm a sculptor trained as an architect and newish to grasshopper. One of the reasons I am learning grasshopper is to explore knots parametrically- my son did his thesis on knot theory with Colin Adams at Williams college and I had wanted to model his thesis. This tutorial is exactly what I was trying to do, although I have since been told that his thesis isn't possible to materialize because it has more than 3 dimensions. If anyone can help me understand if there is anything in this paper that I can model parametrically, I would be super appreciative.
Abstract. We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic.
arxiv.org/pdf/1904.06385.pdf
amazing！
😊🙏
This is amazing! I am trying to figure a way to make have this knot follows any curve desired as a wave pattern
That's interesting 👍
merci mon bro
Is it possible to redefine any parametric equation with geometrical parameters ?
Can you explain SHİFT PATH component with a geometric pattern in grasshopper ?
My new drinking game is to take a drink every time you say "In Grasshopper"