Torus Knot

Here's the definition - easier than it looks actually. Link to the obligatory wikipedia article is here.

Also here's a definition for a version that takes an arbitrary base curve for input (in this case an ellipse for simplicity. By using a curve component one can also start with any arbitrary curve of course.

Thanks to my pal Harold for getting me distracted with this!

torus%20knot.gh

torus%20knot2.gh

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Comment by Iremnur Tokac on July 30, 2013 at 2:07am: thanks for sharing this, it is really helpful to understand the geometry

Comment by ĐỒNG VIẾT NGỌC BẢO on August 29, 2011 at 10:44pm: thanks for share!!

Comment by Harold Strang on August 27, 2011 at 12:18pm: OK, I think I figured it out. The 't' is not linearly proportional to the length along the curve. So I used "rs.CurveArcLengthPoint" to find points on the curve at the locations of interest, and then used "rs.CurveClosestPoint" to get the 't' at those locations to feed into the grasshopper "PFrame" component. The result is HERE

Comment by Harold Strang on August 26, 2011 at 2:26pm: I tried your definition and it seems to suffer from the same problem as my attempts so far. The rate of twist around the base curve doesn't appear to be constant. I'm not 100% sure yet, but I think it is dependent on the vertex spacing, such that the same number of twists appear between vertices, regardless how far apart they are.

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