Torus Knot

A torus that ends where it started.

[@MegaGodisreal]

I am interested in buying a few of these torus knots like this one. Any size. Made in plastic or metal. Please send me any info. I know this video is computer generated. But I need to actually have a few of these it in my hands for a lecture.

[@Sunlessmage]

Is this Blender ?

[@HiAdrian]

***** I think I did the scene in Houdini, but the shape itself was C++ directly to an .obj sequence, so if Blender can deal with geometry that way, I'm sure it can be done there just the same.

[@Kris-od3sj]

nice :D

[@ivanfacil]

Absolutely beautiful!

[@PunmasterSTP]

Oh man, this video was definitely knot lame! 😎

[@EhsanYazdani]

I've just discovered Structure Synth. Great software! I wonder how I may know more about tweaking these beautiful shapes. Unfortunately I have no background in programming.

[@HiAdrian]

Unfortunately I can't be of help there either. I have shortly tried Structure Synth and it's really cool, but I didn't spend the time to get into it. The torus above I stumbled upon while struggling (I'm not good at math) to create a more complex shape. It was simply an OBJ file which I animated later in Houdini.

[@EhsanYazdani]

Oh! thanks for your reply! Actually, I'm not a math freak as well, I was planning to create my own model and transfer the OBJ to Maya in order to achieve my goal! Kindda similar to what you didi... ;)

[@HiAdrian]

Ehsan Yazdani What I can tell you from memory is that the _path_ of a Torus Knot can be created by rotating a point around two axes simultaneously, with the first axis being offset from the center. Say you have a regular 3D space as in Maya [x, y, z] with y pointing upwards. If you take a point *P* at [4, 0, 0] (offset in the x-axis) and rotate it around the z-axis, it moves in a circle around the origin [0, 0, 0]. If instead you move the center of that rotation to [2.5, 0, 0] (let's call it *L1*), *P* will rotate around 2.5, so you get a smaller circle that never touches the origin (2.0 would). So *P* going around *L1* draws an eternal circle. We now add another rotation *L2* at the origin [0, 0, 0] which rotates around the y-axis (just like a _carousel_). If we now rotate *P* and *L1* around *L2* (In Maya parent-child terms that's *L2* > *L1* > *P*) the circle no longer sits stationary but instead becomes a "helix" that bends around the origin. Now all you need to do is play with the amount of rotation for each axis. If the torus knot "bites its own tail" too soon, then you can linearly increment one of the rotational axes. *P* will always return to the same positions around *L1*, such as 10°, 20°... 350°, 0°, 10° etc. If you increase this steadily, then it will be at 0.05°, 10.07°, 20.09° until eventually it will have gone from e.g. 19.98° to 20.0° again, closing the path it drew around the _carousel_. Hope that helps!

[@EhsanYazdani]

Dear Adrian Thanks for your quick and precise reply. To be honest with you, it needs more than my knowledge to understand it fully, and I think I have to study more in both MEL and 3D geometry in order to get my very special look! ;) p.s: Your video really made me happy, cause it was a living proof to show me it is actually possible! Respect!

[@HiAdrian]

Ehsan Yazdani Ok, no problem :) I really had to chew on this topic too when I first tried it and still have no intuition _why_ it works, I just learned the basic steps. In case you want to read up on this, the main topics (from math) are _"Vector"_ and _"Transformation Matrix"_ (specifically _Translation_ & _Rotation_ matrices). It may give you a headache, but gets you 90% toward creating such a torus. If you're stuck on some detail, don't hesitate to ask. Good luck!