How to parameterise this equation into individual parameters (15.5 KB)
I’m in my last year of university so I’ve been left mostly to my own devices, and I can’t seem to get my head around this, I’ve been trying to make it work for the past week now. I’ve tried applying logic from different tutorials across youtube, such as the trefoil knot, making 2D parametric geometry from scratch, using parametric equations in grasshopper and re-modeling over the geometry in rhino, using that information for the gh parameters - but nothing seems to apply. I’d really appreciate some fresh eyes on this as I’ve tried out so many different approaches that even if one of them was close to working I’m not sure if I’d even know!

If someone can just point me in the right direction I’m sure I’ll be able to generally work the rest out!

Hi @Grace_Mary,

I’m not clear from your post what you are asking for. Do you have an equation for the curve that you want help implementing in GH? Or are you asking for help identifying the equation that drives that curve?


Hi there,
I want to implement this graph below into GH, but not the way I’ve done it above. I want to define x=cos(at) - cos3(bt) and y= sin(ct)-sin3(dt) into numerical values/number sliders that shift through the curve? Eventually, I want it to be a facade. Simarlily to how it’s done at the end of this tutorial How to make a Trefoil Knot (Parametric Surface) - YouTube . I’m aware of how to make parametric facades and I followed the fore-mentioned tutorial to get my head around breaking down an equation geometrically. I’m struggling to do it for this, and implement it on my own, however. I have a background in motion design and 3D modelling, so this part I’m really stuck on.


HI @Grace_Mary,

I think the fundamental thing here is divide and conquer.

I’d start by examining what you have here. Looking at the final interpolation output it is hard to see what is happening. Start by reducing the number of steps to, say 24. Then take a subset of the first 24 values from the u and v datastreams and see what you get (spoiler: a circle and a displacement). See how they are generated by removing terms from the formulae. Compare what happens with the next 24 values.

You should then understand it well enough to be able to create parametric formulae for generating circles and displacements that have the same effect as your initial model. Once you have that working, consider what you want from your facade. Can you get that with your parametarization? Do you adjust your formulae? Add more parameters? Go into 3D? Change your model a step at a time and make sure it all works properly before moving on - don’t try and change everything at once.

Hopefully, by the end you will have solved your problem and, more importantly, understood it better.


… what that means?

(have you downloaded the file in the description of the video?)
In that video the creator is using 3D curves, then make it a pipe and then slice it … is that a “facade” for you?
If you want something similar, start searching for 3D equations, using only x and y will make you stuck to 2D…
Or you actually want the full shape to stay “flat”?

Your picture is (also) from wikipedia:

parametric (5.4 KB)

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Thank you this is wonderful! Just what I was looking for thanks so much

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