Monkey Saddle Grasshopper

I’d like to reproduce a Monkey Saddle surface, like this:

I’ve found something close, this:
but it’s not based on a circular shape, that is what I’d like to draw.

btw, the above script doesn’t work for me, I think something is missing.

Since I’m new to GH, can anyone give me some indications about how to generate this surface?
Many thanks

Hope it is of some help… (16.2 KB)


here is a little update. If you don’t make the surface periodic you will get a kink at the seam: (20.0 KB)

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Hi Kim,
impressive as always.
A little irrelevant question:
you named the input “x-1” to remember the expression or is there a setting (maybe newer update?) that does that automatically?

For the sake of the topic, the old school (pre expression editor) way. (9.0 KB)

Thanks so much to Michael, Aris, Tom and Kim: I’m going to study (…and learn) from your scripts.
Seems like Monkey Saddle ignited your curiosity as well :slight_smile:

Michael, your solution is very elegant and simple. Since I’m playing around with your script, I was wondering what is the “B” value: what does it refer to?

Also, the “Extent P” looks like to be the number of control points for the saddle surface. Am I correct?

B is dividing the result of the evaluate function. It is the z part of the equation. You can see parametric equations in Wolfram’s website.

and in fact you can just make z part of the evaluate function as well like the other guys did with the expression editor (8.7 KB)

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Ep is the number of grid cells in the polar direction as the description says. It is how many points around the radius. Er is how many points outward from the center.