Monkey Saddle Grasshopper

I’d like to reproduce a Monkey Saddle surface, like this: https://www.dropbox.com/s/onl4zvyfdwo439v/MonkeySaddle.png?dl=0

I’ve found something close, this: https://www.designcoding.net/monkey-saddle-surface/
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…

MonkeySaddle_re.gh (16.2 KB)

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


MonkeySaddle_rere.gh (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?
x

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


Saddle.gh (9.0 KB)

Wow!
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


Saddle.gh (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.