Deriving parametric surface using mathematical equation

I was exploring minimal surfaces and came across various types of minimal surfaces that have been researched by scientists before. One of them is Bour’s surface and I got to learn about its coordinates equation for internet link given below.

Though I have got points that approximate the boundary curves, But how to derive surface from these points is still a challenge. Maybe I need another equation in terms of U and V or the information I have is sufficient to derive the surface. Any help would be appreciated. I am attaching the initial file I have worked on. Thank you.

BOUR’S (11.1 KB)

Parametriccuriosity (19.1 KB)


@Mahdiyar, How did you create that video?

By animating the slider.
CameraCrane for controlling the camera.
Bulk Image Converter for converting image files from BMP to JPG.
AfterEffects for creating Image Sequence animation.


And just to add a more “GH” way, you could use Daniel Piker images to GIF


Thanks @Mahdiyar, @laurent_delrieu, :slight_smile: I actually knew this method but I thought it’s something fancier that I did not know about.

you can also check horster plugin for grasshopper. It is a nice and simple tool to generate animation like those too.

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Thanks a lot Mahdiyar. I think problem with me was to understand math behind it. Your script made it clear both in terms of mathematical logic and process to do it in grasshopper. What I understood is that domain for this surface is sphere that is one variable and radius as another.

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don’t forget to enable interpolate

and if you want more control (u,v points number)

Parametriccuriosity (22.2 KB)

This also will help you :
Math surfaces from