# Parametric irregular minimal surfaces

Hi.
I wondering whether there is a way to parametrize the creation of a structure using minimal surfaces ( rather quadrilateral evolution as opposed to unit cubic cell ).
Tried looking for the Minimal surface plugin (Minimal Surface Plugin - Grasshopper) yet I couldn’t figure out how to create what I am looking for even though it may be possible and couldn’t find any pertinent tutorials.
Here is an approximate 3D showcasing what I am trying to create but it is by no means a minimal surface nor a continuous “neat” surface

And in the attached files, you can see my attempts, I am basically looking for a way to transform the basic patch to create a continuous minimal surface ( that I would be able to control to a certain degree).
For now, I have an issue with millipede getting this error:
“1. Solution exception:Index was out of range. Must be non-negative and less than the size of the collection.
Parameter name: index”

02.gh (34.6 KB)
02.3dm (189.3 KB)

What are minimal surfaces? In theory surfaces with zero mean curvature.

First of all meshes are no real “surfaces”, since they have no underlying formula, they just display a surface. That’s one difference between a mesh and NURBS-Surface. On a NURBS-surface you can create a point anywhere since you have a formula describing each point. You can change this surface and keep the mathematical description, whereas a mesh, created by a parametric formula, looses this ability when its vertices are moved. Meshes also don’t have an overall curvature, since meshes are polygons and flat (thus not always planar).

So in order to create “irregular” minimal surfaces through modelling you need a NURBS-representation, where some minimising algorithm could work.

Now, you cannot create a perfect minimal surface with NURBS since you cannot perfectly make an NURBS having minimal curvature 0 everywhere (at least if not being planar or symmetric). However you can model a shape in a way that the mean curvature gets minimized. For complex shapes you need more than one surface. Its rather hard to code a function like : “Make it minimal, but let me have control over the shape”.
Its not working like this. You can however optimise a modelled shape in a way, that mean curvature gets minimal. Therefore model it in Rhino, analyse it with Rhino curvature analysis and check for mean curvature, modify it…

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