continuous curvature algorythm

Greetings,

First of all, I want to apologize if by any chance this is a repeated subject, I did look beforehand using David's recommended methods.

What I'm trying to do is tessellate a surface with, for example, a hexagonal pattern. And, I want to extrude the edges/elements normally to the surface. The problem with this is that this will imply torsion on behalf of the elements, as shown in this pdf I'm attaching. So, my hope is that if I re-organize the connecting nodes so to maintain a constant curvature amongst the elements, they won't be under torsion. Meaning that length of the elements will be changing based on curvature of the surface, resulting in a (somewhat meaningful) distortion of the tessellation.
I'm thinking that if, for example, the edges of the pentagons and hexagons on a soccer ball are extruded normally to the ball (assuming it's a perfect sphere) the angles between the elements will be such that they won't be twisting. And I'm thinking this is true due to constant curvature, thus there is no need to re distribute the points where the edges connect.

I've looked at previous work done by Christian Tosche and have tried to apply it through grasshopper, but it hasn't been quite successful, so I was wondering if maybe anyone knew of some grasshopper work done with this in mind.

Any help would be greatly appreciated.

Thank you all,


Benjamin