this is not a good task for Galapagos because this is more a sort of “hit or miss” situation, where you can’t evaluate how well or badly you have missed in such a way next generation might improve based on the result of previous one

Galapagos is an evolutionary solver, which very often is interpreted as a “brute force machine” (I -in first place- have been using it like that for a long time… and sometimes I still do…)

you have two arcs, one of them is fixed in space, the other one can have its start and end points moved along Y on a certain interval

why trying all the possible arc-start-point and arc-end-point combinations, if you already know from the beginning there’s just exactly one given solution for each arc-B point, for which the two arcs are intersecting in exactly two points?

this part, for each customizable B-mid-arc point, gives you only the A and C points on XY plane that satisfy the “the two arcs are intersecting in two points” condition

it starts from the idea that, because the two arcs are planar, if they intersect then for sure will intersect on the line identified by the intersection of the very planes they lie on

we find the plane|plane intersection line (white) and intersect it with the arc which is fixed in space (green points)

and then we build a second arc that pass through our point B, and those two points, which for sure intersects the second arc

then extend this arc until it for sure touches the XY plane, and 4) find the intersection points (yellow) with the XY plane

at the end we can even “redraw” the perfect arc with the new A and C points which lie on the XY plane and our point B

I want the surface to be offseted to the middle (on both sides), like that the edges of the surface moves to the middle point. The white line should be an empty space between the anchor and the surface. Membran.gh (19.3 KB)

Thank you, you are very helpful.
And I like it that you not only send the solution. Because you send the explanation too and so I can understand it better and learn it