I am trying to create a contour of equidistant curves on top of a mesh with double curvature. On a planar mesh this is easy to achieve with the Contour component. However on a mesh with double curvature the resulting curves are not at equal distance from each other. Is there any trick to achieve such a geometric result.

You could try the compass method which was once introduced by Frei Otto. There were some Plug-Ins, when I searched some months ago, but I ended up scripting a very buggy one myself.

I think David is asking about sets of curves going all the way across the surface in each direction at equal distance from the adjacent curves, not a grid of equal length segments(aka Chebyshev net) like you might use the compass method for.

I think that for a general mesh, finding these equidistant curves is an unavoidably iterative problem, so will require looping in some fashion, either with scripting or plugins (or just chaining repeated components together if you donâ€™t need a huge number).

A simple approach can be to pipe the starting curve, find the intersections, pipe the intersection curves etc

I have managed to create a working loop and the results are close to perfect.
I get small deviations when it comes to the length of the individual quad edges.
What I notice is that the quads that result from this method progressively lose their orthogonality.
Do you know of a method to keep the quads as square as possible? They donÂ´t need to be planar.
Or maybe it is impossible to achieve this as well?
I upload a result here. Equidistant Mesh.3dm (151.3 KB)

I wouldnâ€™t expect these to stay orthogonal as you get further out.

Can I ask whatâ€™s the end result youâ€™re aiming for with this?
Iâ€™m guessing itâ€™s maybe something to do with cutting patterns for a fabric structure?

If so, depending on whether youâ€™re aiming to minimise twist within each strip in the assembled form, or to keep the flat pieces as straight as possible, or with least width variation, or some trade-off between these,
you might want different curves, eg the 2 principal curvatures (which will intersect orthogonally), geodesics, or contours of geodesic distance.

Yes these quads.
I wonder if it is possible to create an ortogonal cable net and then fill the quads with simple fabric squares.
Such a thing is very simple to do with plane geometry. Troubles arise when you try to do it with doubly curved shape.