Off-grid isocurve

Hey folks!

I’m looking for a way to get shifted/rotated isocurves on a NURBS surface. Could you please give me some guidance?

So for example given a cylinder (from circle extruded in z direction, let’s say the z direction), if I look for isovurve at some uv point (1, 2) on it, it grasshopper would give two results: (1) vertical line (let’s say this is u direction) and (2) horizontal line (let’s say this is v direction). So if I unroll this cylinder into a surface, the two lines would be like u=1 and v=2, right?

What I want is the isocurve through this uv point but rotated at a degree (in the uv domain). Is this possible?

Thanks a ton!!

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Before trying to build up a solution, may I ask why you need this?

Do they have to be actual “isocurves but rotated”? (which means the new surface must be also larger and trimmed, and other things)
Or you need just curves, that are at a tilted angle in relation to the UV parametrization of a surface… ?

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Thanks Riccardo! I was thinking of a bizarre situation I have encountered in the past, where this could really help. Certainly, there are better ways for the specific problem below, but I just want to know how/if this ‘rotated isocurve’ way would work:

S is a closed surface. It’s like a pipe/horn thingy, and we are looking from the side view. Problem is, it’s flipped at the tip (like you see in some flowers), so I want to trim away the flipped part, so I can easily cap it (to get close volume)

What I need is to trim this along some want_this(x, y). I wanted to use isocurve(x) and isocurve(y) but, because of how the surface is, they are slanted/rotated in a weird way.

Now, I’ve tried doing surface_geodeisic(x, y) and surface_geodeisic(y, x) to try look for a fix. However, they don’t have continuity to each other and look ugly. What I like about isocurve() is that the line is smoothly wrapping all the way around the surface.

Here’s this illustration but on a cylinder (simpler case)

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If you consider u as a weight or an height if it is a plane I have tools to transform that to vectors with à given angle.

But as grid is not orthogonal there is chancevangle will not be the same on the other axis.

For 45 deg follow the values where u+v = constant

Same for others angle cos angle × u + sin angle × v = constant. Or something like that

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