Interpolate curve on several surface

I’d like to interpolate curve on several surfaces at the same time.
Is there way to do it?
Why it has to be only one surface to draw? Is there some technical reason?
I’d like to choose several surfaces and then draw curve…


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This command?

It’s because the interpolation happens in a single coordinate space. Either in world XYZ or in surface UV. Once the curve has to cross from one coordinate space to another, the problem becomes both much harder and somewhat less defined.

The most obvious solution would be to perform the interpolation in 3D, and afterwards pull the projected curve back onto the polysurface.

Unless I misunderstood your question and what you’re asking is how to create multiple interpolated curves on different surfaces in one go, in which case @martinsiegrist’s answer should have you covered.