Works for me in Rhino for Windows if I start NetworkSrf command without any curves selected, and then select curves. However it doesn’t work if I select the curves and then start the command.
If the attached isn’t what you’re after, then maybe it would be better to extend the red curves to make it more rectangular, and trim the result with the green.Problem73A.3dm (144.6 KB) Maybe @BrianJ has another idea.
Depending on what you need to connect to adjacent to this surface and how closely that relates to the green curves, you may want to try a Patch surface at 100x50 like the attached. Problem73_patch.3dm (495.3 KB)
In order to get tangent continuity, you have to make sure the new curve that meets at the kink has end tangent that is coplanar with both parts of the curve that was broken at the kink. Otherwise, you’re asking for something that is not mathematically possible. Here Problem73c.3dm (119.1 KB) I’ve made lines tangent to the two parts of the green curve, made a 3 point plane from the lines, extended the plane, and projected the second-to-end control point of the black curve to that plane. Now the two network surfaces are tangent.