Curves are used by ObiRope as a blueprint for creating ropes, in very much the same way ObiCloth uses ObiMeshTopology. In Obi versions prior to 4.0, there used to be two different kinds of curves. In 4.0 and later, there's only one: ObiCurve.
You can add a curve component to any GameObject in your scene, then assign it to the "Rope path" property of your rope. Several ropes can share the same curve, however they will be generated on top of each other. You may want to translate them elsewhere after generating them. It is usual practice to add the curve component of your choice to your rope object itself, so that each rope uses its own curve.
These are based on Bézier curves. When you enter curve editing mode by pressing the "Edit Curve " button in the curve inspector, you can control its shape by moving the control points (small white spheres) or tangent handles (small orange squares). You can select multiple control points at once by holding "shift", or you can drag a selection marquee using "ctrl". Translate, rotate and scale gizmos work in the same way as they do with regular GameObjects, so do the pivot and transform space toggles.
A curve can be either open(both ends are independent) or closed (the curve follows a closed path, with both ends sharing the same position and tangent), there's a checkbox in their inspector to toggle the mode.
Each tangent handle has three modes of operation, which can be set per-handle: Free, Aligned, or Mirrored.
When in edit curve mode, a small menu will appear in the top left corner of the scene view. This lets you bulk add/remove control points, set their orientation and their handle mode.
This toggle enables a tool to add control points to the spline visually. A red dotted line will appear between the mouse cursor and the closest point in the spline. Clicking will insert a new control point in the curve at that position.
This will delete all selected control points.
This tool allows you to define the orientation of each control point. Useful when using the curve to generate ObiRods, as this lets you specify the initial twist of the rod.