Since designing a surface made from geodesic curves requires a simultaneous top-to-bottom and bottom-to-top understanding , it’s important to develop some intuitive understanding of how geodesic curve components will behave and how they will affect your resulting surface. Consider how multiple geodesic lines can connect the same two points on a cone, for example.
Here are the basic types of elastic bending (starting in straight segments thus requiring geodesic geometry) using a strip of paper. These are single segments, not derived from any surface in particular. Obviously wood would not bend so easily at this scale, but it demonstrates/labels some principles that we can use to discuss issues that may come up.
Case 1 – Two loose ends pushed together
Case 2 – One clamped end, the loose end is pushed
Case 3 – Both ends clamped together to form a loop
Case 4 – Both ends clamped to form a loop, but with a distance sideways between endpoints
Case 5 – Both ends clamped and twisted to form a loop
Here is a website that has many interesting and useful resources, including other people developing grasshopper scripts for elastic bending.