Unrolling a curve in Rhino

Here is what I want to do.

Lets say we take the classic example of writing the word rhino on the surface of a sphere.

What I want to do it to take the letters and unroll them from the surface, lay them flat, cut them on the CNC on a very flexible substrate so that I can then roll them back around the sphere and have them fit perfectly.

On the sphere they have no apparent distortion since they are created using spherical geometry. When they are “unrolled off of the sphere and layed flat” they have to then take on a built in distortion similar to that of a flat projecting map we all saw in school, then when they are again rolled onto the sphere they then lie undistorted with the same spherical geometry they were created with.


Hi Steven - you can try CreateUVCrv/ApplyCrv- this will unroll the text curves much like the map example you give but there is no certainlty that the distortion matches any particular material characteristics in mapping back to the sphere.
For doubly curved surfaces, if you are trying to replicate the behavior of a particular material that will be flat and then applied to the surface in a predictable way, there is no really completely accurate solution in Rhino. If the curves on the sphere are in a relatively small area of the sphere you can use Squish to get some control over the unrolling - you’d split the sphere just around the text - maybe even one letter at a time.