The patterns are flat pieces that once joined come as close as possible to the warped surface (not flat) of a membrane. This means that if the membrane was completely rigid (i.e. had no deformation) what we would get would be a faceted surface: a surface made up of flat triangles joined on their sides.
Fortunately, the textile membranes support small deformations that are used to provide continuous warped surfaces. This happens most of the time, if you have made a correct pattern. However there are many occasions in which we will have to correct the pattern to avoid geometric problems. The case of patterns on Arcs is an example of these problems.
This topic is covered in depth in one of the blog posts of WinTess: Cross compensation