Tensile membrane surfaces are almost never flat. In fact, they should not never be. They are warped surfaces. These surfaces can be classified into two groups:
Those are that there is the same curvature at all points. That means the intersection of a plane perpendicular to this surface produces a line of intersection that is always concave towards the same side. In the case shown on the image it is towards the inside.
They are those that there is a double curvature at all points. That mans the intersection of a plane perpendicular to surface produces a line of intersection that is concave to one side, while the intersection of a plane perpendicular to the former produces a line of intersection that is concave to the opposite side.
In the image on the left, a perpendicular plane containing the two high points produces a concave upwards, while another involving two low points produces a concave downward.
Whatever the type of surface, to build it, we need to put patterns together obtained from a flat material, usually served in membrane rolls.
In the same way that we cut the fabric and sew to make a dress, we have to cut patterns and join them. Today, joining by sewing is little used in textile architecture. Instead, welding by high frequency (microwaves) is the method often used for joining. They can also be joined by gluing, but this method is also not used much.
The process of finding these flat patterns, which, once joined, give us a synclastic or anticlastic warped surface, is not easy. We see that the aesthetic quality of the tensile membrane depends very much on the process of patterning. Even the structural behaviour can be affected.
Wrinkles, deformations, large quantity of waste material, etc. are, often, result of wrong patterning.
The method used to transpose a warped surface into flat consists of dividing the warped surface into triangles. The triangles are always flat, so if we transfer adjacent triangles, side by side, we obtain a geometric shape in the form of elongated pattern which we are are looking for.
To make the process of patterning is correct, these triangles must be virtually stuck to the surface. One of the possible causes of a wrong pattern is to use too large triangles that are detached from the surface.
But which points we are going to use to make these triangles? We could use the same nodes of the mesh used for the calculation, but surely we would get some patterns very curved (shaped like banana), too much differences different between them and difficult to manipulate. However, in some rare cases of very regular shapes, it is possible that we can use the mesh for the patterning.