The natural progression after working out successful structure for permanent, strong folds is to take those straight folds and utilize the power of a jacquard loom to introduce lines that couldn’t be done so easily on a regular loom. 

By curving the pleats, the fabric also begins to twist, giving the folds a bit more rigidity. This rigidity is also seen in insect wings. When insects have wings which are considerably larger than their body, their wings fold up when closed in particular ways that urilize curved folds to strengthen the wing which would otherwise be too large to support through more conventional muscular structures.