The bias is the most elastic part of the weave, so cutting and planning your project on the bias, or cross, will allow the greatest flexibility. Cross cut fabric will stretch more, will lie around curves and will fit to form.
It is a technique with sculptural potential–as Madame Madeleine Vionnette, the French couturier who became the legendary ‘Queen of the bias’, discovered when she cut the highly fashionable, figure-hugging classical dresses of the early to mid 20th C.
Lampshade linings are always cut on the bias and then stretched until each panel takes the form of the frame. Piping always works best when cut on the cross and especially when a 45o turn of the fabric produces an interesting self contrast. Cross cutting stripes and any fabric for frills and raw edges, is one way to create different effects and finishes within one fabric.