Fabric Choice, Stiffeners and Stabilizers
In general, stiffer fabrics will resist pull and distortion better.
Fabric stiffening aids and stabilizers will combat pull and make alignment easier. In particular, iron-on backing helps to resist fabric distortion. You may wish to apply this to the fabric before marking the hoop centers or making any other alignment marks.
Hoop Templates and Printed Worksheets
When hooping up each section, align the center marked on the fabric against the hoop template to guide the position of the fabric in the hoop. If you do not have a hoop template, use the printed worksheet at 100% scale for the section. You could also print the worksheet on transparency paper.
You may also wish to mark lines between the hoop center points so you can line up the fabric to the center marks on the frame of the hoop. This is especially helpful if you do not have a hoop template. Use a light-reactive fading pen to mark temporary lines just before you hoop the fabric. An alternative is to iron creases into the fabric as lines between the center points.