What fabric structure involves a pre-determined pattern, typically represented by diagonal lines?

The fabric structure that involves a pre-determined pattern, typically represented by diagonal lines, is twill. Twill is characterized by its weaving method, which creates a distinctive pattern of diagonal ribs or lines on the fabric. This structure not only adds visual interest but also contributes to the fabric's durability and draping qualities. The diagonal pattern is formed by the weaving technique that shifts the warp and weft threads, resulting in a fabric that is often used in various applications, including clothing like denim and upholstery.

The other options, while they have their own unique properties, do not exhibit the diagonal lines characteristic of twill. Sateen, for example, is known for its smooth, lustrous surface created through a specific weave but does not feature the diagonal pattern. Canvas is a sturdy fabric often made using a plain weave and is primarily characterized by its durability rather than any particular pattern. Brocade features intricate designs created by weaving with contrasting thread colors but does not produce the diagonal patterns associated with twill. Thus, twill is the correct answer because of its defining diagonal structure.