Types of Woven Fabrics. Woven fabrics are classified as to weave or structure according to the manner in which warp and weft cross each other. The three fundamental weaves, of which others are variations, are the plain, twill, and satin. In plain weave, also known as calico, tabby, taffeta, or homespun weaves, the weft passes over alternate warp threads, requiring two harnesses only. The relatively simple construction suits it to cheap fabrics, heavy yarns, and printed designs.