Abstract: This invention discloses woven materials in which the constructed woven materials have a myriad of desired two- and three-dimensional shapes. The invention specifically discloses woven materials that are constructed by continuously varying the density and/or direction of the warp and/or weft fibers or yarns, as well as their angle of contact, at will during the mechanical weaving process. These two- and three-dimensional woven materials can also be used as reinforcers of variously shaped flexible or rigid composite materials.