The appearance of woven fabrics is intrinsically determined by the geometric details of their meso/micro scale structure. In this paper, we propose a multiscale representation and tessellation approach for woven fabrics. We extend the Displaced Subdivision Surface (DSS) to a representation named Interlaced/Intertwisted Displacement Subdivision Surface (IDSS). IDSS maps the geometric detail, scale by scale, onto a ternary interpolatory subdivision surface that is approximated by Bezier patches. This approach is designed for woven fabric rendering on DX11 GPUs. We introduce the Woven Patch, a structure based on DirectX's new primitive, patch, to describe an area of a woven fabric so that it can be easily implemented in the graphics pipeline using a hull shader, a tessellator and a domain shader. We can render a woven piece of fabric at 25 frames per second on a low-performance NVIDIA 8400 MG mobile GPU. This allows for large-scale representations of woven fabrics that maintain the geometric variances of real yarn and fiber.