Woven textiles are increasingly a medium through which HCI is inventing new technologies. Key challenges in integrating woven textiles in HCI include the high level of textile knowledge required to make effective use of the new possibilities they afford and the need for tools that bridge the concerns of textile designers and concerns of HCI researchers. This paper presents AdaCAD, a parametric design tool for designing woven textile structures. Through our design and evaluation of AdaCAD we found that parametric design helps weavers notate and explain the logics behind the complex structures they generate. We discuss these finding in relation to prior work in integrating craft and/or weaving in HCI, histories of woven notation, and boundary object theory to illuminate further possibilities for collaboration between craftspeople and HCI practitioners.