The state-of-the-art in computer drawing programs is based on a number of concepts that are over two decades old. One such concept is the use of layers for ordering the surfaces in a drawing from top to bottom. Unfortunately, the use of layers unnecessarily imposes a partial ordering on the depths of the surfaces and prevents the user from creating a large class of potential drawings, e.g., of Celtic knots and interwoven surfaces. In this paper we describe a novel approach which only requires local depth ordering of segments of the boundaries of surfaces in a drawing rather than a global depth relation between entire surfaces. Our program provides an intuitive user interface which allows a novice to create complex drawings of interwoven surfaces that would be difficult and time-consuming to create with standard drawing programs.