Abstract: This paper introduces a parametric model of oriented, navigable surfaces in virtual environments. An oriented, navigable surface in 3D space is modeled as a ribbon which has a central axis and can be twisted around the central axis. The axis is represented with a cubic spline curve and is approximately arc-length parameterized. The profile of the ribbon along the axis is described by a slant function. With the representation of the ribbon axis and the ribbon profile, a point on the ribbon surface can be expressed as a function of two parameters: the arc length along the axis and the offset from the axis. The parametric model of a ribbon naturally forms a local ribbon coordinate system which provides a frame of reference for behavior code. In order to provide an uniform, continuous frame of reference for an agent to navigate through connected ribbons, we unite the ribbons to form a ribbon called a path.