Nonphotorealistic rendering (NPR) can help make comprehensible but simple pictures of complicated objects by employing an econ- omy of line. But current nonphotorealistic rendering is primarily a batch process. This paper presents a real-time nonphotorealistic renderer that deliberately trades accuracy and detail for speed. Our renderer uses a method for determining visible lines and surfaces which is a modification of Appel's hidden-line algorithm, with im- provements which are based on the topology of singular maps of a surface into the plane. The method we describe for determining visibility has the potential to be used in any NPR system that re- quires a description of visible lines or surfaces in the scene. The major contribution of this paper is thus to describe a tool which can significantly improve the performance of these systems. We demon- strate the system with several nonphotorealistic rendering styles, all of which operate on complex models at interactive frame rates.