Abstract: We describe a method to parameterize lines generated from animated 3D models in the context of animated line drawings. Cartoons and mechanical illustrations are popular subjects of non-photorealistic drawings and are often generated from 3D models. Adding texture to the lines, for instance to depict brush strokes or dashed lines, enables greater expressiveness, e.g. to distinguish between visible and hidden lines. However, dynamic visibility events and the evolving shape of the lines raise issues that have been only partially explored so far. In this paper, we assume that the entire 3D animation is known ahead of time, as is typically the case for feature animations and off-line rendering. At the core of our method is a geometric formulation of the problem as a parameterization of the space-time surface swept by a 2D line during the animation. First, we build this surface by extracting lines in each frame. We demonstrate our approach with silhouette lines. Then, we locate visibility events that would create discontinuities and propagate them through time. They decompose the surface into charts with a disc topology. We parameterize each chart via a least-squares approach that reflects the specific requirements of line drawing. This step results in a texture atlas of the space-time surface which defines the parameterization for each line. We show that by adjusting a few weights in the least-squares energy, the artist can obtain an artifact-free animated motion in a variety of typical non-photorealistic styles such as painterly strokes and technical line drawing.