Revealing the sketching sequence of a line drawing can be visually intriguing and used for video-based storytelling. Typically this is enabled based on tedious recording of artists' drawing process. We demonstrate that it is often possible to estimate a reasonable drawing order from a static line drawing with clearly defined shape geometry, which looks plausible to a human viewer. We map the key principles of drawing order from drawing cognition to computational procedures in our framework. Our system produces plausible animated constructions of input line drawings, with no or little user intervention. We test our algorithm on a range of input sketches, with varying degree of complexity and structure, and evaluate the results via a user study. We also present applications to gesture drawing synthesis and drawing animation creation especially in the context of video scribing.