Understanding semantic intricacies and high-level concepts is essential in image sketch generation, and this challenge becomes even more formidable when applied to the domain of videos. To address this, we propose a novel optimization-based framework for sketching videos represented by the frame-wise Bézier Curves. In detail, we first propose a cross-frame stroke initialization approach to warm up the location and the width of each curve. Then, we optimize the locations of these curves by utilizing a semantic loss based on CLIP features and a newly designed consistency loss using the self-decomposed 2D atlas network. Built upon these design elements, the resulting sketch video showcases notable visual abstraction and temporal coherence. Furthermore, by transforming a video into vector lines through the sketching process, our method unlocks applications in sketch-based video editing and video doodling, enabled through video composition.