1. Trivial reject a. if both ends are higher than y0, reject b. if both ends are lower than y1, reject c. if both ends are larger than x1, reject d. if both ends are smaller than x0, reject
2. 'Trivial reject' is fast and should clip many of the polygon sides. if you are not satisfied and want to cut more, you might look into algorithm like Cohen-Sutherland Line-Clipping. here is a link: