- Finding the convex hull of n points in the plane requires O(n log n) time in general. In Devroye and Toussaint  and Golin et al.  the problem of computing the convex hull of the intersection points of n lines was considered, where the lines are chosen randomly according to two various models. In both models, linear-time algorithms were developed. Here we improve the results of Devroye and Toussaint  by giving a universal algorithm for a wider range of distributions.