This paper presents convex hulls algorithms for a sorted set of points on a word model reconfigurable mesh. The algorithms are designed for two input cases: sparse input (i.e. one point is given for each column) and dense input (i.e. one point is given for each processor). For sparse input, the convex hull ofnpoints can be computed inO(log2n/log2m + 1) time on ann × mreconfigurable mesh. For dense input, the convex hull ofnmpoints can be computed inO(log2n/logm + log2m) time on ann × mreconfigurable mesh. As a corollary, for every fixed ε > 0, ann × nεreconfigurable mesh is sufficient to compute the convex hull ofnpoints in constant time, and ann/2log2/3n × 2log2/3nreconfigurable mesh can compute the convex hull ofnpoints inO(log4/3n) time.