Algorithms for computing centroids

Algorithms are given for the computation of centroids of discrete, polygonal, and continuous convex regions in the plane. These include the zero-dimensional center-of-gravity for discrete systems, and the area, perimeter, and curvature centroids for both discrete and continuous regions. The zero-dimensional center-of-gravity is motivated through analytic, arithmetic, and geometric formulations, and is an integral part of the computations of the area, perimeter, and curvature centroids. Several remarks are made that connect the computation of the centroid points to optimization theory and their practical application in various fields. The complexity of each algorithm is also examined.