Calculating Centroids in Constrained Mixture Experiments

In constrained mixture experiments the centroid of a constraint region has traditionally been defined as the average of all extreme vertices of the region. This differs from the classical physics definition of a centroid as the center of mass (or volume) of a region. An algorithm for calculating a centroid based on the center of mass definition is discussed and illustrated with an example. This centroid calculation technique can be used to calculate centroids of various dimensional faces and edges of the constraint region as well as of the overall centroid. Results of the center-of-mass and averaged-extreme-vertices centroid computation techniques are compared using examples from the literature.