A viewpoint is a pair (X,D), where X = { x1,..., xn} is a set of variables, and D = { D1,..., Dn} is a set of associated domains for all xi X.
Once having choosen the variables and their domains, the next step is to search for a set of constraints such that the solutions to the problem are determined by the solution to the constraints. Obviously, the choice of the viewpoint affects the set of constraints we need. So, different viewpoints for a problem result in different sets of constraints and finally in completely different models for a problem.