1. A computer-implemented method comprising: receiving a neutral animated expression; receiving a first set of vertex displacements that represent the difference between a first animated expression and the neutral animated expression; receiving a second set of vertex displacements that represent the difference between a second animated expression and the neutral animated expression; combining, in a nonlinear manner, the first set of vertex displacements with the second set of vertex displacements, wherein: the number of vertices associated with the first set of vertex displacements of the first animated expression is equivalent to the number of vertices associated with the second set of vertex displacements of the second animated expression; and the combining includes an averaging function for at least one vertex displacement included in the first set of vertex displacements and a corresponding vertex displacement included in the second set of vertex displacements.