A system includes a computing device that includes a memory for storing instructions. The computing device also includes a processor configured to execute the instructions to perform a method that includes combining, in a nonlinear manner, a first set of vertex displacements that represent the difference between a first animated expression and a neutral animated expression with a second set of vertex displacements that represent the difference between a second animated expression and the neutral animated expression. 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.