1. An apparatus for natural inter-viseme animation of a 3D model driven by speech recognition, comprising: a speech recognition engine that identifies phonemes in a sequence of speech; and a processor programmed to associate the phonemes with corresponding visemes which represent facial expressions in said 3D model; said processor programmed to determine and limit any of velocity and acceleration of a normalized parameter vector, the velocity or acceleration occurring in movement from a first one of the visemes to a second one of the visemes; said processor programmed to establish and apply a maximum value to the velocity or acceleration to limit the velocity or acceleration, wherein as a distance between the first viseme and the second viseme decreases, the velocity or acceleration decreases from the maximum value to zero.