The disclosure is directed to an improved method and apparatus for generating a sequence of video frames representative of three-dimensional animation. A plurality of key frames are stored, each key frame including a common figure having one or more joints, and each joint having associated therewith a set of vectors defining a limb. Each joint is defined in each frame by operator-controllable parameters which determine the three-dimensional position, rotational orientation, and scale factors of a local coordinate system in which the limb vectors are placed. A plurality of in-between frames are generated, the in-between frames including the common figure having one or more joints and limbs corresponding to the joints and limbs of the common figure in the key frames. The parameters of the joints of the in-between frames are obtained by interpolating in three dimensions, the position, rotational orientation, and scale factors of the corresponding joints of the key frames. In the preferred embodiment, the joints of each figure are arranged in hierarchical order, and the positional coordinates and rotational orientations of the local coordinate system for a particular joint are determined with respect to the local coordinate system of the next higher joint in the hierarchy. Also, the operator can control the interpolation during display of the in-between frames, so as to change the motion of a figure limb.