A deformable character can be controlled by a hierarchy of rigid bones rather than by keyframing every mesh vertex independently.

Each vertex stores weights $w_i$ describing how strongly nearby bones influence it, with weights commonly normalized so

$$\sum_i w_i=1.$$

For bone transformation matrices $M_i$, linear blend skinning computes a deformed vertex approximately as

$$\mathbf{p}'=\sum_i w_i M_i\mathbf{p}.$$

Bone transforms come from the animated hierarchy, while inverse bind-pose transforms account for the mesh's original reference pose.

This method is efficient and works well for many motions, but linearly blending matrices can collapse volume or produce twisting artifacts around some joints. More sophisticated deformation methods address those limitations.

Skeletal animation separates a compact articulated control structure from the much denser rendered surface, allowing one animation to drive thousands of vertices coherently.