Skeletal animation

Bone translations and joint rotations.

• Node: a point of joint rotation
• Arc: Connects two nodes (edge)

Kinematics: study of movement positions without considering the forces that brought it into motion.

Degrees of Freedom: Set of independent translational/rotational displacement specifying an object’s pose.

Typical set of DoF for one bone: ${x, y, z, \text{roll, pitch, yaw}}$

Work space: The space in which object’s coordinates are defined (usually $R^3, R^2$).

Configuration space: (aka Joint space) The space of possible object configurations (usually defined by degrees of freedom).

Forward Kinematics

Input: Joint Angles Output: Location of end effectors.

Depth first traversal of skeleton gives a path to the effector.

• $L_0R_0$ is the position and rotation of the root segment.
• Each subsequent $L_k$ is the $k$th link translation
  • Link translation: Frame location relative to parent.
• Each subsequent $R__k$ is the $k$th joint rotation
• Can be achieved with glPushMatrix, glTranslate, glRotate, draw, ...

Inverse Kinematics

Input: Desired location of end effectors Output: Joint angles required