A COMPARISON AND EVALUATION OF MOTION INDEXING ...

position, velocity, acceleration, and their rotational counterparts: orientation, angular
velocity, and angular acceleration.
Two useful kinematic analysis tools are forward kinematics and inverse kine-
matics. Forward kinematics is a process of computing world coordinates of joints
based on specified DOF values. The position and orientation of the subject are calcu-
lated from information of joints at a specified time . Inverse kinematics is a process of
computing a set of DOF values from the position of a joint at a desired world space.
The representation for joints (position and orientation) plays an important role in
these kinematics [8].
A skeleton can be described as a framework of bones connected by articulated
joints. The relative movement within the skeleton is provided by these joints which are
represented mathematically by 4x4 linear transformation matrices. Different varieties
of joints are constructed by combining rotations, translations, scales, and shears with
these matrices. Most joints in the skeleton are associated with rotational data. There
are a number of ways of representing rotations: matrices, quaternions, and Euler
angles.
Matrices are the most accurate and least limited way of representing rotations.
Mathematically, a matrix is a grid of numbers. When these numbers are applied to
another matrix, or number, or a point, in the correct order, they can modify the
values of what they are being applied to. For example, a rotation matrix can place a
point in a new position by multiplying the point with itself which yields rotation of
that point.
Euler angles represent the spatial orientation of any coordinate system as a
composition of rotations from a reference coordinate system. An Euler angle is one
of the three parameters required to describe such an orientation. In other words,
any orientation can be achieved by combining three elemental rotations. Euler angles
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