Secondly, we quantitatively compare these generation methods by computing the average joint error between the ground
truth mocap data and synthetic motions performed by animated characters. We generate five different walking motions in three different shape models (humanoid, female and
male). In mocap data, the motion is represented as relative
rotation angles of each joint. Hence, the kinematic error is
defined as the joint rotation angle difference. The ground
truth of the ith motion is denoted by a sequence of rotation
angles Θ
i
= {θ
i
(k)|k = 1, ..., K }, where K is the number of
joints in the skeleton. Similarly, the corresponding synthetic
motion is defined as the joint rotation sequence of the shape
model skeleton, represented as Φ
i
= {φ
i
(k)|k = 1, ..., K }.
The kinematic error of two motions is written as