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Modeling ranges of limb motion for real-time inverse kinematics

Accurate modeling of range of joint motions (joint ROM) is a fundamental problem of articulated figure animation. The joint ROM should be carefully designed to avoid an impossible pose, requiring tedious work because of the complexity and extensiveness of human joints, especially shoulders and hips. Although many joint ROM models have been proposed in the field of biomechanics and graphics, they still have two issues. The first is that a ROM of spherical joint is defined in a spherical domain. A traditional approach respectively defines a range of yaw, pitch and roll of joint rotation, which often causes an unexpected artifact due to the nonlinearity of the Euler angles. Another method uses a sophisticated parameterization of 3D rotation [Herda et al. 2005] or a 3D geometrical model to represent a boundary of joint orientation. These methods, however, require extra computational cost. The second issue is that a joint ROM is separately defined for each joint. Previous models often neglect a strong dependency between adjacent joints; a shoulder's joint ROM varies depending on elbow angle for example. A complex mechanism is therefore required to simulate such dependency [Herda et al. 2005].