Animation of articulated figures has always been an interesting subject of computer graphics due to a wide range of applications, like military, ergonomic design etc. An articulated figure is usually modelled as a set of segments linked with joints. Changing the joint angles brings the articulated figure to a new posture. An animator can define the joint angles for a new posture (forward kinematics). However, it is difficult to estimate the exact joint angles needed to place the articulated figure to a predefined position. Instead of it, an animator can specify the desired position for an end-effector, and then an algorithm computes the joint angles needed (inverse kinematics). In this thesis, we present the implementation of an inverse kinematics algorithm using nonlinear optimization methods. This algorithm computes a potential function value between the end-effector and the desired posture of the end-effector called goal. Then, it tries to minimize the value of the function. If the goal can not be reached due to constraints then an optimum solution is found and applied by the algorithm. The user may assign priority to the joint angles by scaling initial values estimated by the algorithm. In this way, the joint angles change according to the animator's priority.

Keywords: animation, human motion, inverse kinematics, nonlinear programming, optimization.