Motion fairing using genetic algorithms

In this paper, we solve the motion smoothing problem using genetic algorithms. Smooth motion generation is essential in the computer animation and virtual reality area. The motion of a rigid body in general consists of translation and orientation. The former is described by a space curve in three-dimensional Euclidean space while the latter is represented by a curve in the unit quaternion space. By adopting the geometric approach, the smoothness of both translation data and orientation data is measured from the strain energy perspective and a nonlinear optimization problem is formulated that aims to minimize the weighted sum of the strain-energy and the sum of the squared errors. A hybrid algorithm that combines genetic algorithms and local search schemes is deployed to solve this optimization problem and the experiments show that both smoothness and shape preservation of the resulting motion can be achieved by the proposed algorithm.