Abstract: In this paper, we propose a new method to efficiently synthesize character motions that involve close contacts such as wearing a T-shirt, passing the arms through the strings of a knapsack, or piggy-back carrying an injured person. We introduce the concept of topology coordinates, in which the topological relationships of the segments are embedded into the attributes. As a result, the computation for collision avoidance can be greatly reduced for complex motions that require tangling the segments of the body. Our method can be combinedly used with other prevalent frame-based optimization techniques such as inverse kinematics.