Interactive simulation of one-dimensional flexible parts

In this paper, we present a system for simulating one dimensional flexible parts such as cables or hose. The modelling of bending and torsion follows the Cosserat model. For this purpose we use a generalized spring–mass system and describe its configuration by a carefully chosen set of coordinates. Gravity and contact forces as well as the forces responsible for length conservation are expressed in Cartesian coordinates. But bending and torsion effects can be dealt with more effectively by using quaternions to represent the orientation of the segments joining two neighbouring mass points. This augmented system allows an easy formulation of all interactions with the best appropriate coordinate type and yields a strongly banded Hessian matrix. An energy minimizing process accounts for a solution exempt from the oscillations that are typical of spring–mass systems. The whole system is numerically stable and can be solved at interactive frame rates. It is integrated in a virtual reality software for use in applications such as cable routing and assembly simulation.