# Real-Time Virtual Cables Based on Kinematic Simulation

#### Elke Hergenroether, Technische Universitaet Darmstadt

#### Patrick Daehne, Zentrum fuer Graphische Datenverarbeitung e.V.

### Abstract

We present an algorithm for the real-time simulation of virtual cables using inverse kinematics. A cable is
modeled by consecutive cylinder segments of equal size. The segments are connected by ball joints. At
every joint there ist a spiral spring acting against the excursion of the joint. Given a start and an end
position of the cable, the algorithm calculates the shape of the cable that leads to minimal total energy. The
total energy is the sum of the potential energies of the segments and the elastic energies of the springs.
First, the algorithm calculates a cable with minimal total energy consisting of two segments. This is taken
as a starting basis for the computation of a cable consisting of four segments . At each following step, the
number of segments is doubled and a new shape of the cable is calculated based on the solution of the
previous step. The great advantage of this approach is the easy accommodation of the solution exactness to
the avaible computation time. If the user of the Virtual Reality application is moving the cable, he gets a fast but
rough feedback. If he stops moving it, he gets an exact shape.