our reef knot |
standard reef knot |

It is often necessary to model deformable materials such as rope for graphics and simulation applications. Real time simulation of models sufficiently realistic to train surgeons is needed. In microsurgery simulation, laparoscopic surgery simulation, and other surgical simulations, realistic real-time simulation of rope to tie knots for surgical suturing is identified as a task. To do this we must provide a robust dynamics model and integration as well as a robust solution to the collision detection problem for deformable self-intersecting shapes.

Our work develops a method for knot tying with simulated rope in a physically based dynamics simulation. Our experiments consist of pulling a loosely knotted rope configuration tight and witnessing that the knot was maintained. We provide examples of tying an overhand knot and a reef knot.

Our rope is a spline of linear springs. The topology of the rope varies adaptively to maintain the surface of the rope. Self-intersections on the rope are discrete event simulated using the impulse model of collision in the interpolation step of the physical simulation. During the adaptive reparameterization of the rope, some care must be taken to maintain conservation of mass, energy and momentum. This also must be done during the numerical integration of the resulting differential equations. The errors in our solution are sufficiently small that they can be balanced with a reasonable amount of damping.

The dynamics simulation must be able to cope adaptively as the configuration of the rope varies and must be approximately continuous over time. We demonstrate that a simple but carefully chosen model can be used successfully in simulated knot tying.

- As an example, you can see a movie of a reef knot and an overhand knot being tightened. The simulation for these movies took 5 and 3 minutes, respectively, to generate (including graphical rendering) on a 900 Mhz workstation.