This thesis deals with developing a robust, mathematically based, knot tying simulation, with focus on realistic knot tightening and knot identification, for minimally invasive surgical training. Mathematically based simulation does not consider the physical properties of the system, thereby avoiding the inherent instabilities associated with physically based real time simulations, like unnatural jerks, undetected collisions and generation of unnaturally large forces. A mathematical algorithm called Follow the Leader (Brown et al, 2004) has been implemented to simulate the knot movement, given the external interaction. The collision detection scheme called Bounding Volume Hierarchy is used to detect the self collision in the thread as well as the collision between external objects.;For any virtual simulation training task, there is a need for a quantitative way of detecting the completion of the task, in this case, the tying of a knot. Based on the knot theory, a framework is introduced which detects the knot tied in the thread. The regular knot identification scheme, which detects knot based solely based on the topology of the thread, has been modified such that, the collision between the participating thread elements is also considered, so that a knot is detected only when the it has been tightened sufficiently. The framework thus developed can support identification of any type of knot defined in knot theory. A basic trefoil knot identification scheme was built into the simulation and tested. Also, the simulation system was built to accommodate the tying of multiple knots in different parts of the thread.
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