Virtual Reality (VR) based surgical simulators create a simulated, realistic three dimensional surgical environments using advanced graphic and haptic rendering techniques. Virtual objects, which are geometric surface polygonal models of different human organs and instruments, are rendered in a common viewing volume. Such deformable or non-deformable polygonal models interact with each other. In order to provide a realistic response in real-time, detection of collisions in such models is the greatest challenge in the field of VR based simulators. Once collision is detected, the overlapping region and the largest penetration distance for a pair of intersecting objects need to be determined so that realistic deformations of the objects can be calculated and rendered.

This thesis presents a simple and efficient algorithm to detect collisions between two objects and to calculate the penetration depth from the overlapping region. In a surgical simulator, there are two types of object pair interactions: deformable to non-deformable and, deformable to deformable object interactions. This work examines tissue to rigid body and, tissue to tissue interactions and provides realistic deformation to the interacting tissues in both cases.