Endoscopic techniques require small perforation holes only as entries for optical and surgical instruments; such enabling the treatment of injuries with a minimized damage of the surrounding health tissue. But the surgeon has to operate in a 3D domain by looking at a distorted 2D image at the screen. It is well known, that a good surgeon needs a continuous training to perform such operations reliable in a top quality. To overcome the high costs and tight ethical restrictions of animal based education and training has result in an increasing development and application of virtual surgery simulators [1]. One of the main issues of surgery simulators is to ensure simultaneously the real time performance of the device, the high-level image representation and an acceptable force-feedback behavior. The basics of such simulators are mathematical models of the involved soft tissues, which have to perform in a realistic physical manner, with dynamic nonlinear large deformations, including the interaction of the different constituents (instrument/organ, organ/organ, organ by itself, cutting, bleeding etc). In the paper the focus is on realistic organ models and the realization of a fast contact search and reaction algorithm.

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