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VAST stands for Virtual Arthroscopic Surgery Trainer. This simulator is developed as a part of the PhD thesis of the author. It helps new surgeons to test and practice their skills for minimal invasive surgery operations. It is composed of a joystick coupled with feedback force ability as well as models of the wrist and knee of the human being. Different algorithms for objects segmentation as well as 3D reconstructions were introduced and others were proposed as new algorithms in the filed. New algorithms were also proposed for collision detection and proximity query computation in virtual reality based on linear programming. A state of the art comparison between different collision detection algorithms is also presented in detail.