Accurately describing interactions between medical devices and anatomical structures, or between anatomical structures themselves, is an essential step towards the adoption of computer-based medical simulation as an alternative to traditional training methods. However, while substantial work has been done in the area of real-time soft tissue modeling, little has been done to study the problem of contacts occurring during tissue manipulation. In this paper we introduce a new method for correctly handling complex contacts between various combination of rigid and deformable objects. Our approach verifies Signorini's law by combining Lagrange multipliers and the status method to solve unilateral constraints. Our method handles both concave and convex surfaces by using a displacement subdivision strategy, and the proposed algorithm allows interactive computation times even in very constrained situations. We demonstrate the efficiency of our approach in the context of interventional radiology, with the navigation of catheters and guidewires in tortuous vessels and with the deployment of coils to treat aneurysms.
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