Virtual reality has been proved indispensable in computer-assisted surgery, especially for surgical planning, and simulation systems. Collision detection is an essential part of surgery simulators and its accuracy and computational efficiency play a decisive role in the fidelity of simulations. Nevertheless, current collision detection methods in surgical simulation and planning struggle to meet precise requirements, especially for detailed and complex physiological structures. To address this, the primary objective of this study was to develop a new algorithm that enables fast and precise collision detection to facilitate the improvement of the realism of virtual reality surgical procedures.

The method consists of two main parts, bounding spheres formation and two-level collision detection. A specified surface subdivision method is devised to reduce the radius of basic bounding spheres formed by circumcenters of underlying triangles. The spheres are then clustered and adjusted to obtain a compact personalized hierarchy whose position is updated in real time during surgical simulation, followed by two-level collision detection. Triangular facets with collision potential through interaction between hierarchies and then accurate results are obtained by means of precise detection phase. The effectiveness of the algorithm was evaluated in various models and surgical scenarios and was compared with prior relevant implementations.

Results on multiple models demonstrated that the method can generate a personalized hierarchy with fewer and smaller bounding spheres for tight wrapping. Simulation experiments proved that the proposed approach is significantly superior to comparable methods under the premise of error-free detection, even for severe model-model collision.

The algorithm proposed through this study enables higher numerical efficiency and detection accuracy, which is capable of significantly enlarging the fidelity/realism of haptic simulators and surgical planning methods.