Effective And Accurate Collision Response Algorithms In The Surgical Simulation

In this paper we focus on the surgical simulator and two important components, which are named as collision response and constraint particle system. Currently the surgical simulator is a hot research topic and attracts the attention from many international research institute like INRIA and ETHZ. It provides an immersive environment for surgery training, which can replace the traditional cadaver based training approach and hence decrease the cost. Collision response algorithm is one of the most important modules of surgical simulator, whose purpose is to resolve the penetration between objects and generate feedback force for haptic simulation. Constraint particle system is a deformable model, which employ the mathematical formula to describe the deformation of soft objects. Both of the two algorithms are significant for the surgical simulation.This paper presents an novel hybrid collision response algorithm. It divides the whole algorithm to three separate phases. In each phase many algorithms are designed for different requirements. It integrates the advantages of three traditional collision response method. Besides, it also provides an approach to generate the reasonable feedback force. This paper also designs three self-defined constraints of the constraint particle system according to the characteristics of the surgical simulator. Experiments are performed to evaluate the performance of these two novel algorithms. The main achievements are listed in the following:1. A hybrid collision response algorithm is advanced. This algorithm divides a whole problem to three sub-problems and conquers them separately. The three phases is named as the pre-processing phase, deformation phase and feedback force phase. In each phase several algorithms are designed. Due to the low coupling degree, these algorithms in different phases can be arbitrarily chosen according to the requirements of different systems. For instance, some systems prefer real-time ability, while others like stability.2. Three methods are employed to calculate the reasonable penetration vector. The traditional method defines the penetration vector as the fastest separate direction. This paper presents the weighted average value, return-back method and the related velocity approach to determine a more reasonable penetration vector.3. Compared to the local method, a global one is presented to calculate the feedback force. It considers the collision object as a mass point, and thus the feedback force can represents the global information of the object, such as the speed and movement direction.4. During the post processing for the feedback force, the inverse function of the tangent function are employed to scale the force generating from the collision response module. The scaled force is transmitted to the haptic device. Then linear interpolation is employed to smooth the force. Such mechanism improves the continuity of the feedback force and avoids the leap.5. Several experiments are designed to compare the deformation effect and the continuity of the feedback force. Three novel formulas are advanced to evaluate the continuity of the feedback force.6. The constraint particle system is extended according to the surgical simulator. Three novel constraints are presented, which are named as the related position constraint, original position constraint and the fixed position constraint. They improve the stability of the deformable model. The original position constraint also prevent the organ from escaping. Meanwhile they don't increase the time complexity.