Real time collision detection and soft tissue deformation for haptic simulation of laparoscopic surgery

This dissertation describes the research, development and implementation of a prototype laparoscopic surgery simulator. Theoretical solutions to the collision detection and deformation problems are developed. These two topics form the major part of this research since they are two of the most challenging problems in virtual reality based medical simulation and other applications that demand intensive simulated interaction.; Specifically, this research addresses collision detection problems in complicated simulation scenarios, in which there are highly deformable objects with varying convex or concave shapes, objects with topological complexity such as bundled, porous or spongy structures, particle systems and polygon soup, changing topology due to cutting or suturing operations and, a large number of moving objects. Real time applications with some of these complexities demands robust, generic and fast solutions. This dissertation presents an algorithm, which uses a spatial occupancy test, and a hashed and cascaded data structure (OHC) to solve real time collision detection problems. This algorithm can be a generic solution for specific collision detection scenarios in various applications. In addition, this dissertation also proposes and implements schemes that optimize the algorithm for certain applications. The OHC algorithm has been validated in several real time virtual environments, including surgery simulation with haptic feedback. The real time performance of this method is analyzed with an emphasis on the correlation between collision detection time and collision ratio.; For deformations at haptic rates an enhancement to the existing mass spring modeling method is derived. In this approach, shape constraint such as volume and area elasticity is studied, and the constraint vectors are determined by a new circumcenter alignment method. The classic mass spring model can be enhanced and simplified with a balloon model employing isotropic and homogeneous assumptions; one which computes global volume or area constraints for elastic objects, replaces the bending or shearing springs, and offers more flexibility in adjusting bending and shearing resistances. Compared with the mass spring model, the balloon model has achieved improved elastic effects in modeling surface objects. This model can also be used to simplify the volumetric mass spring structures or to reduce the computation load.