| With the fast development of modern medicine, computer graphic and virtual reality technology, virtual surgery simulation as a new application field arised from the virtual reality that combines many technologies. The objective of virtual surgery research is to provide a reusable and realism environment in the aspect of visualization and force feedback for surgery planning, operation guidance, training, surgery education and recovery. Therefore, the researches for this field have important theoretical significance and bright future in medicine. Several key techniques are studied such as geometry modeling, model optimization, physical modeling, calculation modeling, collision detection and so on. They are interrelated and interact on each other. Detail works are listed as below:(1) Geometry modeling is the base of virtual surgery, this thesis mainly focused on the Delaunay tetrahedral modeling methods. Therefore, a new Delaunay tetrahedral soft tissue modeling method (Restricted Delaunay Incremental Insertion Algorithm, RDIIA) is proposed for the problem of boundary convergence. Firstly, this method adds a constraining condition that helps recover missing boundary occurred in conventional incremental insertion algorithm, the boundary edge/face is undeletable and unchangeable during the model constructing and optimizating. Secondly, it combines the local transformation and boundary recovery method, which efficiently recovers the missing boundary and improves the quality of the Delaunay tetrahedral soft tissue models.(2) Quality measures criterion of tetrahedral model is a criterion to measure the quality of mesh models. A good measure criterion is very important for measure the quality and model optimization, but there is not an acknolowledge and absolute criterion to measure and evaluate the quality of tetrahedral mesh. This thesis summarized and analysised the existing quality measures criterion. Moreover, the relationship between quality measures are proved and analyzed. When we optimize the tetrahedral model, we should statistic on the quality of tetrahedral using different quality measures criterion or combine several quality measures criterion according to the different types of tetrahedral.(3) The Sliver elements in Delaunay tetrahedron model is an important factor that affect the quality of model and the following operation of virtual surgery. Therefore, the properties of sliver elements, node perturbation and Delaunay refinement method are summarized. A new hybrid sliver element elimination algorithm is proposed to refine the tetrahedron models. The sliver elements in tetrahedron model is separated different types, and different sliver elimination methods are applied according to different place which sliver element located. The objective of this method is to eliminate original sliver elements and do not introduce any new sliver elements in Delaunay model, and solve the problems of complexity and quality.(4) Finite element method is widely applied to deformation calculation because of its distinguishing features, but it does not meet the real-time requirements for surgery simulation. In the respect of response time, the linear elastic hybrid condensation finite element model is proposed which bear many common features such as tetrahedron model, continuum mechanics based deformation, linear elastic finite element modeling. Linear elastic is applied to represent the behaviours of soft tissue deformation, and combines the dynamic linear elastic model with quasi-static model. In order to reduce the computational complexity, condensation technology is used to divide the operation region into deformation region and non-deformation region. Moreover, the minimum deformation region extract method and data structure is proposed which using the collision detection techology to improve the computation rate for soft tissue deformation simulation.(5) Due to the self-collision detection just occurred at the surface of model, collision detection between the adjacent triangulars may costs a lot of calculation time. In order to reduce the redundance detection, a new soft tissue self-collision detection method based potentially colliding set is proposed which divided into broad phase and narraw phase. The possible collision set is extracted based on the curvature of soft tissue. The self-collision detection was only processed in possible collision sets. In addition, the feature detection method is used to test the overlap between the primitives, which can reduce the number of redundancy detection and accelerate the velocity of collision detection.
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