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As minimally invasive surgical techniques become widely known to patients, medical training systems based on virtual simulation are highly desired. These systems help surgeon trainees to acquire, practice and evaluate their surgical skills. A key component in a virtual training system is to simulate the dynamics that occur in surgical procedures. Tissue cutting, as a common phenomenon during surgery, has attracted many research efforts in computer simulation. In this paper, we propose an approach to endoscopic image cutting simulation which is based on both mass-spring model and Computational Geometry. In the cutting simulation model, the springs to be cut off are imagined into line segments. In the calculation of the elastic force on mass points, we have found that whether some adjacent springs of a mass point to be eliminated or not during a cutting is critical. If a spring intersects the cutting plane, we set the elastic force of this spring to zero. We adopted properties of cross product and related algorithms (the rapid exclusion test, the crossover test) in Computational Geometry to determine the springs that are intersected with the cutting plane. And then, we utilized the bilinear interpolation and OpenGL techniques to render the cutting procedure of the soft tissue. The experimental results show that our cutting simulation is effective and practical. [ABSTRACT FROM AUTHOR]

Reconstruction of freeform surfaces from scattered coordinate data is a difficult problem encountered in many surface fitting and geometric modeling applications. Conventional tessellation and parametric surface fitting techniques are limited because they require prior knowledge about the connectivity between the sampled points. The method of surface reconstruction described in this paper exploits the learning capability of a self-organizing feature map (SOFM) to adaptively fit a deformable sphere to the unorganized 3D coordinate data. The learning algorithm automatically establishes the connectivity between the measured points by iteratively changing the topological relationships within the map. By incorporating additional constraints during the learning process it is possible to have the deformable map follow the shape of objects with surface holes and cavities. Several examples of freeform surfaces with varying levels of complexity are discussed in order to demonstrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]