Real-time deformable objects in collaborative virtual environments

This thesis presents a method for deformations on closed surfaces in 3D over a network, which is suitable for simulation of tissue and organs for training purposes, as well as cloth simulation in collaborative virtual environments (CVE). CVE's are extensively used for training, design and gaming for several years. To demonstrate a deformable object on a CVE, we employ a real-time physical simulation of a uniformtension- membrane, based on linear finite-element-discretization of the surface yielding a sparse linear system of equations, which is solved using the Runge-Kutta Fehlberg method. The proposed method introduces an architecture that distributes the computational load of physical simulation between clients. As our approach requires a uniform-mesh representation of the simulated structure, we also designed and implemented an algorithm that converts irregularly triangulated genus zero surfaces into a uniform triangular mesh with regular connectivity. This algorithm uses springembedders for stretch optimization of the spherical parameterization step. The strength of our approach comes from the subdivision methodology that enables to use multi-resolution surfaces for graphical representation, physical simulation, and network transmission, without compromising simulation accuracy and visual quality