This PhD thesis takes place in the context of real time physical simulation. The first goal of this work is to propose a 1D deformable model. Such a model finds lots of applications in virtual reality or in animation especially in simulation of thready deformable object like rope, string, lace... We propose a real time 1D deformable model based on a spline geometry animated with physical law of Lagrange. This model is based on the works of Yannick Rémion and its LERI’s team. This type of model reveals to be particularly adapted to surgical simulation for the thread modelling in suture or organs (intestines, fallopian tubes). For some applications, it may be useful that the model verify some specific conditions expressed as constraint equations. These constraints are taken into account in the dynamic system thanks to the Lagrange multipliers method. In this context of constrained simulation, one of the major contributions is the proposition of a new class of constraints called smooth constraints. These constraints allow, for example, a thread to pass through a specific point in space. Such constraints is particularly useful to simulate a suture in a surgical context, but answer to specific need in animation (shoelace, hang rope,...) too. Some applications, such as the suture of an organ, deal with the simulation of many models inter- acting all together. For such a simulation, we propose a software architecture allowing the simulation of articulated objects (rigids or deformables) whatever the physical formalism are. This proposition has many applications like surgical simulation, swing simulation... Multi-resolution permits a local adaptation of the model in order to be precisely defined in the interaction area and not time-consuming. The computation time is then concentrated in the interesting area and it is less important in the other place. A criteria based on the curvature of the curve is used to get a finer model. This technique is particularly well suited for knot simulation by permitting the model to increase its number of degrees of freedom and giving it a geometric flexibility in the tightening area.
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