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Surgical simulation covers a set of very large fields. Medical physics simulation, which aims to virtually reproduce the behavior of organic tissues, tries to stick, as far as possible, with reality. This last field poses many concrete problems currently very incompletely resolved, and the extreme mechanical complexity of living tissues. The mechanical interaction between organs, the large number of different tissues and topologies, make the physical simulation of a human organism totally utopian at the present time. The best scientific results for the moment manage to simulate this or that type of organ, with, in terms of interaction, certain simple operations, such as primitive cutting of organs. These organs are modeled by meshes whose resolution depends on the cutting zone: the mesh associated with this zone must be defined at several scales to extract all or part of the organ considered. In addition, taking into account any cuts previously made in the vicinity of the zone considered remains an open problem that needs to be resolved. It leads to modifications of the topological model associated with the mesh. Our study therefore focuses on the adaptive resolution subdivision of triangles and tetrahedra in a mesh. Operations must preserve mesh consistency and must be robust. We propose a topology-based model that meets this need. We define and implement adaptive resolution subdivision operations in a triangular and tetrahedral mesh.

Surgical simulation covers a set of very large fields. Medical physics simulation, which aims to virtually reproduce the behavior of organic tissues, tries to stick, as far as possible, with reality. This last field poses many concrete problems currently very incompletely resolved, and the extreme mechanical complexity of living tissues. The mechanical interaction between organs, the large number of different tissues and topologies, make the physical simulation of a human organism totally utopian at the present time. The best scientific results for the moment manage to simulate this or that type of organ, with, in terms of interaction, certain simple operations, such as primitive cutting of organs. These organs are modeled by meshes whose resolution depends on the cutting zone: the mesh associated with this zone must be defined at several scales to extract all or part of the organ considered. In addition, taking into account any cuts previously made in the vicinity of the zone considered remains an open problem that needs to be resolved. It leads to modifications of the topological model associated with the mesh. Our study therefore focuses on the adaptive resolution subdivision of triangles and tetrahedra in a mesh. Operations must preserve mesh consistency and must be robust. We propose a topology-based model that meets this need. We define and implement adaptive resolution subdivision operations in a triangular and tetrahedral mesh.

We describe a method for the visual interactivesimulation of wires contacting with rigid multibodies. Thephysical model used is a hybrid combining lumped elementsand massless quasistatic representations. The latter is basedon a kinematic constraint preserving the total length of thewire along a segmented path which can involve multiple bodiessimultaneously and dry frictional contact nodes used for roping,lassoing and fastening. These nodes provide stick and slidefriction along edges of the contacting geometries. The lumpedelement resolution is adapted dynamically based on local stabilitycriteria, becoming coarser as the tension increases, and up to thepurely kinematic representation. Kinematic segments and contactnodes are added and deleted and propagated based on contactgeometries and dry friction configurations. The method givesdramatic increase on both performance and robustness becauseit quickly decimates superfluous nodes without loosing stability,yet adapts to complex configurations with many contacts andhigh curvature, keeping a fixed, large integration time step.Numerical results demonstrating the performance and stabilityof the adaptive multiresolution scheme are presented along withan array of representative simulation examples illustrating theversatility of the frictional contact model.

We describe a method for the visual interactivesimulation of wires contacting with rigid multibodies. Thephysical model used is a hybrid combining lumped elementsand massless quasistatic representations. The latter is basedon a kinematic constraint preserving the total length of thewire along a segmented path which can involve multiple bodiessimultaneously and dry frictional contact nodes used for roping,lassoing and fastening. These nodes provide stick and slidefriction along edges of the contacting geometries. The lumpedelement resolution is adapted dynamically based on local stabilitycriteria, becoming coarser as the tension increases, and up to thepurely kinematic representation. Kinematic segments and contactnodes are added and deleted and propagated based on contactgeometries and dry friction configurations. The method givesdramatic increase on both performance and robustness becauseit quickly decimates superfluous nodes without loosing stability,yet adapts to complex configurations with many contacts andhigh curvature, keeping a fixed, large integration time step.Numerical results demonstrating the performance and stabilityof the adaptive multiresolution scheme are presented along withan array of representative simulation examples illustrating theversatility of the frictional contact model.

We describe a method for the visual interactivesimulation of wires contacting with rigid multibodies. Thephysical model used is a hybrid combining lumped elementsand massless quasistatic representations. The latter is basedon a kinematic constraint preserving the total length of thewire along a segmented path which can involve multiple bodiessimultaneously and dry frictional contact nodes used for roping,lassoing and fastening. These nodes provide stick and slidefriction along edges of the contacting geometries. The lumpedelement resolution is adapted dynamically based on local stabilitycriteria, becoming coarser as the tension increases, and up to thepurely kinematic representation. Kinematic segments and contactnodes are added and deleted and propagated based on contactgeometries and dry friction configurations. The method givesdramatic increase on both performance and robustness becauseit quickly decimates superfluous nodes without loosing stability,yet adapts to complex configurations with many contacts andhigh curvature, keeping a fixed, large integration time step.Numerical results demonstrating the performance and stabilityof the adaptive multiresolution scheme are presented along withan array of representative simulation examples illustrating theversatility of the frictional contact model.

We describe a method for the visual interactivesimulation of wires contacting with rigid multibodies. Thephysical model used is a hybrid combining lumped elementsand massless quasistatic representations. The latter is basedon a kinematic constraint preserving the total length of thewire along a segmented path which can involve multiple bodiessimultaneously and dry frictional contact nodes used for roping,lassoing and fastening. These nodes provide stick and slidefriction along edges of the contacting geometries. The lumpedelement resolution is adapted dynamically based on local stabilitycriteria, becoming coarser as the tension increases, and up to thepurely kinematic representation. Kinematic segments and contactnodes are added and deleted and propagated based on contactgeometries and dry friction configurations. The method givesdramatic increase on both performance and robustness becauseit quickly decimates superfluous nodes without loosing stability,yet adapts to complex configurations with many contacts andhigh curvature, keeping a fixed, large integration time step.Numerical results demonstrating the performance and stabilityof the adaptive multiresolution scheme are presented along withan array of representative simulation examples illustrating theversatility of the frictional contact model.

We describe a method for the visual interactivesimulation of wires contacting with rigid multibodies. Thephysical model used is a hybrid combining lumped elementsand massless quasistatic representations. The latter is basedon a kinematic constraint preserving the total length of thewire along a segmented path which can involve multiple bodiessimultaneously and dry frictional contact nodes used for roping,lassoing and fastening. These nodes provide stick and slidefriction along edges of the contacting geometries. The lumpedelement resolution is adapted dynamically based on local stabilitycriteria, becoming coarser as the tension increases, and up to thepurely kinematic representation. Kinematic segments and contactnodes are added and deleted and propagated based on contactgeometries and dry friction configurations. The method givesdramatic increase on both performance and robustness becauseit quickly decimates superfluous nodes without loosing stability,yet adapts to complex configurations with many contacts andhigh curvature, keeping a fixed, large integration time step.Numerical results demonstrating the performance and stabilityof the adaptive multiresolution scheme are presented along withan array of representative simulation examples illustrating theversatility of the frictional contact model.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.

This paper introduces a continuum mechanics based thread model for use in real-time simulation. The model includes both rotary inertia, shear deformation and torsion. It is based on a three-dimensional beam model, using a corotational approach for interactive simulation speeds as well as adaptive mesh resolution to maintain accuracy. Desirable aspects of this model from a numerical and implementation point of view include a true constant and symmetric mass matrix, a symmetric and easily evaluated tangent stiffness matrix, and easy implementation of time-stepping algorithms. From a modeling perspective interesting features are deformation of the thread cross section and the use of arbitrary cross sections without performance penalty.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.