This paper presents a robust, adaptive method for animating dynamic visco-elastic deformable objects that provides a guaranteed frame rate. Our approach uses a novel automatic space and time adaptive level of detail technique, in combination with a largedisplacement (Green) strain tensor formulation. The body is partitioned in a non-nested multiresolution hierarchy of tetrahedral meshes. The local resolution is determined by a quality condition that indicates where and when the resolution is too coarse. As the object moves and deforms, the sampling is refined to concentrate the computational load into the regions that deform the most. Our model consists of a continuous differential equation that is solved using a local explicit finite element method. We demonstrate that our adaptive Green strain tensor formulation suppresses unwanted artifacts in the dynamic behavior, compared to adaptive mass-spring and other adaptive approaches. In particular, damped elastic vibration modes are shown to be nearly unchanged for several levels of refinement. Results are presented in the context of a virtual reality system. The user interacts in real-time with the dynamic object through the control of a rigid tool, attached to a haptic device driven with forces derived from the method.

We introduce an algorithm that consistently and accurately processes arbitrary intersections in tetrahedral meshes in real-time. The intersection surfaces are modeled up to the current cut tool position at every point in time. Tetrahedra are subdivided by using a progressive method, which inserts the required sub-structures step by step. A state machine tracks the topology of each tetrahedron and controls the progressive subdivision. In order to keep the state machine as small and clear as possible, each topological pattern of a tetrahedral intersection appears only once. These topological patterns are mapped onto the actual case of a tetrahedral intersection by some given transformation operations. The state transitions, which contain the specific subdivision operations, are described in a predefined lookup table, which is written in a simple script language. The handling of reverse movements and possible trembling of the users hand, as well as a recursive continuation of the state machine concept, complement the proposed algorithm. In three examples, covering free form modeling, volume visualization, and surgery simulation, we indicate the large field of applications in which our algorithm can be utilized.

We present schemes for real-time generalized interactions such as probing, piercing, cauterizing and ablating virtual tissues. These methods have been implemented in a robust, real-time (haptic rate) surgical simulation environment allowing us to model procedures including animal dissection, microsurgery, hysteroscopy, and cleft lip repair.

A central training objective of virtual reality based surgical simulation is the removal of pathologic tissue. This necessitates stable, real-time updates of the underlying mesh representation. Within the framework of a hysteroscopy simulator, we have developed a hybrid cutting approach for tetrahedral meshes. It combines the topological update by subdivision with adjustments of the existing topology. Moreover, the mechanical and the visual model are decoupled, thus allowing different resolutions for the underlying mesh representations. With our method, we can closely approximate an arbitrary, user-defined cut surface while avoiding the creation of small or badly shaped elements, thus strongly reducing stability problems in the subsequent deformation computation. The presented approach has been integrated into a virtual reality training system for hysteroscopic interventions. The performance of the algorithm is demonstrated by examples of intra-uterine tumor ablations.

Virtual reality based surgical simulators offer a very elegant approach to enhancing traditional training in endoscopic surgery. In this context a realistic soft tissue model is of central importance. The most accurate procedures for modeling elastic deformations of tissue use the Finite Element Method to solve the governing mechanical equations. Therapeutic

The design of simulators for surgical training and planning poses a great number of technical challenges. Therefore the focus of systems and algorithms was mostly on the more restricted minimal invasive surgery. This paper tackles the more general problem of open surgery and presents efficient solutions to several of the main difficulties. In addition to an improved collision detection scheme for computing interactions with even heavily moving tissue, a hierarchical system for the haptic rendering has been realized in order to reach the best performance of haptic feedback. A flexible way of modeling complex surgical tools out of simple basic components is proposed. In order to achieve a realistic and at the same time fast relaxation of the tissue, the approach of explicit finite elements has been substantially improved. We are able to demonstrate realistic simulations of interactive open surgery scenarios.

The problem of defining a model for deformable objects which allows the user to perform cuts is still open.

Objects deform in response to contact forces exerted on them. The deformation depends on material properties, the geometry of the object and external forces. This thesis develops a robotic system for automatically acquiring observations of a deforming object and for estimating a model of the deformation from these observations. Models of deformable objects are in wide-spread use in simulation, computer graphics and virtual reality. Deformation, impact and fitting simulation aid manufacturing. In computer graphics deformable objects are designed and animated. Medical simulators incorporating physical models of organs and tissue are a significant emerging virtual reality application.

We present an interface between a deformable body mechanics model and a rigid body mechanics model. What is novel with our approach is that the physical representation in both the models is the same, which ensures behavioral correctness and allows great flexibility. We use a mass-spring representation extended with the concept of volume, and thus contact and collision. All physical interaction occurs between the mass elements only, and thus there is no need for explicit handling of rigid-deformable or rigid-rigid body interaction. This also means that bodies can be partially rigid and partially deformable. It is also possible to change whether part of a body should be rigid or not dynamically. We present a demonstration example, and also possible applications in conceptual design engineering, geometric modeling, as well as computer animation. Key words: mechanics model, deformation, collision, deformable bodies, geometric modeling, conceptual design, rigid body 1

We present a method for producing cuts in triangulated surfaces. This method keeps the mesh size low and element quality high. We show the method for triangle meshes in two dimensions, and then generalize it to three dimensional curved surfaces, where bifurcations and annihilations of incisions may occur. This method could be applied to simulating surgery of membrane-like structures, such as veins or intestine.