Data-driven methods have received increasing attention in recent years in order to meet real-time requirements in computationally intensive tasks. In our current work we examine the application of such approaches in soft-tissue simulation. The core idea is to split deformations into a coarse approximation and a differential part that contains the details. We employ the data-driven stamping approach to enrich a fast simulation surface with details that have been extracted from a set of example deformations obtained in offline computations. In this paper we detail our technique, and suggest further extensions over our previous work. First, we propose an improved method for correlating the current coarse approximation to the examples in the database. The new correlation metric combines Euclidean distances with cosine similarity. It allows for better example discrimination, resulting in a well-conditioned linear system. This also enables us to use a non-negative least squares solver that leads to a better regression and guarantees positive stamp blending weights. Second, we suggest a frequency-space stamp compression scheme that saves memory and, in most instances, is faster, since many operations can be done in the compressed space. Third, cutting is included by employing a physically-inspired influence map that allows for proper handling of material discontinuities that were not present in the original examples. We thoroughly evaluate our method and demonstrate its practical application in a surgical simulator prototype.

Passive haptics, also known as tactile augmentation, denotes the use of a physical counterpart to a virtual environment to provide tactile feedback. Employing passive haptics can result in more realistic touch sensations than those from active force feedback, especially for rigid contacts. However, changes in the virtual environment would necessitate modifications of the physical counterparts. In recent work space warping has been proposed as one solution to overcome this limitation. In this technique virtual space is distorted such that a variety of virtual models can be mapped onto one single physical object. In this paper, we propose as an extension adaptive space warping; we show how this technique can be employed in a mixed-reality surgical training simulator in order to map different virtual patients onto one physical anatomical model. We developed methods to warp different organ geometries onto one physical mock-up, to handle different mechanical behaviors of the virtual patients, and to allow interactive modifications of the virtual structures, while the physical counterparts remain unchanged. Various practical examples underline the wide applicability of our approach. To the best of our knowledge this is the first practical usage of such a technique in the specific context of interactive medical training.

We present a novel hybrid method to allow large time steps in explicit integrations for the simulation of deformable objects. In explicit integration schemes, the time step is typically limited by the size and the shape of the discretization elements as well as by the material parameters. We propose a two-step strategy to enable large time steps for meshes with elements potentially destabilizing the integration. First, the necessary time step for a stable computation is identified per element using modal analysis. This allows determining which elements have to be handled specially given a desired simulation time step. The identified critical elements are treated by a geometric deformation model, while the remaining ones are simulated with a standard deformation model (in our case, a corotational linear Finite Element Method). In order to achieve a valid deformation behavior, we propose a strategy to determine appropriate parameters for the geometric model. Our hybrid method allows taking much larger time steps than using an explicit Finite Element Method alone. The total computational costs per second are significantly lowered. The proposed scheme is especially useful for simulations requiring interactive mesh updates, such as for instance cutting in surgical simulations.

Treating the interactions of soft tissue with rigid user-guided tools is a difficult problem. This is particularly true if the soft tissue has a slender shape, i.e., resembling a thin shell, and if the underlying numerical time-integration scheme employs large time steps. In this case, large mutual displacements of both the tool and the soft tissue occur frequently, resulting in deep interpenetrations or breakthroughs. As a consequence, the computation of spatially and temporally coherent contact spaces turns out to be very challenging. In this paper, an approach is proposed that is tailored to these kinds of interactions. To solve this problem, a novel spatially reduced representation of the soft tissue geometry is employed where the dominant dimensions of the object are approximated by a 2D triangle surface, while the third dimension is given in terms of nodal radii. To construct a feasible, nonpenetrating configuration, a novel manifold projection scheme is presented where the colliding triangles are rasterized into a distance field in order to robustly estimate the contact spaces, even for large intersections. The method produces physically plausible results, albeit it is purely geometric, and the material parameters are neglected at the collision response stage. Various examples, including an interactive prototype arthroscopy simulator, underline the wide applicability of the approach.

Abstract Elastic rods are thin flexible objects typically undergoing large non‐linear deformations that cannot be modeled with linear methods. They are used in a number of research fields, e.g., to represent hair or ropes in animations, or catheters or needles in medical simulations. In this paper, we propose a deformation model for inextensible elastic rods. The method of Lagrange multipliers is employed to enforce the inextensibility of the rod, and to couple the material frames with the centerline. The resulting system is banded, allowing for an efficient linear time solution. We also propose a manifold projection method to incorporate the non‐penetration constraints resulting from contact handling into our constrained Lagrangian mechanics (CLM) problem. We further augment the contact model by treating torsional friction. This allows to reproduce friction effects such as dynamic rolling and twisting of rods. Various examples underline the benefits and applicability of our model. Copyright © 2010 John Wiley & Sons, Ltd.

Cosserat nets are networks of elastic rods that are linked by elastic joints. They allow to represent a large variety of objects such as elastic rings, coarse nets, or truss structures. In this paper, we propose a novel approach to model and dynamically simulate such Cosserat nets. We first derive the static equilibrium of the elastic rod model that supports both bending and twisting deformation modes. We further propose a dynamic model that allows for the efficient simulation of elastic rods. We then focus on the simulation of the Cosserat nets by extending the elastic rod deformation model to branched and looped topologies. To round out the discussion, we evaluate our deformation model. By comparing our deformation model to a reference model, we illustrate both the physical plausibility and the conceptual advantages of the proposed approach.

Abstract In this paper, we present an adaptive model for dynamically deforming hyper‐elastic rods. In contrast to existing approaches, adaptively introduced control points are not governed by geometric subdivision rules. Instead, their states are determined by employing a non‐linear energy‐minimization approach. Since valid control points are computed instantaneously, post‐stabilization schemes are avoided and the stability of the dynamic simulation is improved. Due to inherently complex contact configurations, the simulation of knot tying using rods is a challenging task. In order to address this problem, we combine our adaptive model with a robust and accurate collision handling method for elastic rods. By employing our scheme, complex knot configurations can be simulated in a physically plausible way.