Jonas Spillmann

An Adaptive Contact Model for the Robust Simulation of Knots

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.

Efficient updates of bounding sphere hierarchies for geometrically deformable models

We present a new approach for efficient collision handling of meshless objects undergoing geometric deformation. The presented technique is based on bounding sphere hierarchies. We show that information of the geometric deformation model can be used to significantly accelerate the hierarchy update. The cost of the presented hierarchy update depends on the number of primitives in close proximity, but not on the total number of primitives. Further, the hierarchical collision detection is combined with a level-of-detail response scheme. Since the collision response can be performed on any level of the hierarchy, it allows for balancing accuracy and efficiency. Thus, the collision handling scheme is particularly useful for time-critical applications.

Cosserat Nets

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.

Robust interactive cutting based on an adaptive octree simulation mesh

We present an adaptive octree based approach for interactive cutting of deformable objects. Our technique relies on efficient refine- and node split-operations. These are sufficient to robustly represent cuts in the mechanical simulation mesh. A high-resolution surface embedded into the octree is employed to represent a cut visually. Model modification is performed in the rest state of the object, which is accomplished by back-transformation of the blade geometry. This results in an improved robustness of our approach. Further, an efficient update of the correspondences between simulation elements and surface vertices is proposed. The robustness and efficiency of our approach is underlined in test examples as well as by integrating it into a prototype surgical simulator.

A Geometric Deformation Model for Stable Cloth Simulation

We propose an adapted shape-matching approach for the efficient and robust simulation of clothing. A combination of two different cluster types is employed to account for high stretching and shearing, and low bending resistance. Due to the inherent handling of overshooting issues, the proposed shape-matching deformation model is robust. The proposed cluster types allow for a computationally efficient handling of bending. The geometric deformation model is combined with a novel collision handling approach. The technique employs spatial subdivision to detect collisions and self-collisions. The response scheme is derived from an existing approach for elastic rods. To illustrate the physically plausible dynamics of our approach, it is compared to a traditional physically-based deformation model. Experiments indicate that similar cloth properties can be reproduced with both models. The computational efficiency of the proposed scheme enables the interactive animation of clothing and shells.

Adaptive Space Warping to Enhance Passive Haptics in an Arthroscopy Surgical Simulator

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.

Maintaining Large Time Steps in Explicit Finite Element Simulations Using Shape Matching

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.

Element-wise mixed implicit-explicit integration for stable dynamic simulation of deformable objects

In order to evolve a deformable object in time, the underlying equations of motion have to be numerically integrated. This is commonly done by employing either an explicit or an implicit integration scheme. While explicit methods are only stable for small time steps, implicit methods are unconditionally stable. In this paper, we present a novel methodology to combine explicit and implicit linear integration approaches, based on element-wise stability considerations. First, we detect the ill-shaped simulation elements which hinder the stable explicit integration of the element nodes as a pre-computation step. These nodes are then simulated implicitly, while the remaining parts of the mesh are explicitly integrated. As a consequence, larger integration time steps than in purely explicit methods are possible, while the computation time per step is smaller than in purely implicit integration. During modifications such as cutting or fracturing, only newly created or modified elements need to be reevaluated, thus making the technique usable in real-time simulations. In addition, our method reduces problems due to numerical dissipation.

Enriching coarse interactive elastic objects with high-resolution data-driven deformations

Efficient approximate deformation models allow to interactively simulate elastic objects. However, these approaches usually cannot reproduce the complex deformation behavior governed by geometric and material non-linearities. In addition, objects having slender shapes require dense simulation meshes, which necessitates additional computational effort. We propose an approach where a dynamic interactive coarse simulation is enriched with details stemming from a more accurate quasi-static simulation in a data-driven way. While the coarse simulation is based on a low-resolution (low-res) mesh and a fast linear deformation model the accurate simulation employs a quasi-static non-linear deformation model at a higher mesh resolution (high-res). We pre-compute pairs of low-res mesh deformations and corresponding high-res details by applying a series of training interactions on both the coarse and the accurate model. At run-time, we only run the coarse simulation and correlate the current state to the training states. Subsequently, we blend detail data in order to obtain a spatio-temporally smooth displacement field that we super-impose on the surface skin, resulting in a plausible display of the non-linearly deformed object at real-time rates. We present examples from both computer animation and medical simulation.

Filtering of high modal frequencies for stable real-time explicit integration of deformable objects using the Finite Element Method

The behavior, performance, and run-time of mechanical simulations in interactive virtual surgery depend heavily on the type of numerical differential equation solver used to integrate in time the dynamic equations obtained from simulation methods, such as the Finite Element Method. Explicit solvers are fast but only conditionally stable. The condition number of the stiffness matrix limits the highest possible time step. This limit is related to the geometrical properties of the underlying mesh, such as element shape and size. In fact, it can be governed by a small set of ill-shaped elements. For many applications this issue can be solved a priori by a careful meshing. However, when meshes are cut during interactive surgery simulation, it is difficult and computationally expensive to control the quality of the resulting elements. As an alternative, we propose to modify the elemental stiffness matrices directly in order to ensure stability. In this context, we first investigate the behavior of the eigenmodes of the elemental stiffness matrix in a Finite Element Method. We then propose a simple filter to reduce high model frequencies and thus allow larger time steps, while maintaining the general mechanical behavior.