Meshless Animation of Fracturing Solids

A Novel Haptic Interactive Approach to Simulation of Surgery Cutting Based on Mesh and Meshless Models

In the present work, the majority of implemented virtual surgery simulation systems have been based on either a mesh or meshless strategy with regard to soft tissue modelling. To take full advantage of the mesh and meshless models, a novel coupled soft tissue cutting model is proposed. Specifically, the reconstructed virtual soft tissue consists of two essential components. One is associated with surface mesh that is convenient for surface rendering and the other with internal meshless point elements that is used to calculate the force feedback during cutting. To combine two components in a seamless way, virtual points are introduced. During the simulation of cutting, the Bezier curve is used to characterize smooth and vivid incision on the surface mesh. At the same time, the deformation of internal soft tissue caused by cutting operation can be treated as displacements of the internal point elements. Furthermore, we discussed and proved the stability and convergence of the proposed approach theoretically. The real biomechanical tests verified the validity of the introduced model. And the simulation experiments show that the proposed approach offers high computational efficiency and good visual effect, enabling cutting of soft tissue with high stability.

A System for High-Resolution Topology Optimization

A key requirement in 3D fabrication is to generate objects with individual exterior shapes and their interior being optimized to application-specific force constraints and low material consumption. Accomplishing this task is challenging on desktop computers, due to the extreme model resolutions that are required to accurately predict the physical shape properties, requiring memory and computational capacities going beyond what is currently available. Moreover, fabrication-specific constraints need to be considered to enable printability. To address these challenges, we present a scalable system for generating 3D objects using topology optimization, which allows to efficiently evolve the topology of high-resolution solids towards printable and light-weight-high-resistance structures. To achieve this, the system is equipped with a high-performance GPU solver which can efficiently handle models comprising several millions of elements. A minimum thickness constraint is built into the optimization process to automatically enforce printability of the resulting shapes. We further shed light on the question how to incorporate geometric shape constraints, such as symmetry and pattern repetition, in the optimization process. We analyze the performance of the system and demonstrate its potential by a variety of different shapes such as interior structures within closed surfaces, exposed support structures, and surface models.

Data-Driven Simulation of Detailed Surface Deformations for Surgery Training Simulators

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.

Stable cutting of deformable objects in virtual environments using XFEM

Most deformable object simulators suffer from stability problems caused by material slivers in the cut vicinity. The extended finite element method (XFEM) is a novel approach that uses element enrichment to effectively model discontinuities. In combination with an appropriate mass-lumping technique, XFEM provides a stable simulation regardless of cut location.

Meshless Modeling of Deformable Shapes and their Motion

We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object's volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes.