Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations. Although adaptive solvers can be of great value in reducing the often high computational cost of simulations they are not employed broadly. Indeed, building adaptive solvers can be a daunting task especially for 3D finite elements. In this paper we are introducing a new approach to produce conforming, hierarchical, adaptive refinement methods (CHARMS). The basic principle of our approach is to refine basis functions, not elements. This removes a number of implementation headaches associated with other approaches and is a general technique independent of domain dimension (here 2D and 3D), element type (e.g., triangle, quad, tetrahedron, hexahedron), and basis function order (piecewise linear, higher order B-splines, Loop subdivision, etc.). The (un-)refinement algorithms are simple and require little in terms of data structure support. We demonstrate the versatility of our new approach through 2D and 3D examples, including medical applications and thin-shell animations.

In this paper we present a fast and robust approach for simulating elasto-plastic materials and fracture in real time. Our method extends the warped stiffness finite element approach for linear elasticity and combines it with a strain-state-based plasticity model. The internal principal stress components provided by the finite element computation are used to determine fracture locations and orientations. We also present a method to consistently animate and fracture a detailed surface mesh along with the underlying volumetric tetrahedral mesh. This multi-resolution strategy produces realistic animations of a wide spectrum of materials at interactive rates that have typically been simulated off-line thus far.

The linear strain measures that are commonly used in real-time animations of deformable objects yield fast and stable simulations. However, they are not suitable for large deformations. Recently, more realistic results have been achieved in computer graphics by using Green's non-linear strain tensor, but the non-linearity makes the simulation more costly and introduces numerical problems.

In this paper, we present a versatile and robust model for geometrically complex deformable solids. Our approach can be applied to deformable tetrahedral meshes and to deformable triangle meshes. The model considers elastic and plastic deformation. It handles a large variety of material properties ranging from stiff to fluid-like behavior. Due to the computational efficiency of our approach, complex environments consisting of up to several thousand primitives can be simulated at interactive speed.

This thesis presents a framework for low-latency interactive simulation of linear elastostatic models and other systems associated with linear elliptic partial differention equations. This approach makes it feasible to interactively simulate large-scale physical models. Linearity is exploited by formulating the boundary value problem (BVP) solution in terms of Green’s functions (GFs) which may be precomputed to provide speed and cheap lookup operations. Runtime BVPs are solved using a collection of Capacitance Matrix Algorithms (CMAs) based on the Sherman-Morrison-Woodbury formula. Temporal coherence is exploited by caching and reusing, as well as sequentially updating, previous capacitance matrix inverses. Multiresolution enhancements make it practical to simulate and store very large models. Efficient compressed representations of precomputed GFs are obtained using secondgeneration wavelets defined on surfaces. Fast inverse wavelet transforms allow fast summation methods to be used to accelerate runtime BVP solution. Wavelet GF compression factors are directly related to interactive simulation speedup, and examples are provided with

Abstract. We are developing a simulation of needle insertion and radioactive seed implantation to facilitate surgeon training and planning for brachytherapy for treating prostate cancer. Inserting a needle into soft tissues causes the tissues to displace and deform: ignoring these effects during seed implantation leads to imprecise seed placements. Surgeons should learn to compensate for these effects so seeds are implanted close to their pre-planned locations. We describe a new 2-D dynamic FEM model based on a 7-phase insertion sequence where the mesh is updated to maintain element boundaries along the needle shaft. The locations of seed implants are predicted as the tissue deforms. The simulation, which achieves 24 frames per second using a 1250 triangular element mesh on a 750Mhz Pentium III PC, is available for surgeon testing by contacting ron@ieor.berkeley.edu. 1.

Abstract − Medical procedures such as seed implantation, biopsies, and treatment injections require inserting a needle tip to a specific target location inside the human body. This is difficult because (1) needle insertion causes soft tissues to displace and deform, and (2) it is often difficult or impossible to obtain precise imaging data during insertion. We are developing a sensorless planning system for needle insertion that incorporates numerical optimization with a soft tissue simulation based on a dynamic FEM formulation that models the effects of needle tip and frictional forces using a 2D mesh. In this paper we describe a sensorless planning algorithm for radioactive seed implantation that computes needle insertion offsets that compensate for tissue deformations. We apply the method to seed implantation during permanent seed prostate brachytherapy to minimize seed placement error in simulation without relying on real-time imaging. I.

Objects and scenes in virtual worlds such as 3-d computer games are typically represented by polygonal surface meshes. On the other hand, physically-based simulations of deformations or fracture effects require volumetric representations such as tetrahedral meshes. In this paper we propose techniques to generate volumetric meshes dynamically for objects represented by surface meshes allowing the simulation of physical effects such as motion, deformation and fracture.

This article describes an efficient method to synthesize the nonlinear haptic response of deformable objects from data obtained by offline simulation or measurements. This capability is useful to create surgical simulators with high-fidelity haptic feedback, as various effects of contact mechanics can be reproduced accurately and in a passive manner.

Real-time finite element (FE) analysis can be used to represent complex deformable geometries in virtual environments. The need for accurate surgical simulation has spurred the development of many of the new real-time FE methodologies that enable haptic support and real-time deformation. These techniques are computationally intensive and it has proved a challenge to achieve the high modeling resolutions required to accurately represent complex anatomies. The authors present a new real-time methodology based on linear FE analysis that is appropriate for a wide range of surgical simulation applications. A methodology based is proposed that is characterized by high model resolution, low preprocessing time, unrestricted multi-point surface contact and adjustable boundary conditions. These features make the method ideal for modeling suturing, which is an element common to almost every surgical procedure. This paper describes constraints in the context of a Suturing Simulator currently being developed by the authors. I.