Sean Mauch

3D scan conversion of CSG models into distance volumes

A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the object being represented by the volume. Distance volumes are a useful representation in a number of computer graphics applications. We present a technique for generating a distance volume with sub-voxel accuracy from one type of geometric model, a constructive solid geometry (CSG) model consisting of superellipsoid primitives. The distance volume is generated in a two step process. The first step calculates the shortest distance to the CSG model at a set of points within a narrow band around the evaluated surface. Additionally, a second set of points, labeled the zero set, which lies on the CSG models surface are computed. A point in the zero set is associated with each point in the narrow band. Once the narrow band and zero set are calculated, a fast marching method is employed to propagate the shortest distance and closest point information out to the remaining voxels in the volume. Our technique has been used to scan convert a number of CSG models, producing distance volumes which have been utilized in a variety of computer graphics applications, e.g. CSG surface evaluation, offset surface generation, and 3D model morphing.

A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of the Center for Simulating the Dynamic Response of Materials at the California Institute of Technology. The compressible fluid flow is simulated with a Cartesian finite volume method and treating the solid as an embedded moving body, while a Lagrangian finite element scheme is employed to describe the structural response to the hydrodynamic pressure loading. A temporal splitting method is applied to update the position and velocity of the boundary between time steps. The boundary is represented implicitly in the fluid solver with a level set function that is constructed on-the-fly from the unstructured solid surface mesh. Block-structured mesh adaptation with time step refinement in the fluid allows for the efficient consideration of disparate fluid and solid time scales. We detail the design of the employed object-oriented mesh refinement framework AMROC and outline its effective extension for fluid–structure interaction problems. Further, we describe the parallelization of the most important algorithmic components for distributed memory machines and discuss the applied partitioning strategies. As computational examples for typical VTF applications, we present the dynamic deformation of a tantalum cylinder due to the detonation of an interior solid explosive and the impact of an explosion-induced shock wave on a multi-material soft tissue body.

A Virtual Test Facility for the Simulation of Dynamic Response in Materials

The Center for Simulating Dynamic Response of Materials at the California Institute of Technology is constructing a virtual shock physics facility for studying the response of various target materials to very strong shocks. The Virtual Test Facility (VTF) is an end-to-end, fully three-dimensional simulation of the detonation of high explosives (HE), shock wave propagation, solid material response to pressure loading, and compressible turbulence. The VTF largely consists of a parallel fluid solver and a parallel solid mechanics package that are coupled together by the exchange of boundary data. The Eulerian fluid code and Lagrangian solid mechanics model interact via a novel approach based on level sets. The two main computational packages are integrated through the use of Pyre, a problem solving environment written in the Python scripting language. Pyre allows application developers to interchange various computational models and solver packages without recompiling code, and it provides standardized access to several data visualization engines and data input mechanisms. In this paper, we outline the main components of the VTF, discuss their integration via Pyre, and describe some recent accomplishments in large-scale simulation using the VTF.

Efficient Formulations for Exact Stochastic Simulation of Chemical Systems

One can generate trajectories to simulate a system of chemical reactions using either Gillespies direct method or Gibson and Brucks next reaction method. Because one usually needs many trajectories to understand the dynamics of a system, performance is important. In this paper, we present new formulations of these methods that improve the computational complexity of the algorithms. We present optimized implementations, available from http://cain.sourceforge.net/>, that offer better performance than previous work. There is no single method that is best for all problems. Simple formulations often work best for systems with a small number of reactions, while some sophisticated methods offer the best performance for large problems and scale well asymptotically. We investigate the performance of each formulation on simple biological systems using a wide range of problem sizes. We also consider the numerical accuracy of the direct and the next reaction method. We have found that special precautions must be taken in order to ensure that randomness is not discarded during the course of a simulation.

Algorithms for Interactive Editing of Level Set Models

Level set models combine a low‐level volumetric representation, the mathematics of deformable implicit surfaces and powerful, robust numerical techniques to produce a novel approach to shape design. While these models offer many benefits, their large‐scale representation and numerical requirements create significant challenges when developing an interactive system. This paper describes the collection of techniques and algorithms (some new, some pre‐existing) needed to overcome these challenges and to create an interactive editing system for this new type of geometric model. We summarize the algorithms for producing level set input models and, more importantly, for localizing/minimizing computation during the editing process. These algorithms include distance calculations, scan conversion, closest point determination, fast marching methods, bounding box creation, fast and incremental mesh extraction, numerical integration and narrow band techniques. Together these algorithms provide the capabilities required for interactive editing of level set models.

3D Scan-Conversion of CSG Models into Distance, Closest-Point and Colour Volumes

Volume graphics is a growing field that generally involves representing three-dimensional objects as a rectilinear 3D grid of scalar values, a volume dataset. Given this kind of representation, numerous algorithms have been developed to process, manipulate and render volumes. Volume datasets may be generated in a variety of ways. Certain scanning devices, e.g. MRI and CT, generate a rectilinear grid of scalar values directly from their scanning process. The scalar values can represent the concentration of water or the density of matter at each grid point (voxel). Additionally, volume datasets can be generated from conventional geometric models, using a process called 3D scan-conversion.

3D Metamorphosis Between Different Types of Geometric Models

We present a powerful morphing technique based on level set methods, that can be combined with a variety of scan conversion/model processing techniques. Bringing these techniques together creates a general morphing approach that allows a user to morph a number of geometric model types in a single animation. We have developed techniques for converting several types of geometric models (polygonal meshes, CSG models and MRI scans) into distance volumes, the volumetric representation required by our level set morphing approach. The combination of these two capabilities allows a user to create a morphing sequence regardless of the model type of the source and target objects, freeing him/her to use whatever model type is appropriate for a particular animation.

A virtual test facility for simulating detonation-induced fracture of thin flexible shells

The fluid-structure interaction simulation of detonation- and shock-wave-loaded fracturing thin-walled structures requires numerical methods that can cope with large deformations as well as topology changes. We present a robust level-set-based approach that integrates a Lagrangian thin shell finite element solver with fracture and fragmentation capabilities with an Eulerian Cartesian detonation solver with optional dynamic mesh adaptation. As an application example, the rupture of a thin aluminum tube due to the passage of an ethylene-oxygen detonation wave is presented.

Coupled Eulerian-Lagrangian simulations using a level set method

Publisher Summary This chapter presents an algorithm for the coupled solution of high-velocity fluid-structure interaction problems, in which the simulation of the fluid is accomplished using Eulerian methods, whereas the simulation of the solid utilizes a Lagrangian approach. The algorithm is a variant of the ghost fluid method coupled with a new linear time approach to compute the distance function. The approach wherein the solid boundary is captured using level-set-based techniques is used. The level-set information is used to inform the fluid mechanics solver of the location, velocities, and accelerations of the solid and, in turn, can inform the solid solver of the load induced by the fluid. The “solid solver” in this approach can be as simple as a purely rigid solid to something as complex as a fully Lagrangian solver based on finite elements. An advantage of this approach is that there is no need to generate dynamically conforming meshes for the fluid mechanics.

Parallel finite element computation of contact-impact problems with large deformations

Publisher Summary This chapter presents a framework for the parallel explicit dynamics simulation of frictional contact-impact problems involving shells and solids on distributed memory architectures. Contact detection is performed in parallel with orthogonal range queries based on a sparse bucket data structure. The size and complexity of problems, which can be tackled in a parallel computing environment, require particularly robust and efficient contact algorithms. A common approach for deriving contact enforcement methods, such as the penalty or the Lagrangian multiplier method, is to start on the continuum level and to discretize the nonsmooth differential equations. This approach leads to the well-known robustness problems, including the nonuniqueness of the normal and nonsmoothness of the discretized contact surfaces.