Particle-Based Sampling and Meshing of Surfaces in Multimaterial Volumes

Methods that faithfully and robustly capture the geometry of complex material interfaces in labeled volume data are important for generating realistic and accurate visualizations and simulations of real-world objects. The generation of such multimaterial models from measured data poses two unique challenges: first, the surfaces must be well-sampled with regular, efficient tessellations that are consistent across material boundaries; and second, the resulting meshes must respect the nonmanifold geometry of the multimaterial interfaces. This paper proposes a strategy for sampling and meshing multimaterial volumes using dynamic particle systems, including a novel, differentiable representation of the material junctions that allows the particle system to explicitly sample corners, edges, and surfaces of material intersections. The distributions of particles are controlled by fundamental sampling constraints, allowing Delaunay-based meshing algorithms to reliably extract watertight meshes of consistently high-quality.Engineering and Applied Science

Towards shape representation using trihedral mesh projections

This paper explores the possibility of approximating a surface by a trihedral polygonal mesh plus some triangles at strategic places. The presented approximation has attractive properties. It turns out that the Z-coordinates} of the vertices are completely governed by the Z-coordinates assigned to four selected ones. This allows describing the spatial polygonal mesh with just its 2D projection plus the heights of four vertices. As a consequence, these projections essentially capture the “spatial meaning” of the given surface, in the sense that, whatever spatial interpretations are drawn from them, they all exhibit essentially the same shape.This work was supported by the project 'Resolución de sistemas de ecuaciones cinemáticas para la simulación de mecanismos, posicionado interactivo de objetos y conformación de moléculas' (070-722).Peer Reviewe

Multi-Material Mesh Representation of Anatomical Structures for Deep Brain Stimulation Planning

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. The proposed method decomposes an ambiguous grid cube into a set of tetrahedral cells and uses novel polygon generation rules that produce 2-manifold and watertight surface meshes with good-quality triangles. These meshes, being watertight and 2-manifold, are geometrically correct, and therefore can be used to initialize tetrahedral meshes. The 2-manifold DC method has been extended into the multi-material domain. Due to its multi-material nature, multi-material surface meshes will contain non-manifold elements along material interfaces or shared boundaries. The proposed multi-material DC algorithm can (1) generate multi-material surface meshes where each material sub-mesh is a 2-manifold and watertight mesh, (2) preserve the non-manifold elements along the material interfaces, and (3) ensure that the material interface or shared boundary between materials is consistent. The proposed method is used to generate multi-material surface meshes of deep brain anatomical structures from a digital atlas of the basal ganglia and thalamus. Although deep brain anatomical structures can be labeled as functionally separate, they are in fact continuous tracts of soft tissue in close proximity to each other. The multi-material meshes generated by the proposed DC algorithm can accurately represent the closely-packed deep brain structures as a single mesh consisting of multiple material sub-meshes. Each sub-mesh represents a distinct functional structure of the brain. Printed and/or digital atlases are important tools for medical research and surgical intervention. While these atlases can provide guidance in identifying anatomical structures, they do not take into account the wide variations in the shape and size of anatomical structures that occur from patient to patient. Accurate, patient-specific representations are especially important for surgical interventions like deep brain stimulation, where even small inaccuracies can result in dangerous complications. The last part of this research effort extends the discrete deformable 2-simplex mesh into the multi-material domain where geometry-based internal forces and image-based external forces are used in the deformation process. This multi-material deformable framework is used to segment anatomical structures of the deep brain region from Magnetic Resonance (MR) data

Mechanics of Materials

The rapid advances of modern fabrications technologies require a thorough understanding of physical and mechanical properties of materials as influenced by their atomic composition, processing history and structure at the micro- and nanometer length scales. Carbon nanotubes, nanometer sized crystals, thin films and coatings, MEMS, smart materials and bio-inspired multifunctional materials are current examples employing technologies and processes that heavily depend on material properties at very small length scales. Today’s leading materials for a range of applications are hierarchical, having characteristics of structure at multiple length scales to satisfy a complex set of performance requirements and constraints. Composite materials and advanced alloy systems for transportation and infrastructure increasingly must rely on theoretical understanding at each of a range of length scales from the atomic scale upward to improve existing materials and to develop new materials to meet critical societal needs. Modern day efforts in mechanics of materials exploit recent advances in mechanics of materials that draws upon concurrent use of solid state physics, mathematics and information technology, continuum and discrete (statistical) mechanics and materials chemistry. Advanced materials derive their outstanding properties, durability and multifunctionality from heterogeneity of their underlying microstructure. There is a richness of outstanding problem sets at the intersection of theoretical and applied mathematics and materials mechanics. This state of affairs motivates the central goals of this workshop, namely to explore new and emerging mathematical approaches to multiscale modelling of evolving microstructures and to identify new and emerging mathematical approaches to interfaces in materials

Watertight and 2-Manifold Surface Meshes Using Dual Contouring With Tetrahedral Decomposition of Grid Cubes

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. The advantage of DC is that it can reproduce sharp features by inserting vertices anywhere inside the grid cube, as opposed to the Marching Cubes (MC) algorithm that can insert vertices only on the grid edges. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. Our method decomposes an ambiguous grid cube into a maximum of twelve tetrahedral cells; we introduce novel polygon generation rules that produce 2-manifold and watertight surface meshes. We have applied our proposed method on realistic data, and a comparison of the results of our proposed method with results from traditional DC shows the effectiveness of our method

Geometric modeling, simulation, and visualization methods for plasmid DNA molecules

Plasmid DNA molecules are a special type of DNA molecules that are used, among other applications, in DNA vaccination and gene therapy. These molecules are characterized by, when in their natural state, presenting a closed-circular conformation and by being supercoiled. The production of plasmid DNA using bacteria as hosts implies a purification step where the plasmid DNA molecules are separated from the DNA of the host and other contaminants. This purification process, and all the physical and chemical variations involved, such as temperature changes, may affect the plasmid DNA molecules conformation by uncoiling or even by open them, which makes them useless for therapeutic applications. Because of that, researchers are always searching for new purification techniques that maximize the amount of supercoiled plasmid DNA that is produced. Computer simulations and 3D visualization of plasmid DNA can bring many advantages because they allow researchers to actually see what can happen to the molecules under certain conditions. In this sense, it was necessary to develop reliable and accurate geometric models specific for plasmid DNA simulations. This dissertation presents a new assembling algorithm for B-DNA specifically developed for plasmid DNA assembling. This new assembling algorithm is completely adaptive in the sense that it allows researchers to assemble any plasmid DNA base-pair sequence along any arbitrary conformation that fits the length of the plasmid DNA molecule. This is specially suitable for plasmid DNA simulations, where conformations are generated by simulation procedures and there is the need to assemble the given base-pair sequence over that conformation, what can not be done by conventional predictive DNA assembling methods. Unlike traditional molecular visualization methods that are based on the atomic structure, this new assembling algorithm uses color coded 3D molecular surfaces of the nucleotides as the building blocks for DNA assembling. This new approach, not only reduces the amount of graphical objects and, consequently, makes the rendering faster, but also makes it easier to visually identify the nucleotides in the DNA strands. The algorithm used to triangulate the molecular surfaces of the nucleotides building blocks is also a novelty presented as part of this dissertation. This new triangulation algorithm for Gaussian molecular surfaces introduces a new mechanism that divides the atomic structure of molecules into boxes and spheres. This new space division method is faster because it confines the local calculation of the molecular surface to a specific region of influence of the atomic structure, not taking into account atoms that do not influence the triangulation of the molecular surface in that region. This new method also guarantees the continuity of the molecular surface. Having in mind that the aim of this dissertation is to present a complete set of methods for plasmid DNA visualization and simulation, it is also proposed a new deformation algorithm to be used for plasmid DNA Monte Carlo simulations. This new deformation algorithm uses a 3D polyline to represent the plasmid DNA conformation and performs small deformations on that polyline, keeping the segments length and connectivity. Experiments have been performed in order to compare this new deformation method with deformation methods traditionally used by Monte Carlo plasmid DNA simulations These experiments shown that the new method is more efficient in the sense that its trial acceptance ratio is higher and it converges sooner and faster to the elastic energy equilibrium state of the plasmid DNA molecule. In sum, this dissertation successfully presents an end-to-end set of models and algorithms for plasmid DNA geometric modelling, visualization and simulation

Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees

pre-printWe introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach

Automated Extraction of Flow Features

Computational Fluid Dynamics (CFD) simulations are routinely performed as part of the design process of most fluid handling devices. In order to efficiently and effectively use the results of a CFD simulation, visualization tools are often used. These tools are used in all stages of the CFD simulation including pre-processing, interim-processing, and post-processing, to interpret the results. Each of these stages requires visualization tools that allow one to examine the geometry of the device, as well as the partial or final results of the simulation. An engineer will typically generate a series of contour and vector plots to better understand the physics of how the fluid is interacting with the physical device. Of particular interest are detecting features such as shocks, re-circulation zones, and vortices (which will highlight areas of stress and loss). As the demand for CFD analyses continues to increase the need for automated feature extraction capabilities has become vital. In the past, feature extraction and identification were interesting concepts, but not required in understanding the physics of a steady flow field. This is because the results of the more traditional tools like; isc-surface, cuts and streamlines, were more interactive and easily abstracted so they could be represented to the investigator. These tools worked and properly conveyed the collected information at the expense of a great deal of interaction. For unsteady flow-fields, the investigator does not have the luxury of spending time scanning only one "snapshot" of the simulation. Automated assistance is required in pointing out areas of potential interest contained within the flow. This must not require a heavy compute burden (the visualization should not significantly slow down the solution procedure for co-processing environments). Methods must be developed to abstract the feature of interest and display it in a manner that physically makes sense