Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates

This paper studies mathematical models of biopolymer supramolecular aggregates that are formed by the self-assembly of single monomers. We develop a new multiscale numerical approach to model the structural properties of such aggregates. This theoretical approach establishes micro-macro relations between the geometrical and mechanical properties of the monomers and supramolecular aggregates. Most atomistic-to-continuum methods are constrained by a crystalline order or a periodic setting and therefore cannot be directly applied to modeling of soft matter. By contrast, the energy matching method developed in this paper does not require crystalline order and, therefore, can be applied to general microstructures with strongly variable spatial correlations. In this paper we use this method to compute the shape and the bending stiffness of their supramolecular aggregates from known chiral and amphiphilic properties of the short chain peptide monomers. Numerical implementation of our approach demonstrates consistency with results obtained by molecular dynamics simulations

Surface networks

© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou

Multi-scale data storage schemes for spatial information systems

This thesis documents a research project that has led to the design and prototype implementation of several data storage schemes suited to the efficient multi-scale representation of integrated spatial data. Spatial information systems will benefit from having data models which allow for data to be viewed and analysed at various levels of detail, while the integration of data from different sources will lead to a more accurate representation of reality. The work has addressed two specific problems. The first concerns the design of an integrated multi-scale data model suited for use within Geographical Information Systems. This has led to the development of two data models, each of which allow for the integration of terrain data and topographic data at multiple levels of detail. The models are based on a combination of adapted versions of three previous data structures, namely, the constrained Delaunay pyramid, the line generalisation tree and the fixed grid. The second specific problem addressed in this thesis has been the development of an integrated multi-scale 3-D geological data model, for use within a Geoscientific Information System. This has resulted in a data storage scheme which enables the integration of terrain data, geological outcrop data and borehole data at various levels of detail. The thesis also presents details of prototype database implementations of each of the new data storage schemes. These implementations have served to demonstrate the feasibility and benefits of an integrated multi-scale approach. The research has also brought to light some areas that will need further research before fully functional systems are produced. The final chapter contains, in addition to conclusions made as a result of the research to date, a summary of some of these areas that require future work

Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices

This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using basic ideas from probability theory and builds upon an algorithm from discrete Morse theory with a strong mathematical foundation. While a formal proof is only hinted at, we do provide a thorough numerical evaluation of our method and compare it to established algorithms.Comment: 17 pages, 7 figure

Single-Strip Triangulation of Manifolds with Arbitrary Topology

Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few long strips. In this paper, we present a new algorithm for creating a single triangle loop or strip from a triangulated model. Our method applies a dual graph matching algorithm to partition the mesh into cycles, and then merges pairs of cycles by splitting adjacent triangles when necessary. New vertices are introduced at midpoints of edges and the new triangles thus formed are coplanar with their parent triangles, hence the visual fidelity of the geometry is not changed. We prove that the increase in the number of triangles due to this splitting is 50% in the worst case, however for all models we tested the increase was less than 2%. We also prove tight bounds on the number of triangles needed for a single-strip representation of a model with holes on its boundary. Our strips can be used not only for efficient rendering, but also for other applications including the generation of space filling curves on a manifold of any arbitrary topology.Comment: 12 pages, 10 figures. To appear at Eurographics 200

TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes

We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the pre-processing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware

Survey of semi-regular multiresolution models for interactive terrain rendering

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multiresolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster-based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accurac

Consistent Density Scanning and Information Extraction From Point Clouds of Building Interiors

Over the last decade, 3D range scanning systems have improved considerably enabling the designers to capture large and complex domains such as building interiors. The captured point cloud is processed to extract specific Building Information Models, where the main research challenge is to simultaneously handle huge and cohesive point clouds representing multiple objects, occluded features and vast geometric diversity. These domain characteristics increase the data complexities and thus make it difficult to extract accurate information models from the captured point clouds. The research work presented in this thesis improves the information extraction pipeline with the development of novel algorithms for consistent density scanning and information extraction automation for building interiors. A restricted density-based, scan planning methodology computes the number of scans to cover large linear domains while ensuring desired data density and reducing rigorous post-processing of data sets. The research work further develops effective algorithms to transform the captured data into information models in terms of domain features (layouts), meaningful data clusters (segmented data) and specific shape attributes (occluded boundaries) having better practical utility. Initially, a direct point-based simplification and layout extraction algorithm is presented that can handle the cohesive point clouds by adaptive simplification and an accurate layout extraction approach without generating an intermediate model. Further, three information extraction algorithms are presented that transforms point clouds into meaningful clusters. The novelty of these algorithms lies in the fact that they work directly on point clouds by exploiting their inherent characteristic. First a rapid data clustering algorithm is presented to quickly identify objects in the scanned scene using a robust hue, saturation and value (H S V) color model for better scene understanding. A hierarchical clustering algorithm is developed to handle the vast geometric diversity ranging from planar walls to complex freeform objects. The shape adaptive parameters help to segment planar as well as complex interiors whereas combining color and geometry based segmentation criterion improves clustering reliability and identifies unique clusters from geometrically similar regions. Finally, a progressive scan line based, side-ratio constraint algorithm is presented to identify occluded boundary data points by investigating their spatial discontinuity