999 research outputs found

    Monte Carlo Results for Projected Self-Avoiding Polygons: A Two-dimensional Model for Knotted Polymers

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    We introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modeled by a closed polygon drawn on the square diagonal lattice, with possible crossings describing pairs of strands of polymer passing on top of each other. Each polygon configuration can be viewed as the two- dimensional projection of a particular knot. We study numerically the statistics of large polygons with a fixed knot type, using a generalization of the BFACF algorithm for self-avoiding walks. This new algorithm incorporates both the displacement of crossings and the three types of Reidemeister transformations preserving the knot topology. Its ergodicity within a fixed knot type is not proven here rigorously but strong arguments in favor of this ergodicity are given together with a tentative sketch of proof. Assuming this ergodicity, we obtain numerically the following results for the statistics of knotted polygons: In the limit of a low crossing fugacity, we find a localization along the polygon of all the primary factors forming the knot. Increasing the crossing fugacity gives rise to a transition from a self-avoiding walk to a branched polymer behavior.Comment: 36 pages, 30 figures, latex, epsf. to appear in J.Phys.A: Math. Ge

    PROSPECTIVE UPON MULTI-SOURCE URBAN SCALE DATA FOR 3D DOCUMENTATION AND MONITORING OF URBAN LEGACIES

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    Abstract. The investigation on the built urban heritage and its current transformations can progressively benefit from the use of geospatial data related to urban environment. This is even more interesting when urban design studies of historical and stratified cities meet the contribution of 4D geospatial data within the urban morphology researches, aiming at quickly and accurately identifying and then measuring with a spatial relationship, both localized transformation (volumes demolitions, addition, etc
) and wide-scale substantial modification resulting from urban zones of diversification spaces that incorporates urban legacies. In this domain, the comparison and analysis of multi-source and multi-scale information belonging to Spatial Data Infrastructures (SDI) organized by Municipality and Region Administration (mainly, orthoimages and DSM and digital mapping) are a crucial support for multi-temporal spatial analysis, especially if compared with new DSMs related to past urban situations. The latter can be generated by new solution of digital image-matching techniques applicable to the available historical aerial images. The goal is to investigate the amount of available data and their effectiveness, to later test different experimental tools and methods for quick detection, localization and quantification of morphological macro-transformation at urban scale. At the same time, it has been examined the opportunity to made available, with up-and-coming Mobile Mapping Systems (MMS) based on image- and range-based techniques, a rapid and effective approach of data gathering, updating and sharing at validated urban scales. The presented research, carried out in the framework of the FULL@Polito research lab, applies to urban legacies and their regeneration, and is conducted on a key redevelopment area in northern Torino, the Parco Dora, that was occupied by steel industries actively working up to 1992. The long-standing steel structures of the Ferriere FIAT lot have been refurbished and incorporated in the new urban park, generating a contemporary space with a new evolving urban fabric, and being integrated in the new updated geo-spatial databases as well.</p

    Morphing of Building Footprints Using a Turning Angle Function

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    We study the problem of morphing two polygons of building footprints at two different scales. This problem frequently occurs during the continuous zooming of interactive maps. The ground plan of a building footprint on a map has orthogonal characteristics, but traditional morphing methods cannot preserve these geographic characteristics at intermediate scales. We attempt to address this issue by presenting a turning angle function-based morphing model (TAFBM) that can generate polygons at an intermediate scale with an identical turning angle for each side. Thus, the orthogonal characteristics can be preserved during the entire interpolation. A case study demonstrates that the model yields good results when applied to data from a building map at various scales. During the continuous generalization, the orthogonal characteristics and their relationships with the spatial direction and topology are well preserve

    Robust arbitrary-view gait recognition based on 3D partial similarity matching

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    Existing view-invariant gait recognition methods encounter difficulties due to limited number of available gait views and varying conditions during training. This paper proposes gait partial similarity matching that assumes a 3-dimensional (3D) object shares common view surfaces in significantly different views. Detecting such surfaces aids the extraction of gait features from multiple views. 3D parametric body models are morphed by pose and shape deformation from a template model using 2-dimensional (2D) gait silhouette as observation. The gait pose is estimated by a level set energy cost function from silhouettes including incomplete ones. Body shape deformation is achieved via Laplacian deformation energy function associated with inpainting gait silhouettes. Partial gait silhouettes in different views are extracted by gait partial region of interest elements selection and re-projected onto 2D space to construct partial gait energy images. A synthetic database with destination views and multi-linear subspace classifier fused with majority voting are used to achieve arbitrary view gait recognition that is robust to varying conditions. Experimental results on CMU, CASIA B, TUM-IITKGP, AVAMVG and KY4D datasets show the efficacy of the propose method

    Building Footprint Extraction from LiDAR Data and Imagery Information

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    This study presents an automatic method for regularisation of building outlines. Initially, building segments are extracted using a new fusion method. Data- and model-driven approaches are then combined to generate approximate building polygons. The core part of the method includes a novel data-driven algorithm based on likelihood equation derived from the geometrical properties of a building. Finally, the Gauss-Helmert and Gauss-Markov models adjustment are implemented and modified for regularisation of building outlines considering orthogonality constraints

    QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

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    QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

    Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations

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    We describe an algebro-geometric construction of polygon-bounded minimal surfaces in ADS_5, based on consideration of what we call the "boundary ring" of polynomials. The first non-trivial example of the Nambu-Goto (NG) solutions for Z_6-symmetric hexagon is considered in some detail. Solutions are represented as power series, of which only the first terms are evaluated. The NG equations leave a number of free parameters (a free function). Boundary conditions, which fix the free parameters, are imposed on truncated series. It is still unclear if explicit analytic formulas can be found in this way, but even approximate solutions, obtained by truncation of power series, can be sufficient to investigate the Alday-Maldacena -- BDS/BHT version of the string/gauge duality.Comment: 42 pages, 5 figure

    Hinged Dissections Exist

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    We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our common dissection result to edge-hinged dissections of solid 3D polyhedra that have a common (unhinged) dissection, as determined by Dehn's 1900 solution to Hilbert's Third Problem. Our proofs are constructive, giving explicit algorithms in all cases. For a constant number of planar polygons, both the number of pieces and running time required by our construction are pseudopolynomial. This bound is the best possible, even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.Comment: 22 pages, 14 figure
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