92 research outputs found

    Geometric Rounding and Feature Separation in Meshes

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    Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical algorithms. We present a practical geometric rounding algorithm for 3D triangle meshes that preserves the topology of the mesh. The basis of the algorithm is a novel strategy: 1) modify the mesh to achieve a feature separation that prevents topology changes when the coordinates change by the rounding unit; and 2) round each vertex coordinate to the closest floating point number. Feature separation is also useful on its own, for example for satisfying minimum separation rules in CAD models. We demonstrate a robust, accurate implementation

    Planar shape manipulation using approximate geometric primitives

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    We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is \bigo(n\log n+k) for an input of size nn with k=\bigo(n^2) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms in floating point using sequences of six set operations and Euclidean transforms on shapes bounded by curves of algebraic degree~1 to~6. We test generic and degenerate inputs. Keywords: robust computational geometry, plane subdivisions, set operations

    Table Based Detection of Degenerate Predicates in Free Space Construction

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    The key to a robust and efficient implementation of a computational geometry algorithm is an efficient algorithm for detecting degenerate predicates. We study degeneracy detection in constructing the free space of a polyhedron that rotates around a fixed axis and translates freely relative to another polyhedron. The structure of the free space is determined by the signs of univariate polynomials, called angle polynomials, whose coefficients are polynomials in the coordinates of the vertices of the polyhedra. Every predicate is expressible as the sign of an angle polynomial f evaluated at a zero t of an angle polynomial g. A predicate is degenerate (the sign is zero) when t is a zero of a common factor of f and g. We present an efficient degeneracy detection algorithm based on a one-time factoring of every possible angle polynomial. Our algorithm is 3500 times faster than the standard algorithm based on greatest common divisor computation. It reduces the share of degeneracy detection in our free space computations from 90% to 0.5% of the running time

    The EMBARC European Bronchiectasis Registry:protocol for an international observational study

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    Bronchiectasis is one of the most neglected diseases in respiratory medicine. There are no approved therapies and few large-scale, representative epidemiological studies. The EMBARC (European Multicentre Bronchiectasis Audit and Research Collaboration) registry is a prospective, pan-European observational study of patients with bronchiectasis. The inclusion criterion is a primary clinical diagnosis of bronchiectasis consisting of: 1) a clinical history consistent with bronchiectasis; and 2) computed tomography demonstrating bronchiectasis. Core exclusion criteria are: 1) bronchiectasis due to known cystic fibrosis; 2) age <18 years; and 3) patients who are unable or unwilling to provide informed consent. The study aims to enrol 1000 patients by April 2016 across at least 20 European countries, and 10 000 patients by March 2020. Patients will undergo a comprehensive baseline assessment and will be followed up annually for up to 5 years with the goal of providing high-quality longitudinal data on outcomes, treatment patterns and quality of life. Data from the registry will be available in the form of annual reports. and will be disseminated in conference presentations and peer-reviewed publications. The European Bronchiectasis Registry aims to make a major contribution to understanding the natural history of the disease, as well as guiding evidence-based decision making and facilitating large randomised controlled trials.info:eu-repo/semantics/publishedVersio

    An Inconsistency Sensitive Arrangement Algorithm for Curve Segments

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