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Related Concept Videos

Mesh Analysis01:20

Mesh Analysis

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Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
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Boundary Conditions: Lossless Lines01:21

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Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Low-Resolution Remeshing Using the Localized Restricted Voronoi Diagram.

Dong-Ming Yan, Guanbo Bao, Xiaopeng Zhang

    IEEE Transactions on Visualization and Computer Graphics
    |September 11, 2015
    PubMed
    Summary

    Generating suitable Voronoi diagrams for Centroidal Voronoi Tessellation (CVT)-based remeshing is challenging. This study introduces the localized restricted Voronoi diagram (LRVD), ensuring connected Voronoi cells for improved mesh processing, especially with few vertices.

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    Area of Science:

    • Computational Geometry
    • Computer Graphics
    • Mesh Processing

    Background:

    • Triangular remeshing faces challenges when triangle size approaches feature size.
    • Centroidal Voronoi Tessellation (CVT)-based remeshing is hindered by difficulties in computing suitable Voronoi diagrams.

    Purpose of the Study:

    • Introduce the localized restricted Voronoi diagram (LRVD) for mesh surfaces.
    • Address limitations of the restricted Voronoi diagram (RVD) in handling disjoint Voronoi regions.
    • Ensure each Voronoi cell is a single connected region for improved mesh processing.

    Main Methods:

    • Extend the concept of the restricted Voronoi diagram (RVD) to mesh surfaces.
    • Develop a definition for LRVD that guarantees connected Voronoi cells.
    • Combine local discrete clustering with global exact computation to derive the LRVD.

    Main Results:

    • The LRVD ensures connected Voronoi cells, unlike RVD which can produce disjoint regions.
    • LRVD is crucial for sampling meshes with a low number of points.
    • LRVD effectively handles sampling of closely situated surface areas, such as nearby sheets.

    Conclusions:

    • The LRVD is a valuable extension for mesh processing techniques, particularly surface remeshing.
    • LRVD enables more efficient and accurate remeshing with a reduced vertex count.
    • The proposed LRVD computation method combines local and global techniques for robust results.