Singularities in structured meshes and cross-fields

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    Singularities in structured meshes are vertices that have an irregular valency.
    The integer irregularity in valency is called the singularity index of the vertex
    of the mesh. Singularities in cross-fields are closely related which are isolated
    points where the cross-field vectors are defined in its limit neighbourhood
    but not at the point itself. For a closed surface the genus determines the
    minimum number of singularities that are required in a structured mesh or
    in a cross-field on the surface. Adding boundaries and forcing conformity of
    the mesh or alignment of the cross-field to them also affects the minimum
    number of singularities required. In this paper a simple formula is derived
    from Bunin’s Continuum Theory for Unstructured Mesh Generation [1] that
    specifies the net sum of singularity indices that must occur in a cross-field
    with even numbers of vectors on a face or surface region with alignment
    conditions. The formula also applies to mesh singularities in quadrilateral
    and triangle meshes and the correspondence to 3-D hexahedral meshes is
    related. Some potential applications are discussed.
    Original languageEnglish
    Number of pages15
    Pages (from-to)11-25
    JournalComputer-Aided Design
    Journal publication dateDec 2018
    Volume105
    Early online date05 Jul 2018
    DOIs
    StateEarly online date - 05 Jul 2018

    ID: 154587731