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Planar Hexagonal Meshing for Architecture.

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    This study introduces planar hexagonal (PH) meshes for architectural paneling. The method uses surface geometry to create PH meshes, enabling efficient and appealing freeform surface construction.

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    Area of Science:

    • Computational geometry
    • Computer-aided design
    • Architectural engineering

    Background:

    • Freeform architectural surfaces require efficient paneling methods.
    • Planar hexagonal (PH) meshes offer node simplicity and aesthetic appeal.
    • Constraints of PH mesh properties by surface geometry are not fully understood.

    Purpose of the Study:

    • To investigate the geometric constraints on PH mesh face shape, size, and pattern.
    • To develop an effective method for paneling freeform architectural surfaces using PH meshes.
    • To compute necessary support structures for manufacturing.

    Main Methods:

    • Constructing an ideal triangulation of a smooth surface guided by its geometry.
    • Utilizing tangent duality to achieve Dupin-regular PH meshes.
    • Developing techniques to mitigate mesh layout issues from surface curvature singularities.
    • Computing exact vertex and approximate edge offsets for support structures.

    Main Results:

    • An effective method for paneling freeform surfaces with PH meshes was developed.
    • The method ensures PH faces are constrained by surface geometry.
    • Novel techniques address mesh layout challenges arising from surface curvature.
    • Accurate support structures for panel manufacturing were computed.

    Conclusions:

    • The developed method enables efficient and geometrically constrained paneling of freeform surfaces with PH meshes.
    • The approach integrates surface geometry, mesh generation, and manufacturing considerations.
    • Validated through architectural examples, the method demonstrates practical applicability.