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    Area of Science:

    • Computational geometry
    • Computer-aided design
    • Geometric modeling

    Background:

    • Shape approximation is essential for manufacturing processes.
    • Existing methods may lack precision or efficiency in surface normal control.
    • Discrete sets of surface normals are often required for fabrication.

    Purpose of the Study:

    • To develop an algorithm for shape approximation with discrete surface normal constraints.
    • To achieve prescribed Hausdorff error bounds using a minimal set of geometric primitives.
    • To enhance the applicability of computational geometry in manufacturing.

    Main Methods:

    • The algorithm computes maximal interior polytopes of the input shape.
    • It then selects a subset of offsets from these polytopes.
    • The selected offsets collectively cover the original shape within a defined error tolerance.

    Main Results:

    • The method provides approximations with guaranteed Hausdorff error bounds.
    • The approximations utilize a significantly reduced number of geometric primitives.
    • The algorithm effectively restricts surface normals to a discrete set.

    Conclusions:

    • The proposed algorithm offers an efficient and accurate solution for manufacturing-oriented shape approximation.
    • It successfully balances approximation accuracy with the complexity of the resulting geometric representation.
    • This approach advances the integration of geometric modeling techniques in industrial applications.