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    This study introduces a method to approximate shapes using minimal medial balls, optimizing for large balls under geometric constraints. This approach aids in creating simplified models and generating robust porous structures.

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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Geometric Modeling

    Background:

    • The medial axis transform completely encodes shape information.
    • Approximating complex shapes with simpler representations is a fundamental challenge in geometric modeling.
    • Existing methods may not efficiently balance shape approximation accuracy with model complexity.

    Purpose of the Study:

    • To develop a method for approximating enclosed volumes using a minimal set of medial balls.
    • To propose a selection strategy that favors larger medial balls while adhering to geometric constraints.
    • To introduce a speedup technique for medial ball selection based on power cell adjacency.

    Main Methods:

    • A progressive, top-down selection of medial balls to enlarge the approximated region.
    • A strategy encouraging large medial balls within specified geometric constraints.
    • A speedup technique leveraging the relationship between medial ball intersection and power cell adjacency.

    Main Results:

    • An efficient algorithm for approximating shapes with a minimal number of medial balls.
    • A validated speedup technique for medial ball selection.
    • Demonstrated applications in developing a user-friendly ball-stick modeling system and generating porous structures.

    Conclusions:

    • The proposed medial ball approximation method effectively balances shape representation with model simplicity.
    • The speedup technique significantly enhances the efficiency of medial ball selection.
    • The method provides a versatile framework for applications in modeling and material design.