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    This study presents novel surface averaging operators for multiresolution modeling, enabling smooth subdivision and reverse subdivision for arbitrary degree surfaces with enhanced continuity properties.

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    Area of Science:

    • Computer Graphics
    • Geometric Modeling
    • Applied Mathematics

    Background:

    • Existing surface subdivision methods often lack the ability to perform reverse subdivision or achieve arbitrary continuity.
    • Previous work by Stam, Zorin, and Schröder focused on forward subdivision only.
    • Generalizing B-Spline multiresolution to arbitrary topology surfaces remains a challenge.

    Purpose of the Study:

    • To introduce local surface averaging operators with local inverses.
    • To develop a method for surface multiresolution (subdivision and reverse subdivision) of arbitrary degree.
    • To achieve enhanced continuity properties for subdivision surfaces.

    Main Methods:

    • Development of two local surface averaging operators with local inverses.
    • Application of these operators to devise a surface multiresolution method.
    • Configuration of operators to generalize B-Spline multiresolution to arbitrary topology surfaces.

    Main Results:

    • The proposed method supports both subdivision and reverse subdivision of arbitrary degree.
    • Subdivision surfaces exhibit C^d continuity at regular vertices and C^1 continuity at extraordinary vertices.
    • The operators involve only direct neighbors of a vertex, simplifying the process.

    Conclusions:

    • The introduced method provides a robust framework for surface multiresolution with arbitrary degree and enhanced continuity.
    • The operators generalize B-Spline multiresolution to arbitrary topology surfaces.
    • Smooth reverse and non-uniform subdivisions are supported, offering flexibility in geometric modeling.