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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Differential Geometry

    Background:

    • Global conformal parameterization is crucial for various applications in computer graphics and geometry processing.
    • Existing methods, particularly those based on holomorphic one-forms, have limitations in the space of achievable parameterizations.
    • High-genus meshes present significant challenges for traditional parameterization techniques.

    Purpose of the Study:

    • To develop a novel algorithm for computing global conformal parameterizations of high-genus meshes.
    • To leverage discrete holomorphic quadratic differentials for robust mesh parameterization.
    • To provide a method with a larger parameterization space compared to existing techniques.

    Main Methods:

    • Designing a novel diffusion method for computing pole-free discrete harmonic measured foliations.
    • Defining discrete holomorphic quadratic differentials using horizontal and vertical harmonic measured foliations.
    • Developing a practical algorithm to approximate discrete natural coordinates for holomorphic quadratic differentials.

    Main Results:

    • The proposed method successfully computes global conformal parameterizations for high-genus meshes.
    • Demonstrated robustness across numerous configurations and meshes.
    • The approach provides a larger space of parameterizations than methods based on holomorphic one-forms.

    Conclusions:

    • The algorithm offers a simple and effective method for global conformal parameterization of high-genus meshes.
    • The use of discrete holomorphic quadratic differentials expands the capabilities of mesh parameterization.
    • This technique is robust and suitable for complex mesh structures.