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    Area of Science:

    • Computer Graphics
    • Image Processing
    • Computational Geometry

    Background:

    • Smooth vector graphics research is divided into gradient meshes and diffusion curves.
    • Existing methods lack a unified mathematical framework.

    Purpose of the Study:

    • To propose a unified mathematical formulation for gradient meshes and diffusion curves.
    • To enhance artistic control in vector graphics.
    • To enable development of new rasterization and vectorization tools.

    Main Methods:

    • Developed a unified mathematical formulation solving a Poisson problem.
    • Introduced an intermediate non-overlapping patch representation.
    • Incorporated boundary conditions and Laplacians for raster image synthesis.

    Main Results:

    • Successfully unified gradient meshes and curve-based approaches.
    • Demonstrated enhanced artistic degrees of freedom, including Neumann conditions.
    • Validated the method on various test scenes with existing primitives.

    Conclusions:

    • The unified formulation offers a new perspective on smooth vector graphics.
    • Compatibility with existing pipelines and tools is maintained.
    • Potential for future advancements in rasterization and vectorization tools is high.