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    This survey unifies research on smooth vector graphics, covering representation, creation, and rasterization. It categorizes methods by mathematical models and pipeline contributions for artists and researchers.

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    Area of Science:

    • Computer Graphics
    • Image Processing
    • Computational Geometry

    Background:

    • Smooth vector graphics are crucial for scalable image content.
    • Research has diverged into specific mathematical models like gradient meshes and diffusion curves.
    • Existing work often focuses narrowly on subproblems like representation or automatic vectorization.

    Purpose of the Study:

    • To provide a unified survey of established computational models for smooth vector graphics.
    • To categorize research based on mathematical representations and contributions to the content creation pipeline.
    • To facilitate knowledge transfer and serve as an entry point for artists and researchers.

    Main Methods:

    • Categorization of vector graphics research based on underlying mathematical representations.
    • Analysis of contributions across the vector graphics content creation pipeline: representation, creation, rasterization, and automatic vectorization.
    • Consistent notation to describe diverse computational models.

    Main Results:

    • Established computational models are presented using a consistent notation.
    • Research is categorized by mathematical foundations and pipeline stages.
    • Recent advances in each field are leveraged to bridge knowledge gaps.

    Conclusions:

    • A unified understanding of smooth vector graphics research is presented.
    • The survey aims to spur further research and collaboration.
    • Future research directions and challenges in vector graphics are outlined.