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Solid Mathematical Marbling.

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    This study introduces mathematical marbling for 3D solids, enabling compact texture representation. The novel approach generates high-quality, feature-preserving textures efficiently for real-time applications.

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    Area of Science:

    • Computer Graphics
    • Geometric Modeling
    • Texture Synthesis

    Background:

    • Extensive research exists for 2D computer-generated marbling.
    • 3D solid marbling remains an underexplored area in computer graphics.

    Purpose of the Study:

    • To present a novel method for mathematical marbling of three-dimensional solids.
    • To develop a compact, feature-preserving, and resolution-independent texture representation.
    • To enable efficient real-time texture mapping and authoring of 3D marbling.

    Main Methods:

    • Utilizing closed-form 3D pattern tool functions (injection and deformation functions) to create basic and complex marbling patterns.
    • Implementing a compact random-access vector representation for textures.
    • Leveraging the GPU for efficient real-time color evaluation based on 3D coordinates.
    • Developing an intuitive user interface and a genetic algorithm for texture authoring.

    Main Results:

    • Generation of high-quality 3D solid marbling textures that preserve sharp features and smooth color variations.
    • Demonstration of a memory-efficient representation storing only mathematical functions and parameters.
    • Successful implementation on GPU for real-time texture mapping.
    • Validation through various 3D objects and marbling textures.

    Conclusions:

    • The proposed mathematical marbling method effectively generates high-quality, efficient, and authorable 3D solid textures.
    • The compact vector representation and GPU implementation enable real-time applications.
    • This work opens new possibilities for 3D texture synthesis and manipulation.