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Empirical BRDF Model for Goniochromatic Materials and Soft Proofing With Reflective Inks.

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    This study introduces a modified microfacet bidirectional reflectance distribution function (BRDF) model to accurately capture angle-dependent material color, known as goniochromatism, for structural color pigments. The new model simplifies complex calculations for interactive 3D rendering applications.

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    Area of Science:

    • Computer Graphics
    • Materials Science
    • Optics

    Background:

    • Standard bidirectional reflectance distribution functions (BRDFs) fail to model goniochromatism, or angle-dependent material color.
    • Existing extensions to model goniochromatism significantly increase model complexity.
    • Material color is typically defined by diffuse reflectance and a spectral complex index of refraction.

    Purpose of the Study:

    • To develop a simplified BRDF model capable of accurately representing goniochromatism.
    • To enable interactive preview of 3D objects with printed, angle-dependent color textures.

    Main Methods:

    • Measured the goniochromatism of structural color pigments used in additive color printing.
    • Modified the standard microfacet BRDF model by incorporating an empirically based spectral parameter.
    • Replaced the spectral complex index of refraction with a specular reflectance spectrum.

    Main Results:

    • The modified microfacet BRDF model successfully fits the measured spectral angular dependence of bidirectional reflectance.
    • The model accurately represents the goniochromatism of red, green, and blue commercial structural color pigments.
    • The proposed model offers a computationally efficient approach to simulating angle-dependent color.

    Conclusions:

    • A simplified BRDF model effectively captures goniochromatism in structural color pigments.
    • The new model facilitates straightforward implementation in shaders for real-time 3D rendering.
    • This research advances the accurate digital representation of materials with angle-dependent optical properties.