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    Area of Science:

    • Computer Graphics
    • Material Science
    • Optics

    Background:

    • Specular microfacet models are common for material glossiness, often paired with Lambertian terms for color.
    • Existing models require complex numerical simulations for light reflections between interfaces and substrates.
    • Managing Fresnel transmission at interfaces is crucial for accurate material representation.

    Purpose of the Study:

    • To propose an analytical model for Fresnel interfaces on Lambertian substrates.
    • To analytically express multiple light reflections between interface and substrate.
    • To demonstrate the impact of Fresnel transmission on material appearance for diverse surfaces.

    Main Methods:

    • Developed a Fresnel interface on a Lambertian substrate model.
    • Derived analytical solutions for multiple light reflections.
    • Investigated effects on flat and rough surfaces (isotropic/anisotropic).
    • Proposed integration into physically based Monte Carlo rendering systems.
    • Created an approximate representation for GPU applications and data fitting.

    Main Results:

    • The proposed model analytically handles multiple light reflections.
    • Fresnel transmission effects on material appearance are demonstrated.
    • The model generalizes previous approaches, including flat Lambertian and microfacet models.
    • A wide range of material appearances can be rendered.

    Conclusions:

    • The interfaced Lambertian model provides an efficient and accurate method for material rendering.
    • The approach offers a generalized framework for physically based rendering.
    • The model is suitable for both complex simulations and real-time applications.