Vaibhav Rathod's Notes

PathTracer Learning - Concept - Fresnel Effect

3 min read

  • What Is the Fresnel Effect?

    • At any interface between two media, light is partially reflected and partially transmitted
    • The ratio depends on the angle of incidence
    • At grazing angles (θ → 90°): almost all light is reflected
    • At normal incidence (θ = 0°): only a small fraction is reflected
    • This is why water looks like a mirror when viewed at a shallow angle

  • Exact Fresnel Equations (Schlick’s Approximation)

    • Full Fresnel equations (from Maxwell’s equations) are expensive
    • Schlick (1994) approximation — used in virtually all real-time renderers
    • F(θ) = F0 + (1 - F0) * (1 - cos(θ))^5
    • cos(θ) = dot(V, H) — angle between view direction and half-vector
    • F0 — reflectance at normal incidence (0° angle)

  • F0 Values

    • Dielectrics (non-metals: plastic, glass, skin, wood)
      • F0 ≈ 0.04 (4%) for most dielectrics
      • Range: 0.02 (water) to 0.08 (gemstones)
      • Formula from IOR: F0 = ((n - 1) / (n + 1))²
      • Glass (n=1.5): F0 = ((1.5-1)/(1.5+1))² = 0.04
    • Metals (conductors: gold, silver, copper, iron)
      • F0 = base color of the metal (RGB values)
      • Gold: F0 ≈ (1.0, 0.71, 0.29)
      • Silver: F0 ≈ (0.95, 0.93, 0.88)
      • Copper: F0 ≈ (0.95, 0.64, 0.54)
      • Metals absorb transmitted light — no diffuse component

  • Metallic Workflow (PBR)

    • metallic parameter in [0, 1]
    • F0 = lerp(vec3(0.04), baseColor, metallic)
    • diffuse_color = baseColor * (1 - metallic) — metals have no diffuse
    • This is the Disney/Unreal/Godot PBR convention
    • Why: real materials are either dielectric (F0=0.04) or metal (F0=baseColor)
    • Values between 0 and 1 are for blending (e.g., dirty metal, oxidized surface)

  • Energy Conservation with Fresnel

    • Fresnel tells us how much light is reflected vs transmitted
    • For opaque surfaces: transmitted = 1 - F(θ) → absorbed or diffusely scattered
    • Specular contribution: F(θ) * f_specular
    • Diffuse contribution: (1 - F(θ)) * f_diffuse
    • This ensures total reflectance ≤ 1
    • In code:

  • Exact Fresnel (for Reference)

    • For dielectrics (real IOR):
      • rs = (n1*cos(θi) - n2*cos(θt)) / (n1*cos(θi) + n2*cos(θt))
      • rp = (n2*cos(θi) - n1*cos(θt)) / (n2*cos(θi) + n1*cos(θt))
      • F = (rs² + rp²) / 2
      • cos(θt) from Snell’s law: cos(θt) = sqrt(1 - (n1/n2)² * (1 - cos²(θi)))
    • For conductors (complex IOR n + ik):
      • More complex formula involving absorption coefficient k
      • Schlick with measured F0 is a good approximation

  • Total Internal Reflection

    • When light travels from dense to less dense medium (e.g., glass to air)
    • At angles beyond the critical angle: all light is reflected, none transmitted
    • Critical angle: θ_c = arcsin(n2/n1) where n1 > n2
    • In GLSL refract: returns vec3(0) when TIR occurs
    • Check: 1 - eta² * (1 - NdotI²) < 0 → TIR

Graph View

Backlinks