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About this paper
Jonathan Dupuy
The authors derive an exact all-orders BRDF for a homogeneous, semi-infinite microflake medium under Smith shadowing, using a parameter-free quadratic normal distribution. Its closed form, f_r=(z_i+z_o)/(π(1+ω_i·ω_o)), is directly importance-sampled and agrees closely with random-walk histograms at 0°, 45°, and 80° incidence. It is Lambertian at normal incidence, becomes asymmetric toward grazing, and lacks roughness control.
Key insights
- Restricting all microflake normals to the upper hemisphere imposes an ordered transport structure, making arbitrary scattering paths analytically manageable.
- The quadratic NDF is selected not for a tunable roughness interpretation but because its induced azimuthal distribution remains in the Poisson-kernel family under repeated scattering.
- Exact summation and sampling are achieved through the interaction of geometric path ordering, analytically integrated collision depths, convolution closure, and operator contraction.
Summary by alphaXiv.
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