Define Chiang BCSDF normalization

[tdavidovicNV]

While reviewing the Chiang hair equations added in #2964, I found an additional global 1/pi factor that is not present in the cited model. The longitudinal and azimuthal distributions already contain their normalization factors, including 1/(2*pi) for the uniform high-order azimuthal lobe.

Normalization argument

Consider a non-absorbing fiber (T = 1) with unit lobe tints. The attenuation terms in the specification become:

$$A_R = F,\qquad A_{TT} = (1-F)^2,\qquad A_{TRT} = (1-F)^2F,\qquad A_{TRRT+} = (1-F)F^2.$$

They account for all possible paths:

$$A_R + A_{TT} + A_{TRT} + A_{TRRT+} = 1.$$

Consider the simplest case, with zero cuticle tilt, in a constant white environment. A non-absorbing material should return the same unit radiance in every direction: this is the usual white-furnace test. The attenuation terms above divide the incoming energy among the four scattering paths, and their weights add up to 1. The normalized M_p and N_p distributions only determine where each path's share of the energy is scattered.

The familiar 1/pi factor is needed for a constant Lambertian BRDF because its projected hemisphere integral is pi. It is not needed for these already-normalized directional distributions. Applying it to the complete Chiang response reduces the white-furnace result from 1 to 1/pi, losing about 68% of the energy.

This is the normalization tested by the white-furnace result in Figure 5(e) of the original Chiang et al. paper.

Specification change

The specification already denotes a BCSDF by f_c. Following equations 1 and 2 of the cited Chiang paper, this PR defines it directly as:

$$f_c(\omega_i,\omega_o) = \sum_p t_p A_p M_p N_p.$$

The existing f_c notation is retained, and this change does not add a general BCSDF transport convention. Renderer APIs may account for the curve projection factor separately, but that does not introduce a global 1/pi. The PR changes the specification only; the current implementations are not changed.

Implementation notes

• GLSL: Evaluates the same lobe sum and normalized azimuthal distributions, but then applies an additional M_PI_INV.
• OSL (testrender): The MaterialX wrapper emits chiang_hair_bsdf, but testrender does not register this closure in its built-in or BSDL closure sets. The MaterialX OSL network profile skips the Chiang hair fixture, so this path has no normalization result to compare.
• MDL: The current NVIDIA MDL SDK defines normalized azimuthal distributions and accumulates the lobe products without a global 1/pi.

This follows the original Chiang et al. model, equations 1 and 2. PBRT v4 accounts for its renderer-facing measure separately and likewise has no global 1/pi.