# Principled Hair BSDF

Cycles Only

The *Principled Hair* BSDF is a physically-based,
easy-to-use shader for rendering hair and fur.

Tip

Realistic hair should have a minimum of variance between each strand.
The shader allows for this by specifying two values, *Random Color*
and *Random Roughness*, which remap the specified Melanin/Roughness values to
the range \(Color/Roughness \pm Randomization\%\).

## Inputs

### Common

- Color
The RGB color of the strand. Only used in Direct coloring.

Hint

The chosen color is converted to an absorption coefficient with the following formula (section 4.2 of [CBTB16]):

\[\sigma_{a} = \frac{\ln(Color)} {\left(5.969 - 0.215\beta_{N} + 2.532\beta_{N}^{2} - 10.73\beta_{N}^{3} + 5.574\beta_{N}^{4} + 0.245\beta_{N}^{5}\right)^{2}}\]where \(\beta_{N}\) is the radial roughness of the hair after applying randomization (if specified).

- Melanin
Absolute quantity of pigment. Range \([0, 1]\) equivalent to \([0\%, 100\%]\).

Hint

This is a linear mapping to the underlying exponential function:

\[melanin\_qty = -\ln(\max(1.0 - Melanin, 0.0001))\]- Melanin Redness
Ratio of pheomelanin to eumelanin. Range \([0, 1]\) equivalent to \([0\%, 100\%]\).

Hint

The ratio formula is: \(eumelanin = Melanin*(1.0-MelaninRedness)\), \(pheomelanin = Melanin*MelaninRedness\).

The resulting quantities are converted (after randomization, if specified) to absorption concentration via the following formula (section 6.1 of [EFHLA11], adjusted for the range \([0, 1]\)):

\[\begin{split}\sigma_{a} = eumelanin * \left[\begin{matrix} 0.506 \\ 0.841 \\ 1.653 \\ \end{matrix}\right] + pheomelanin * \left[\begin{matrix} 0.343 \\ 0.733 \\ 1.924 \\ \end{matrix}\right]\end{split}\]- Tint
Color used for dyeing the hair after applying the melanin pigment. It is not subject to randomization. It can be disabled by setting the color to white.

Hint

This is converted via the Color mapping above and added to the absorption coefficient of the melanin concentration.

- Absorption Coefficient
Attenuation coefficient \(\sigma\).

- IOR
Index of refraction (IOR) defining how much the ray changes direction. At 1.0 rays pass straight through like in a transparent material; higher values give more refraction. Default value is \(1.55\).

- Offset
Tilts the glint of the hair by increasing the angle of the scales of the hair’s cuticle with respect to the hair shaft. Human hair usually has low values.

- Random Color
For each strand, vary the melanin concentration by \(RandomFactor\). Range \([0, 1]\) equivalent to \([0\%, 100\%]\) of the initial melanin concentration.

Hint

The melanin concentration is multiplied by \(randomFactor\), where \(randomFactor = 1.0 + 2.0*(Random - 0.5) * RandomColor\).

- Random Roughness
For each strand, vary both Roughness values by \(RandomFactor\). Range \([0, 1]\) equivalent to \([0\%, 100\%]\) of the initial roughness values.

Hint

The applied formula is the same one as for

*Random Color*.- Random
Random number source. If no node is connected here, it is automatically instanced with the value obtained from

.

### Chiang Model

The Chiang model is based on a Gaussian distribution with separate roughness along and orthogonal to the hair.

- Roughness
Specify how much the glints are smoothed in the direction of the hair shaft. Too low values will smoothen the hair to the point of looking almost metallic, making glints look like Fireflies; while setting it too high will result in a Lambertian look.

- Radial Roughness
Specify how much the glints are smoothed in the direction of the hair normal. Too low values will concentrate the glint; while setting it too high will spread the light across the width of the strand.

Hint

Mathematically, this parameter is mapped to the logistic distribution’s scale factor \(s\) (section 4.1 of [CBTB16]).

- Coat
Simulate a shiny coat of fur, by reducing the Roughness to the given factor only for the first light bounce (diffuse). Range \([0, 1]\) equivalent to a reduction of \([0\%, 100\%]\) of the original Roughness.

### Huang Model

The Huang model is based on microfacet based reflection and transmission, and supports elliptically shaped hair.

- Aspect Ratio
The ratio of the minor axis to the major axis of an elliptical cross-section. Recommended values are 0.8~1 for Asian hair, 0.65~0.9 for Caucasian hair, 0.5~0.65 for African hair. The major axis is aligned with the curve normal, which can be created with geometry nodes, but is not supported in legacy particle hair.

- Roughness
Microfacet roughness for reflection and transmission.

- Reflection
Optional factor for modulating the first light bounce off the hair surface. The color of this component is always white. Keep this 1.0 for physical correctness.

- Transmission
Optional factor for modulating the transmission component. Picks up the color of the pigment inside the hair. Keep this 1.0 for physical correctness.

- Secondary Reflection
Optional factor for modulating the component which is transmitted into the hair, reflected off the backside of the hair and then transmitted out of the hair. This component is oriented approximately around the incoming direction, and picks up the color of the pigment inside the hair. Keep this 1.0 for physical correctness

## Properties

- Color Parametrization
The shader provides three different ways, or

*parametrizations*, to color the hair strands.- Direct Coloring:
Choose the desired RGB color and the shader will approximate the necessary

*absorption coefficient*(below).- Melanin Concentration:
This mode defines the color as the quantity and ratio of the pigments which are commonly found in hair and fur,

*eumelanin*(prevalent in brown-black hair) and*pheomelanin*(red hair). The quantity is specified in the*Melanin*input, and the ratio between them in*Melanin Redness*. Increasing concentrations darken the hair (the following are with*Melanin Redness*\(1\)):White (Melanin \(0\))

Blonde (Melanin \(0.25\))

Reddish (Melanin \(0.5\))

Brown (Melanin \(0.75\))

Black (Melanin \(1\))

Additionally, the

*Tint*inputs allows to dye the hair with the desired color.- Absorption Coefficient:
Specifies the attenuation coefficient \(\sigma_{a}\), as applied by the Beer-Lambert law. This mode is intended mainly for technical users who want to use coefficients from the literature without any sort of conversion.

## Outputs

- BSDF
Standard shader output.

## References

This shader is an implementation of the papers by Chiang et al. [CBTB16] and Huang et al. [HHH22].

Chiang, M. J. , Bitterli, B. , Tappan, C. and Burley, B. (2016), A Practical and Controllable Hair and Fur Model for Production Path Tracing. Computer Graphics Forum, 35: 275-283. doi:10.1111/cgf.12830

d’Eon, E. , Francois, G. , Hill, M. , Letteri, J. and Aubry, J. (2011), An Energy‐Conserving Hair Reflectance Model. Computer Graphics Forum, 30: 1181-1187. doi:10.1111/j.1467-8659.2011.01976.x

Huang W., Hullin M.B. Hanika J. (2022), A Microfacet-based Hair Scattering Model. Computer Graphics Forum, 41: 79-91. doi:10.1111/cgf.14588