Skip to content

Commit

Permalink
use inline latex
Browse files Browse the repository at this point in the history
  • Loading branch information
bhouston committed Oct 23, 2023
1 parent 23b436c commit ecd02f0
Showing 1 changed file with 11 additions and 13 deletions.
24 changes: 11 additions & 13 deletions extensions/2.0/Khronos/KHR_materials_dispersion/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -24,25 +24,23 @@ Written against the glTF 2.0 spec.

This extension adds one parameters to the metallic-roughness material: `dispersion`.

`dispersion` allows users to configure the strength of the angular separation of colors (chromatic aberration) transmitting through a relatively clear volume. Dispersion is represented in terms of the Abbe number parameterization. The dispersion effect is a result of the wavelength-dependent index of refraction of a material. Dispersion is a widely adopted parameter in modern PBR models. It is present in both OpenPBR and the Dassault Enterprise PBR Shading Model.
`dispersion` allows users to configure the strength of the angular separation of colors (chromatic aberration) transmitting through a relatively clear volume. Dispersion is represented in terms of the Abbe number parameterization \( $V$ \). The dispersion effect is a result of the wavelength-dependent index of refraction of a material. Dispersion is a widely adopted parameter in modern PBR models. It is present in both OpenPBR and the Dassault Enterprise PBR Shading Model.

The Abbe number \( V \) is computed from the index of refraction at three wavelengths of visible light: 486.1 nm (short wavelength blue, Ns), 587.6 nm (central yellow, Nc), and 656.3 nm (long wavelength red, Nl). The Abbe number makes the simplifying assumption that the index of refraction variance is linear:
The Abbe number \( $V$ \) is computed from the index of refraction at three wavelengths of visible light: 486.1 nm (short wavelength blue, $N_s$), 587.6 nm (central yellow, $N_c$), and 656.3 nm (long wavelength red, $N_l$). The Abbe number makes the simplifying assumption that the index of refraction variance is linear:

\[
V = \frac{N_c - 1}{N_l - N_s}
\]
$$V = \frac{N_c - 1}{N_l - N_s}$$

To calculate the index of refraction at a specific wavelength \( \lambda \), given an Abbe number \( V \) and the central index of refraction (assumed to be at the color blue, \( N_d \), as specified by the KHR_materials_ior extension):
To calculate the index of refraction at a specific wavelength \( $\lambda$ \), given an Abbe number \( $V$ \) and the central index of refraction (assumed to be at the color blue, \( $N_d$ \), as specified by the KHR_materials_ior extension):

\[
$$
B = \frac{N_c - 1}{V \times \left( \frac{1}{\lambda_s} - \frac{1}{\lambda_l} \right)}
\]
\[
$$
$$
A = N_c - \frac{B}{\lambda_c}
\]
\[
$$
$$
N(\lambda) = A + \frac{B}{\lambda^2}
\]
$$

![Dispersion on a Gem](./figures/Dispersion.jpg)

Expand Down Expand Up @@ -74,7 +72,7 @@ The default value of 0 has a special meaning in that no dispersion should be use

Here is a table of common material dispersion Abbe numbers:

| Material | Abbe Number |
| Material | Abbe Number (V) |
| -------- | ----------- |
| Polycarbonate | 32 |
| Diamond | 55 |
Expand Down

0 comments on commit ecd02f0

Please sign in to comment.