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improve IndirectLight::irradiance() documentation

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This commit is contained in:
Mathias Agopian
2019-06-12 17:18:05 -07:00
committed by Mathias Agopian
parent f3769d8e86
commit 4e4f7fd4ac
2 changed files with 34 additions and 4 deletions
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4
docs/Filament.md.html
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@@ -3802,14 +3802,14 @@ void computeShBasis(
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[Listing [nonNormalizedSHBasis]: C++ implementation to compute a non-normalized SH basis]
SH bases $y^m_l(s)$ for the first 3 bands:
Normalized SH basis functions $y^m_l(s)$ for the first 3 bands:
Band | $m = -2$ | $m = -1$ | $m = 0$ | $m = 1$ | $m = 2$ |
:-------:|:------------------------------------:|:-------------------------------------:|:---------------------------------------------------:|:-------------------------------------:|:---------------------------------------------:|
$l = 0$ | | | $\frac{1}{2}\sqrt{\frac{1}{\pi}}$ | | |
$l = 1$ | | $-\frac{1}{2}\sqrt{\frac{3}{\pi}}y$ | $\frac{1}{2}\sqrt{\frac{3}{\pi}}z$ | $-\frac{1}{2}\sqrt{\frac{3}{\pi}}x$ | |
$l = 2$ | $\frac{1}{2}\sqrt{\frac{15}{\pi}}xy$ | $-\frac{1}{2}\sqrt{\frac{15}{\pi}}yz$ | $\frac{1}{4}\sqrt{\frac{5}{\pi}}(2z^2 - x^2 - y^2)$ | $-\frac{1}{2}\sqrt{\frac{15}{\pi}}xz$ | $\frac{1}{4}\sqrt{\frac{15}{\pi}}(x^2 - y^2)$ |
[Table [basisFunctions]: Basis functions per band]
[Table [basisFunctions]: Normalized basis functions per band]
### Decomposition and reconstruction

34
filament/include/filament/IndirectLight.h
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@@ -125,8 +125,38 @@ public:
* Sets the irradiance as Spherical Harmonics.
*
* The irradiance must be pre-convolved by \f$ \langle n \cdot l \rangle \f$ and
* specified as Spherical Harmonics coefficients pre-scaled by the basis
* coefficients \f$ K_{l}^{m} \f$.
* specified as Spherical Harmonics coefficients \f$ L_{l}^{m} \f$ pre-scaled by the
* normalization factors \f$ \hat{K_{l}^{m}} \f$ and pre-multiplied by the Lambertian diffuse
* BRDF \f$ \frac{1}{\pi} \f$. The final coefficients can be generated using the `cmgen` tool.
*
* The index in the \p sh array is given by:
*
* `index(l, m) = l * (l + 1) + m`
*
* and:
*
* \f$ \hat{K_{l}^{m}} =
* \begin{cases}
* K_{l}^{m} & \text{ if } m = 0 \\
* \sqrt{2}K_{l}^{m} & \text{ if } m \neq 0
* \end{cases}\f$
*
* With \f$ K_{l}^{m} \f$ the SH basis normalization factors,
*
* \f$ sh[index(l,m)] = L_{l}^{m} \frac{1}{\pi} \hat{K_{l}^{m}} \hat{C_{l}} \f$
*
* index | l | m | \f$ \hat{K_{l}^{m}} \f$ | \f$ \hat{C_{l}} \f$ | \f$ \frac{1}{\pi} \hat{K_{l}^{m}}\hat{C_{l}} \f$ |
* :-----:|:---:|:---:|:------------------------:|:---------------------:|:-------------------------------------------------:
* 0 | 0 | 0 | 0.282095 | 3.1415926 | 0.282095
* 1 | 1 | -1 | 0.488603 | 2.0943951 | 0.325735
* 2 | ^ | 0 | 0.488603 | ^ | 0.325735
* 3 | ^ | 1 | 0.488603 | ^ | 0.325735
* 4 | 2 | -2 | 0.182091 | 0.785398 | 0.045523
* 5 | ^ | -1 | 0.364183 | ^ | 0.091046
* 6 | ^ | 0 | 0.630783 | ^ | 0.157696
* 7 | ^ | 1 | 0.364183 | ^ | 0.091046
* 8 | ^ | 2 | 0.182091 | ^ | 0.045523
*
*
* Only 1, 2 or 3 bands are allowed.
*