Memo of "Clustered Principal Components for Precomputed Radiance Transfer"
This articles is the memo of the "Clustered Principal Components for Precomputed Radiance Transfer".
- 0. Compute the exiting radiance matrix M_p_ij at position p.
- To project SH basis onto the hemisphere, the least-squares optimal projection of the SH is used.
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- Meaning of the symbols.
- p : Position
- i : Index of the source lighting basis function.
- H : Hemisphere
- s : Light direction
- j : Index of the exiting radiance basis function.
- T_p(s, y_j(s)) : Transport effect as position p.
- B(v, s) : BRDF
- s_z : cosine factor (Z component of the s).
- v : view direction
- y_i(v) : Exiting radiance basis function.
- Meaning of the symbols.
- 1. Approximate with the Clustered PCA (CPCA).
- Clustering is done by using LBG algorithm followed by static PCA or iterative PCA.
- Or adaptation of the number of the PCA vector is done by sorting the PCA vectors based on ( D_i )^2 / m_k .
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- Meaning of the symbols.
- x_p is a n-dimensional signal at point p.
- For example, n=25 for diffuse surfaces and n=25*25 for glossy surfaces.
- x_0 : Mean of the cluster
- x^1, ..., x_n' : PCA vectors of the cluster. The total number of the PCA vectors is (n' + 1).
- w^1_p, ..., w^n'_p : Scaler weight of the PCA vectors at point p.
- Meaning of the symbols.
- Reference
- "Clustered Principal Components for Precomputed Radiance Transfer". Peter-Pike Sloan.