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.

    • 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.
  • 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 .

    • 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.