A theory of locally low dimensional light transport

Blockwise or Clustered Principal Component Analysis (CPCA) is commonly used to achieve real-time rendering of shadows and glossy reflections with precomputed radiance transfer (PRT). The vertices or pixels are partitioned into smaller coherent regions, and light transport in each region is approximated by a locally low-dimensional subspace using PCA. Many earlier techniques such as surface light field and reflectance field compression use a similar paradigm. However, there has been no clear theoretical understanding of how light transport dimensionality increases with local patch size, nor of the optimal block size or number of clusters.