Clustered Principal Components for Precomputed Radiance Transfer real-time rendering with shadows and inter-reflections

1. Clustered Principal Components for Precomputed Radiance Transfer real-time rendering with shadows and inter-reflections for objects with complex reflectance Radiance transfer at p from source to transferred incident to exitant. We use a transfer matrix at each p to represent the linear transformation of source radiance into exitant radiance. We use the spherical harmonic basis for these radiance functions. We compress transfer matrices over many points over the surface using CPCA (clustered principal component analysis). It approximates the transfer matrices using an affine subspace over a small number (256) of clusters of points. Using a few PCA vectors per cluster (n'), a good approximation is obtained. Equivalent Rendering Cost Comparison: The three left columns show various approximations that take the same time to render (~45Hz). CPCA provides a much better approximation than a global linear subspace over the whole object (PCA), or a piecewise constant approximation (VQ). 59Hz 27Hz Real-time rendering sample images, using CPCA-encoded transfer matrices 43Hz 27Hz