On the Computational Complexity of Hierarchical Radiosity

The hierarchical radiosity algorithm is an efficient approach to simulation of light with the goal of photo-realistic image rendering. Hanrahan et. al. describe the initialization and the refinement of links between the scene’s patches based upon a user-specified error parameter ε. They state that the number of links is linear in the number of elements if ε is assumed to be a constant. We present a result based upon the assumption that the geometry is constant and ε approaches 0 in a multigridding-procedure. Then the algorithm generates L = Θ(N 2) links where N denotes the number of elements generated by the algorithm