Complex shapes – such as the surface of the human brain – may be represented and analyzed in frequency space by means of a spherical harmonics transformation. A key step of the processing chain is introducing a suitable parametrization of the triangular mesh representing the brain surface. This problem corresponds to mapping a surface of topological genus zero on a unit sphere. An algorithm is described that produces an optimal combination of an area- and angle-preserving mapping. A multi-resolution scheme provides the robustness required to map the highly detailed and convoluted brain surface. More than 1000 datasets were successfully processed by this mature and robust approach.