Allowing for copyright protection and ownership assertion, digital watermarking techniques, which have been successfully applied for classical media types like audio, images and videos, have recently been adapted for the newly emerged multimedia data type of 3D geometry models. In particular, the widely used spread-spectrum methods can be generalized for 3D datasets by transforming the original model to a frequency domain and perturbing the coefficients of the most dominant basis functions. Previous approaches employing this kind of spectral watermarking are mainly based on multiresolution mesh analysis, wavelet domain transformation or spectral mesh analysis. Though they already exhibit good resistance to many types of real-world attacks, they are often far too slow to cope with very large meshes due to their complicated numerical computations. In this paper, we present a novel spectral watermarking scheme using new orthogonal basis functions based on radial basis functions. With our proposed fast basis function orthogonalization, while observing similar persistence with respect to various attacks as other related approaches, our scheme runs faster by two orders of magnitude and thus can efficiently watermark very large models.