Polar Fourier Descriptor(PFD) and Spherical Fourier Descriptor(SFD) are rotation invariant feature descriptors for two dimensional(2D) and three dimensional(3D) image retrieval and pattern recognition tasks. They are demonstrated to show superiorities compared with other methods on describing rotation invariant features of 2D and 3D images. However in order to increase the computation speed, fast computation method is needed especially for applications like realtime systems and large image databases. This paper presents fast computation method for PFD and SFD that based on mathematical properties of trigonometric functions and associated Legendre polynomials. Proposed fast PFD and SFD are 8 and 16 times faster than traditional ones that significantly boost computation process.