The adaptive integral method (AIM) is applied to the scattering and radiation analysis of arbitrarily shaped planar structures. The method extends the well-known conjugate gradient fast Fourier transform (CGFFT) method to the triangular subdomain discretization, which has a much better geometry modeling capability than the rectangular subdomain discretization employed in the traditional CGFFT method. The resulting algorithm has a memory requirement proportional to O(N) and the operation count for the matrix-vector multiplication proportional to O(N log N). Numerical results are presented to demonstrate the efficiency and accuracy of this method.