  The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for
computation of the near-field and far-field in the quasi-cylindrical geometry
has been introduced. The modal expansion coefficient of the vector potentials
${\bf F}$ and ${\bf A}$ within the context of the cylindrical harmonics (TE and
TM modes) can be expressed in the closed-form expression through the
cylindrical addition theorem. For the quasi-cylindrical geometry, the modal
expansion coefficient can be evaluated through FFT with the help of the Taylor
Interpolation (TI) technique. The near-field on any arbitrary cylindrical
surface can be obtained through the Inverse Fourier Transform (IFT). The
far-field can be obtained through the Near-Field Far-Field (NF-FF) transform.
The cylindrical TI-FFT algorithm has the advantages of $\mathcal{O} \left(
\hbox{N} \log_2 \hbox{N} \right)$ computational complexity for $\hbox{N} =
\hbox{N}_\phi \times \hbox{N}_z$ computational grid, small sampling rate (large
sampling spacing) and no singularity problem.
