Degridding involves taking the dot-product of the $uv$ plane with the convolution function shifted to the location of a visibility at an arbitrary location (i.e. not at the center of a $uv$ cell). It is the dual of gridding.

Degridding can be performed analogously to gridding using the fast Gauss transform with *target*-dependent scales (S91). All the same comments about optimisations for gridding (Section \[sec:optimisations\]) apply as for degridding.

Key differences between classical gridding and the FGT
------------------------------------------------------

The key conceptual differences between classical gridding and FGT gridding are described in Table \[tab:vs\]

  Property                                Classical Gridding                      Fast Gauss Transform
  --------------------------------------- --------------------------------------- -------------------------------------------------------------------------------------------------------------
  Accuracy:                               Exact                                   Approximate, but with controllable error.
  Anti-aliasing function:                 Arbitrary.                              Gaussian only.
  Fundamental scale:                      A $uv$-cell, set by imaging geometry.   A box, which can be smaller, or larger than a $uv$-cell.
  Gridding a single visibility updates:   Cells on the $uv$-plane.                Taylor coefficients in a set of boxes. The cells of the $uv$-plane is calculated as a post-processing step.

\[tab:vs\]

Theoretical performance {#sec:performance}
=======================

Here we derive the theoretical performance of the gridding and degridding processes using the fast Gauss transform, and traditional convolutional gridding.

Operations count of the fast Gauss transform
--------------------------------------------

### Gridding

To grid a single 