i.e. wider Gaussians update more boxes. When all sources have been applied, the Taylor coefficients are evaluated at any number of target locations. The algorithm is parameterised by three numbers: $r$, which sets the box size, $p$, which defines number of Taylor coefficients to consider, and $\delta$ which sets the smallest size of Gaussian that will be considered. Reducing the box size, or increasing the number of Taylor coefficients increases the accuracy of the sum.

Gridding with the Fast Gauss Transform  {#sec:gridding}
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Now that we have a Gaussian convolution function (Equation \[eq:conv\_ctw\]), we can solve the sum of Equation \[eq:gridsum\] the FGT with *source-dependant* scales. In the language of gridding visibilities, the evaluation region is the $uv$ plane. The ‘sources’ are the visibilities, with the source position being given by the coordinates of the visibility on the $uv$ plane. The width of the source is related to the $w$ coordinate of the visibility as in Equation \[eq:conv\_variance\], with the minimum width when $w=0$, being essentially the width of the anti-aliasing function. When all the visibilities have been applied to the Taylor coefficients, the Taylor coefficients are evaluated on a regular grid, for each $uv$ cell on the $uv$ plane.

