of $r$ and $p$ calculate:

    $$\epsilon  =  \frac{r^p_p}{1 - r_p}, \label{eq:epsilon}$$

    where $$\begin{aligned}
    r_p & = & r\sqrt{\frac{e}{p+1}} < 1\end{aligned}$$

2.  Partition the $uv$ plane into the set of boxes $B$ with centers $t_B$, and side length $L = r\sqrt{2 \delta}$ parallel to the axes, where $\delta = \min_j \delta_j = \delta_A$ is the smallest Gaussian width to be considered.

3.  For each visibility indexed by $j$, calculate the range $R_j = \sqrt{- \delta_j \log \epsilon}$. Also calculate the order $q \le p$ satisfying

    $$\frac{r^q_{q,j}}{1 - r_{q,j}} \le \epsilon \label{eq:qerror}$$

    where $r_{q,j} = r\sqrt{e \delta/\delta_j (q + 1)}$.

4.  For each box within $R_j$ of the visibility position $t_j$, update the Taylor coefficients according to:

    $$C_\beta = \frac{1}{\beta !} \sum_{\delta_j \ge b} v_j \left (\frac{\delta}{\delta_j} \right )^{|\beta|/2} h_\beta \left( \frac{t_j - t_B}{\sqrt{\delta}} \right) \label{eq:cbeta}$$

    where $\beta$ runs from $0$ to $q$, $v_j$ is the visibility weight, and $h_\beta$ is the Hermite function (see S91).

5.  Once all the visibilities have been applied, evaluate the Taylor coefficients at each cell in the $uv$ plane, by finding the box in which the $uv$ cell is situated, and calculating the sum:

    $$F(t) = \sum_{\beta \le p} C_\beta \left( \frac{t_C - t_B} {\sqrt{\delta}}\right) ^\beta$$

    