source_extract/Algorithm/algo.tex

\begin{algorithm}[!t]
\caption{Parameterized planar $G$-invariant continuous function $f$ evaluation at query point}
\label{alg:eval_G}
\KwIn{Continuous parameterization $\theta \mapsto \varphi_{\theta}$; parameters $\{\theta_i\}_{i=1}^{r}$; query point $\mathbf{p}=(x,y)$}
\KwOut{G-inv func $f(\mathbf{p})$}
\tcp{Map $\mathbf{p}$ to asym unit of $W_a$}
$\hat{\mathbf{p}} \leftarrow \texttt{reflect\_to\_asym\_cell}(\mathbf{p})$\;
$f \leftarrow 0$ \;
\For{$i=1$ \KwTo $r$}{
    \tcp{Get coefs on asym unit}
    $h_i \leftarrow \varphi_{\theta_i}(\hat{\mathbf{p}})$\;
    \tcp{Comb with fixed bases}
    $f \leftarrow f + h_i \cdot \eta_i(\mathbf{p})$\;
}
\Return{$f$}
\end{algorithm}