for each tree node: $${\cal I}_{ij} = \sum_m L_m ({\boldsymbol  r }_{m, i} - \bar{{\boldsymbol  r }}_i)({\boldsymbol  r }_{m, j} - \bar{{\boldsymbol  r }}_j), 
\label{eq:inertia}$$ where the subscripts $i$ and $j$, respectively, indicate $i$-th and $j$-th components of the position vector, i.e. $i$ and $j$ are either $x$, $y$, or $z$; and the subscript $m$ has the same meaning as in Eqn. (\[eq:rms\]). By using $(0, 0)$ and $(1, 1)$ components of the tensor ${\cal I}'$ which is the tensor ${\cal I}$ in the rotated frame so that the target mesh is placed along the $z$-direction from the luminosity centre, we can estimate the angular size of the group of the source in the tree node as $$\theta_{\rm s} = \frac{2 r_{\rm rms}}{D} =  \frac{2}{D} \left(\frac{{\cal I}'_{00} +  {\cal I}'_{11}}{\sum_m L_m} \right)^\frac{1}{2}, 
\label{eq:angularsize}$$ where $D$ is the distance between the luminosity centre and the closest edge of the target mesh. In Fig. \[fig:supermeshrt\], we illustrate the procedure of the RT calculation using the supermeshes.

![A schematic illustration of the RT calculation using supermeshes. The radiation sources in the tree node indicated by red square are regarded as a single bright extended source. The target mesh is coloured by light blue. 