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\end{equation}  where $r$ is the radius and $h$ is the characteristic width of the kernel, otherwise known as the smoothing length. The physical density at any point, $\rho(\bf{r})$, is then represented by the sum  \begin{equation}  \rho(\bf{r}) \rho({\bf r})  \simeq \sum_j m_j W(\bf{r} W({\bf r}  - \bf{r}_j, {\bf r}_j,  h), \end{equation}  As such, creating visualizations that are faithful to the true physical state of the system represented by the SPH particles requires smoothing them over this kernel