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0, & \frac{r}{h} > 1,\\  \end{cases}  \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 over all particles  \begin{equation}  \rho({\bf r}) \simeq \sum_j m_j W({\bf r} - {\bf r}_j, h),  \end{equation}  where $m_j$ is the mass of particle $j$, located at ${\bf r}_j$.  As such, creating visualizations that are faithful to the true physical state of the systemrepresented by the SPH particles  requires smoothing them performing this sum  over all particles of interest;  this kernel can be quite computationally intensive depending on the number of particles involved and the desired resolution.  The SPH particle rendering algorithm at the core of \code{gadfly}'s visualization tools is designed for projecting three-dimensional gas density distributions down to included in \code{gadfly} performs this summation over two dimensions, produces  a two-dimensional image; density-weighted projection;  an example of such a visualization produced by gadfly is shown in Figure \ref{fig:vis}. \code{Gadfly} includes three separate implementations of this algorithm, each of which is best suited to different conditions:  \begin{enumerate}