deletions | additions       diff --git a/3-Visualization.tex b/3-Visualization.tex  index 6931662..13845d1 100644  --- a/3-Visualization.tex  +++ b/3-Visualization.tex 
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\begin{cases}  1 - 6 \left( \frac{r}{h} \right)^2 + 6 \left( \frac{r}{h} \right)^3, & 0 \leq \frac{r}{h} \leq \frac{1}{2}\\  2 \left(1 - \frac{r}{h}\right)^3, & \frac{1}{2} < \frac{r}{h} \leq 1\\  0, & \frac{r}{h} > 1\\ 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 SPH particle rendering algorithm at the core of \code{gadfly}'s visualization tools is designed for projecting three-dimensional gas density distributions down to a two-dimensional image; an example of such a visualization produced by gadfly is shown in Figure \ref{fig:vis}.