I am trying to implement SPH using the directions shown in this paper.
The density needs to be updated using the formula
$$ \rho(\mathbf{x}_i)=\sum_j m_jW_\text{default}(\mathbf{x}_i-\mathbf{x}_j,h) $$
The smoothing kernel is $$ W_\text{default}(\mathbf{r},h)=\frac{315}{64\pi h^9}\cases{(h^2-||\mathbf{r}||^2)^3,\quad 0\leq\mathbf{r}\leq h\\0,\quad\quad\quad\quad\quad ||\mathbf{r}||>h} $$
If there are no particles within the smoothing length($h$), won't the density of a particle become zero based on this formula?