  \v{C}ech complexes are useful simplicial complexes for computing and
analyzing topological features of data that lies in Euclidean space.
Unfortunately, computing these complexes becomes prohibitively expensive for
large-sized data sets even for medium-to-low dimensional data. We present an
approximation scheme for $(1+\epsilon)$-approximating the topological
information of the \v{C}ech complexes for $n$ points in $\mathbb{R}^d$, for
$\epsilon\in(0,1]$. Our approximation has a total size of
$n\left(\frac{1}{\epsilon}\right)^{O(d)}$ for constant dimension $d$, improving
all the currently available $(1+\epsilon)$-approximation schemes of simplicial
filtrations in Euclidean space. Perhaps counter-intuitively, we arrive at our
result by adding additional $n\left(\frac{1}{\epsilon}\right)^{O(d)}$ sample
points to the input. We achieve a bound that is independent of the spread of
the point set by pre-identifying the scales at which the \v{C}ech complexes
changes and sampling accordingly.
