  We introduce numerical algebraic geometry methods for computing lower bounds
on the reach, local feature size, and the weak feature size of the real part of
an equidimensional and smooth algebraic variety using the variety's defining
polynomials as input. For the weak feature size, we also show that
non-quadratic complete intersections generically have finitely many geometric
bottlenecks, and describe how to compute the weak feature size directly rather
than a lower bound in this case. In all other cases, we describe additional
computations that can be used to determine feature size values rather than
lower bounds. We also present homology inference experiments that combine
persistent homology computations with implemented versions of our feature size
algorithms, both with globally dense samples and samples that are adaptively
dense with respect to the local feature size.
