Stochastic billiards can be used for approximate sampling from the boundary
of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm.
This paper studies how many steps of the underlying Markov chain are required
to get samples (approximately) from the uniform distribution on the boundary of
the set, for sets with an upper bound on the curvature of the boundary. Our
main theorem implies a polynomial-time algorithm for sampling from the boundary
of such sets
