This paper presents closed-form solutions for the problem of finding the points of intersection of a 1D line and the boundary of typical matrix sets encountered in control specifically, those defined by linear matrix inequalities. This procedure is referred to as boundary oracle it is the key technical component of various random walk algorithms exploited within the randomized approach to control and optimization. In the paper, several such oracles are devised and generalized to robust formulations where the coefficients of matrix inequalities are subjected to uncertainties.